Measures of Central Tendency

1. What is the mean of a set of numbers?

A) The sum of the numbers divided by the number of values
B) The product of the numbers
C) The largest number in the set
D) The smallest number in the set

Correct Answer: (A) The sum of the numbers divided by the number of values.

2. In the example provided, what is the mean of the numbers 2, 5, 8, 3, and 9?

A) 6
B) 5.4
C) 5
D) 7

Correct Answer: (B) 5.4.

3. What does the formula for arithmetic mean indicate?

A) It multiplies the values together
B) It subtracts the lowest value from the highest value
C) It divides the sum of all observations by their number
D) It adds the highest and lowest values

Correct Answer: (C) It divides the sum of all observations by their number.

4. What is the first property of the arithmetic mean?

A) The mean is always greater than the highest value.
B) The algebraic sum of the deviations from the mean is zero.
C) The mean cannot be calculated for grouped data.
D) The mean is always a whole number.

Correct Answer: (B) The algebraic sum of the deviations from the mean is zero.

5. If every value of a variable is increased by a constant 𝑎, what happens to the arithmetic mean?

A) It decreases by 𝑎
B) It remains the same
C) It increases by 𝑎
D) It becomes zero

Correct Answer: (C) It increases by 𝑎.

6. What does it mean for the arithmetic mean to be dependent on the change of origin and scale?

A) It can be calculated without any values.
B) Changing the starting point or the units will affect the mean.
C) The mean will always remain the same.
D) The mean is not affected by changing values.

Correct Answer: (B) Changing the starting point or the units will affect the mean.

7. What is the minimum property of the sum of the squares of the deviations about the mean?

A) It is maximum.
B) It is random.
C) It is minimum.
D) It is constant.

Correct Answer: (C) It is minimum.

8. How do you find the arithmetic mean of the first 𝑛 natural numbers?

A) By multiplying them
B) By adding them and dividing by 𝑛
C) By taking the highest number
D) By taking the lowest number

Correct Answer: (B) By adding them and dividing by 𝑛.

9. If 8 is the average of six variates and five of them are 8, 15, 0, 6, and 11, how can the sixth variate be determined?

A) By subtracting the average from the sum of the variates
B) By adding the average to the sum of the variates
C) By calculating the total sum of variates and subtracting it from 8
D) By using the formula for the average

Correct Answer: (A) By subtracting the average from the sum of the variates.

10. If the first five variates are 8, 15, 0, 6, and 11, what is the total sum required to find the sixth variate?

A) 40
B) 48
C) 54
D) 30

Correct Answer: (B) 48.

11. What does the value of 𝑁 N represent in a discrete frequency distribution?

A) The total sum of the variable values
B) The total number of observations
C) The average of the data points
D) The highest value in the series

Correct Answer: (B) The total number of observations.

12. In a discrete series, if the value 𝑥₁ occurs 𝑓₁ times and 𝑥₂ occurs 𝑓₂ times, what is the total frequency represented as?

A) Σ 𝑓_𝑖
B) 𝑁
C) 𝑥₁ + 𝑥₂
D) 𝑓₁ + 𝑓₂

Correct Answer: (A) Σ 𝑓_𝑖.

13. Which of the following is NOT one of the methods for calculating the arithmetic mean?

A) Direct method
B) Short-Cut method
C) Step-deviation method
D) Regression method

Correct Answer: (D) Regression method.

14. The arithmetic mean is applicable to which type of series?

A) Only continuous series
B) Only grouped frequency distributions
C) Any type of series
D) Only qualitative data

Correct Answer: (C) Any type of series.

15. What is the value of the mean (𝑋) as provided in the information?

A) 50
B) 55
C) 56
D) 60

Correct Answer: (C) 56.

16. In a discrete frequency distribution, if the frequencies are provided for various variable values, what is this type of data called?

A) Continuous data
B) Categorical data
C) Discrete data
D) Interval data

Correct Answer: (C) Discrete data.

17. What is the purpose of calculating the arithmetic mean in a data set?

A) To determine the highest value
B) To find the total number of observations
C) To identify the central tendency of the data
D) To evaluate the range of the data

Correct Answer: (C) To identify the central tendency of the data.

18. Which method would be most appropriate for quickly calculating the arithmetic mean when dealing with large sets of data?

A) Direct method
B) Short-Cut method
C) Step-deviation method
D) Simple addition

Correct Answer: (B) Short-Cut method.

19. If the total frequency 𝑁 N equals the sum of individual frequencies Σ 𝑓_𝑖, what can be inferred?

A) The data is biased
B) The calculations are incorrect
C) The values are consistent with the definition of frequency distribution
D) The mean cannot be calculated

Correct Answer: (C) The values are consistent with the definition of frequency distribution.

20. In a continuous series, what replaces the class intervals for calculating the mean?

A) Class marks
B) Midpoints of class intervals
C) The product of frequencies
D) The total sum of values

Correct Answer: (B) Midpoints of class intervals.

21. How is the arithmetic mean of a continuous series calculated?

A) By dividing the sum of all values by the total number of observations
B) By using the midpoints of class intervals along with frequencies
C) By taking the square root of the sum of squared deviations
D) By subtracting the smallest value from the largest value

Correct Answer: (B) By using the midpoints of class intervals along with frequencies.

22. What is the primary difference between a continuous series and a discrete series?

A) Continuous series use class intervals, while discrete series use individual values
B) Continuous series use midpoints, while discrete series use the actual data
C) Continuous series have frequencies, while discrete series do not
D) There is no difference once the calculations are done

Correct Answer: (D) There is no difference once the calculations are done.

23. Which of the following is an example of a continuous series?

A) A set of 15 students scoring between 50-60, 10 students between 60-70, and 20 students between 70-80
B) A list of 30 students with exact scores
C) The range of marks obtained by students in a test
D) The total sum of scores of all students

Correct Answer: (A) A set of 15 students scoring between 50-60, 10 students between 60-70, and 20 students between 70-80.

24. Which method is NOT used to find the arithmetic mean of a continuous series?

A) Direct Method
B) Shortcut Method
C) Step Deviation Method
D) Range Method

Correct Answer: (D) Range Method.

25. What is the formula used in the direct method to find the mean in a continuous series?

A) Mean = Σ(f ⋅ x) / N
B) Mean = Σf / N
C) Mean = x − a / d
D) Mean = Midpoint of the class intervals

Correct Answer: (A) Mean = Σ(f ⋅ x) / N.

26. What does the shortcut method for finding the mean involve?

A) Using actual values instead of midpoints
B) Using a reference point (assumed mean) for simplification
C) Calculating the sum of all values
D) Using only the highest and lowest values

Correct Answer: (B) Using a reference point (assumed mean) for simplification.

27. In the step deviation method, what role does the class interval width play?

A) It is subtracted from the frequencies
B) It is used to divide the deviations
C) It is added to the assumed mean
D) It is ignored in the calculation

Correct Answer: (B) It is used to divide the deviations.

28. What is the purpose of the step deviation method?

A) To simplify calculations when the class intervals are unequal
B) To provide an exact value of the arithmetic mean
C) To make calculations easier when the data set is large
D) To find the median of the data

Correct Answer: (C) To make calculations easier when the data set is large.

29. What is an important step in the step deviation method?

A) Taking the deviations from an assumed mean
B) Taking deviations from the midpoint of the intervals
C) Dividing deviations by the class interval width
D) Adding all class intervals

Correct Answer: (C) Dividing deviations by the class interval width.

30. Which method requires the use of an assumed mean for calculating the arithmetic mean?

A) Direct Method
B) Step Deviation Method
C) Shortcut Method
D) Both (B) and (C)

Correct Answer: (D) Both (B) and (C).

31. In the given example of a continuous series, how many students scored between 50 and 60?

A) 10
B) 15
C) 20
D) 25

Correct Answer: (B) 15.

32. How is the mean calculated in the step deviation method?

A) By multiplying the class intervals by their frequencies
B) By dividing the deviations by the class interval width
C) By calculating deviations from an assumed mean and dividing them by class interval width
D) By adding all frequencies together

Correct Answer: (C) By calculating deviations from an assumed mean and dividing them by class interval width.

33. What is the assumed mean used for in the shortcut and step deviation methods?

A) To represent the midpoint of the data
B) To simplify calculations by taking deviations from it
C) To find the median of the data
D) To find the sum of all values

Correct Answer: (B) To simplify calculations by taking deviations from it.

34. What is the geometric mean of a dataset?

A) The sum of the values divided by the number of values
B) The product of the values divided by the number of values
C) The nth root of the product of the values
D) The average of the highest and lowest values

Correct Answer: (C) The nth root of the product of the values.

35. How is the geometric mean of two numbers (a) and (b) calculated?

A) ((a+b)/2)
B) (a+b)
C) (√ab)
D) (ab)

Correct Answer: (C) (√ab).

36. What is the geometric mean of 4 and 16?

A) 4
B) 8
C) 12
D) 16

Correct Answer: (B) 8.

37. Which of the following statements is true regarding the relationship between the arithmetic mean (AM) and geometric mean (GM)?

A) GM is always greater than AM
B) GM is always less than or equal to AM
C) AM and GM are always equal
D) There is no relationship between AM and GM

Correct Answer: (B) GM is always less than or equal to AM.

38. According to the geometric mean theorem, what is the relationship between segments (a), (b), and the altitude (h) in a right triangle?

A) (h=a+b)
B) (h²=a+b)
C) (h²=ab)
D) (h=ab)

Correct Answer: (C) (h²=ab).

39. Which of the following is NOT a property of the geometric mean?

A) GM is always less than or equal to AM
B) The product of the GM is equal to the product of corresponding GM items in two series
C) GM can be calculated using negative numbers
D) GM is a measure of central tendency

Correct Answer: (C) GM can be calculated using negative numbers.

40. In what fields is the geometric mean commonly used?

A) Sports statistics
B) Stock market analysis
C) Social sciences
D) All of the above

Correct Answer: (B) Stock market analysis.

41. How do you find the geometric mean of the numbers 2, 4, 6, 8, 10, and 12?

A) By adding them and dividing by six
B) By taking the product of the numbers and finding the sixth root
C) By finding the average of the two middle values
D) By subtracting the smallest from the largest value

Correct Answer: (B) By taking the product of the numbers and finding the sixth root.

42. What is the product (P) of the numbers 2, 4, 6, 8, 10, and 12?

A) 240
B) 46080
C) 720
D) 1200

Correct Answer: (B) 46080.

43. How is the geometric mean applied in biological processes?

A) To measure average growth rates
B) To find the sum of all biological variables
C) To calculate the maximum growth observed
D) To determine individual growth factors

Correct Answer: (A) To measure average growth rates.

44. What is the definition of the median in a dataset?

A) The value that occurs most frequently
B) The middle value when the data is arranged in order
C) The sum of all values divided by the number of values
D) The highest value in the dataset

Correct Answer: (B) The middle value when the data is arranged in order.

45. What does it mean when it is stated that fifty percent of the goods are above and fifty percent are below their worth?

A) The data is normally distributed
B) The median value divides the dataset into two equal halves
C) The mean is greater than the median
D) There is no central tendency in the data

Correct Answer: (B) The median value divides the dataset into two equal halves.

46. How do you determine the median when the number of observations is even?

A) Use the highest value as the median
B) Take the average of the two middle numbers
C) Take the mode of the dataset
D) Select the middle value directly

Correct Answer: (B) Take the average of the two middle numbers.

47. What are the first steps to compute the median of ungrouped data?

A) Count the total number of observations and sort the data
B) Sort the data and then calculate the mean
C) Calculate the sum of all values and find the highest value
D) Identify the mode and median

Correct Answer: (A) Count the total number of observations and sort the data.

48. What does 'n' represent in the context of median calculation?

A) The total number of observations
B) The median value itself
C) The average of the dataset
D) The highest value in the dataset

Correct Answer: (A) The total number of observations.

49. Why is sorting the data important when calculating the median?

A) To find the mode of the data
B) To ensure the calculation is accurate
C) To identify the highest and lowest values
D) Sorting is not necessary for median calculation

Correct Answer: (B) To ensure the calculation is accurate.

50. In the provided example, how many observations are there in the dataset of heights?

A) 10
B) 11
C) 12
D) 9

Correct Answer: (B) 11.

51. What is the correct order of the heights when arranged in ascending order?

A) 158, 158, 159, 160, 160, 163, 165, 166, 170, 171, 173
B) 158, 159, 160, 163, 165, 166, 170, 171, 173
C) 173, 171, 170, 166, 165, 163, 160, 159, 158, 158
D) 173, 171, 170, 166, 165, 163, 160, 160, 159, 158, 158

Correct Answer: (A) 158, 158, 159, 160, 160, 163, 165, 166, 170, 171, 173.

52. How is the median related to the concept of central tendency?

A) The median is the only measure of central tendency.
B) The median is one of the three primary measures of central tendency.
C) The median cannot be used for ungrouped data.
D) The median is always equal to the mean.

Correct Answer: (B) The median is one of the three primary measures of central tendency.

53. What is the formula to find the position of the median in an ordered dataset?

A) (n+1)
B) (n-1)
C) ((n+1)/2)
D) ((n-1)/2)

Correct Answer: (C) ((n+1)/2).

54. What does the median represent in a discrete series?

A) The most frequently occurring value
B) The middle value of the ordered dataset
C) The sum of all values divided by the number of values
D) The highest value in the dataset

Correct Answer: (B) The middle value of the ordered dataset.

55. In a discrete series, what does 'N' represent?

A) The number of variables
B) The total number of observations
C) The total frequency
D) The mean of the dataset

Correct Answer: (B) The total number of observations.

56. How is the cumulative frequency defined in a discrete series?

A) The frequency of the highest value
B) The sum of frequencies for all values less than or equal to a specific value
C) The frequency of the mode
D) The average of all frequencies

Correct Answer: (B) The sum of frequencies for all values less than or equal to a specific value.

57. What are the first steps to calculate the median of a discrete series?

A) Calculate the mean and sort the data
B) Sort the distribution and identify the frequencies
C) Identify the mode and then calculate the median
D) Count the total observations and find the range

Correct Answer: (B) Sort the distribution and identify the frequencies.

58. When calculating the median item, what does the formula \( \text{Median} = \text{Size of the } \frac{N}{2} \text{ th item} \) indicate?

A) It indicates the average of the first and last values.
B) It determines the position of the median based on total observations.
C) It is used to find the mode of the dataset.
D) It finds the sum of all values in the dataset.

Correct Answer: (B) It determines the position of the median based on total observations.

59. In the example given, how many students received 60 marks?

A) 2
B) 5
C) 3
D) 9

Correct Answer: (D) 3.

60. What is the cumulative frequency if three students receive 60 marks, nine students receive 70 marks, five students receive 80 marks, and two students receive 90 marks?

A) 15
B) 19
C) 27
D) 25

Correct Answer: (C) 27.

61. If the median of a discrete series is given as 12, what does this imply about the dataset?

A) The data is perfectly symmetrical.
B) Half of the values are below 12 and half are above.
C) The mode of the dataset is also 12.
D) There are an equal number of observations on both sides of 12.

Correct Answer: (B) Half of the values are below 12 and half are above.

62. How do you identify the missing frequency in a given series when the median is known?

A) By finding the highest frequency
B) By applying the median formula to solve for the missing value
C) By calculating the mean of the dataset
D) By counting the total observations

Correct Answer: (B) By applying the median formula to solve for the missing value.

63. What is the missing frequency value in the example where the median is 12?

A) 2
B) 3
C) 4
D) 5

Correct Answer: (B) 3.

64. What is the definition of the median in the context of continuous data?

A) The value that occurs most frequently
B) The middle value when the data is arranged in order
C) The point that divides the dataset into two equal halves
D) The highest value in the dataset

Correct Answer: (C) The point that divides the dataset into two equal halves.

65. How is the median calculated in a continuous series?

A) By using the mean of the dataset
B) By taking the average of the two middle values
C) By determining the midpoints of class intervals and applying the median formula
D) By finding the mode of the dataset

Correct Answer: (C) By determining the midpoints of class intervals and applying the median formula.

66. What is the first step in calculating the median of continuous data?

A) Identify the frequencies of the data
B) Sort the data in ascending order
C) Determine the range of the data
D) Calculate the cumulative frequency

Correct Answer: (B) Sort the data in ascending order.

67. In continuous data, how is the class interval related to the calculation of the median?

A) Class intervals are ignored in the median calculation
B) The median is calculated using the class boundaries of each interval
C) The midpoints of class intervals are used to find the median
D) The class interval indicates the highest value

Correct Answer: (C) The midpoints of class intervals are used to find the median.

68. What is the formula for finding the median in a continuous frequency distribution?

A) Median = \( \frac{N}{2} \)
B) Median = \( L + \left( \frac{N}{2} - CF \right) \times h \)
C) Median = \( \frac{\text{Sum of all values}}{n} \)
D) Median = Mean - Mode

Correct Answer: (B) Median = \( L + \left( \frac{N}{2} - CF \right) \times h \).

69. In the median formula \( L + \left( \frac{N}{2} - CF \right) \times h \), what does 'L' represent?

A) The cumulative frequency
B) The lower boundary of the median class
C) The total number of observations
D) The mean of the dataset

Correct Answer: (B) The lower boundary of the median class.

70. What does 'CF' stand for in the median formula?

A) Class Frequency
B) Cumulative Frequency
C) Critical Frequency
D) Central Frequency

Correct Answer: (B) Cumulative Frequency.

71. How do you determine the median class in a continuous frequency distribution?

A) By identifying the class with the highest frequency
B) By calculating the midpoint of all classes
C) By finding the class where the cumulative frequency reaches \( \frac{N}{2} \)
D) By taking the average of the two middle classes

Correct Answer: (C) By finding the class where the cumulative frequency reaches \( \frac{N}{2} \).

72. If the total number of observations (N) is 50, at what cumulative frequency should the median be located?

A) 25
B) 50
C) 20
D) 30

Correct Answer: (A) 25.

73. Why is the median a preferred measure of central tendency for continuous data?

A) It is less affected by extreme values than the mean
B) It considers all data points equally
C) It provides a direct representation of the data distribution
D) It is easier to calculate than the mode

Correct Answer: (A) It is less affected by extreme values than the mean.

74. What is the mode in a dataset?

A) The value that occurs most frequently
B) The middle value when the data is ordered
C) The average of all values
D) The highest value in the dataset

Correct Answer: (A) The value that occurs most frequently.

75. In a dataset, if there are two values that occur with the highest frequency, what is it called?

A) Bimodal
B) Multimodal
C) Trimodal
D) Unimodal

Correct Answer: (A) Bimodal.

76. How do you identify the mode in ungrouped data?

A) By calculating the average of the dataset
B) By sorting the data in ascending order
C) By finding the value with the highest frequency
D) By calculating the cumulative frequency

Correct Answer: (C) By finding the value with the highest frequency.

77. What is the mode of the following dataset: 4, 1, 2, 2, 3, 4, 4, 5?

A) 2
B) 3
C) 4
D) 5

Correct Answer: (C) 4.

78. In discrete data, what does it mean if there is no mode?

A) All values occur with the same frequency
B) The data is skewed
C) There is one value that occurs most frequently
D) The data is continuous

Correct Answer: (A) All values occur with the same frequency.

79. Which of the following statements is true regarding the mode?

A) The mode is always unique.
B) The mode can be used with numerical and categorical data.
C) The mode is always the highest value in the dataset.
D) The mode cannot be used in ungrouped data.

Correct Answer: (B) The mode can be used with numerical and categorical data.

80. How does the mode differ from the median and mean?

A) The mode represents the average of the data.
B) The mode can be more than one value, while mean and median are always one.
C) The mode is less reliable than mean and median.
D) The mode requires the data to be sorted.

Correct Answer: (B) The mode can be more than one value, while mean and median are always one.

81. If the following frequencies are given for discrete data: Value 1 occurs 3 times, Value 2 occurs 5 times, Value 3 occurs 5 times, and Value 4 occurs 2 times, what is the mode?

A) 1
B) 2 and 3
C) 5
D) 4

Correct Answer: (B) 2 and 3.

82. In what scenario is the mode most useful?

A) When the data is continuous
B) When dealing with nominal data
C) When calculating the average
D) When data is symmetrically distributed

Correct Answer: (B) When dealing with nominal data.

83. How do you calculate the mode in a discrete frequency distribution?

A) By averaging the values
B) By identifying the value with the highest cumulative frequency
C) By selecting the value corresponding to the highest frequency
D) By arranging the data in ascending order and finding the middle value

Correct Answer: (C) By selecting the value corresponding to the highest frequency.

84. What is the mode in a continuous dataset?

A) The value that occurs most frequently
B) The range of the dataset
C) The midpoint of the data
D) The value with the highest frequency density

Correct Answer: (D) The value with the highest frequency density.

85. How is the mode determined in a continuous frequency distribution?

A) By calculating the mean of the data
B) By identifying the modal class where the highest frequency occurs
C) By finding the median of the dataset
D) By counting the total number of observations

Correct Answer: (B) By identifying the modal class where the highest frequency occurs.

86. In a continuous distribution, what is the formula used to calculate the mode?

A) Mode = L + (f1 - f0) / (2f1 - f0 - f2) × h
B) Mode = L + (f1 + f2) / 2
C) Mode = (Sum of all values) / n
D) Mode = Median + Range

Correct Answer: (A) Mode = L + (f1 - f0) / (2f1 - f0 - f2) × h.

87. What does 'L' represent in the mode formula for continuous data?

A) The total number of observations
B) The lower boundary of the modal class
C) The upper boundary of the modal class
D) The cumulative frequency

Correct Answer: (B) The lower boundary of the modal class.

88. In the mode formula 𝐿 + (𝑓1 − 𝑓0) / (2𝑓1 − 𝑓0 − 𝑓2) × ℎ, what does 'f1' represent?

A) The frequency of the modal class
B) The frequency of the class before the modal class
C) The frequency of the class after the modal class
D) The total frequency

Correct Answer: (A) The frequency of the modal class.

89. What does 'h' represent in the mode formula?

A) The highest frequency
B) The class width
C) The cumulative frequency
D) The median class

Correct Answer: (B) The class width.

90. If a continuous dataset has multiple modes, what is it called?

A) Unimodal
B) Bimodal
C) Multimodal
D) Trimodal

Correct Answer: (C) Multimodal.

91. How do you identify the modal class in a continuous frequency distribution?

A) By sorting the data
B) By selecting the class with the highest cumulative frequency
C) By selecting the class with the highest frequency
D) By calculating the mean of all classes

Correct Answer: (C) By selecting the class with the highest frequency.

92. Why is the mode important in continuous data analysis?

A) It provides the average value of the dataset
B) It indicates the most common value, which is useful in understanding the distribution
C) It is always equal to the median
D) It is easier to calculate than the mean

Correct Answer: (B) It indicates the most common value, which is useful in understanding the distribution.

93. In a dataset with the following class intervals and frequencies, how is the mode determined?

Class Interval: 10-20 (frequency 5)
20-30 (frequency 15)
30-40 (frequency 20)
40-50 (frequency 10)

A) The mode is in the class interval 10-20
B) The mode is in the class interval 20-30
C) The mode is in the class interval 30-40
D) There is no mode

Correct Answer: (C) The mode is in the class interval 30-40.

94. What are the three measures of central tendency?

A) Mean, Median, Mode
B) Mean, Range, Variance
C) Median, Variance, Standard Deviation
D) Mode, Frequency, Cumulative Frequency

Correct Answer: (A) Mean, Median, Mode

95. In a perfectly symmetrical distribution, what is the relationship between the mean, median, and mode?

A) Mean = Median = Mode
B) Mean > Median > Mode
C) Mean < Median < Mode
D) Median = Mode > Mean

Correct Answer: (A) Mean = Median = Mode

96. In a negatively skewed distribution, which of the following relationships typically holds true?

A) Mean < Median < Mode
B) Mean > Median > Mode
C) Mean = Median = Mode
D) Median < Mean < Mode

Correct Answer: (A) Mean < Median < Mode

97. In a positively skewed distribution, what is the usual order of mean, median, and mode?

A) Mode < Median < Mean
B) Mean < Median < Mode
C) Median < Mode < Mean
D) Mean = Median = Mode

Correct Answer: (A) Mode < Median < Mean

98. Which of the following statements is true regarding the mean, median, and mode?

A) The mean is always the largest value.
B) The median is less affected by outliers than the mean.
C) The mode is always equal to the mean.
D) The mean is the only measure that can be used for categorical data.

Correct Answer: (B) The median is less affected by outliers than the mean.

99. In a dataset with extreme values, which measure of central tendency is likely to provide the most accurate representation of the data?

A) Mean
B) Median
C) Mode
D) None of the above

Correct Answer: (B) Median

100. How is the mean calculated in a set of numbers?

A) By finding the middle value of the ordered set
B) By summing all values and dividing by the number of values
C) By identifying the most frequently occurring value
D) By determining the range of the dataset

Correct Answer: (B) By summing all values and dividing by the number of values.

101. What happens to the mean if an extreme value is added to a dataset?

A) The mean remains unchanged
B) The mean decreases
C) The mean increases
D) The mean becomes equal to the median

Correct Answer: (C) The mean increases

102. In which situation is the mode the most informative measure of central tendency?

A) When the data is normally distributed
B) When dealing with categorical data
C) When the dataset contains extreme values
D) When the dataset is small

Correct Answer: (B) When dealing with categorical data

103. Which of the following best describes the median?

A) The average of the dataset
B) The middle value that divides the dataset into two equal halves
C) The most frequently occurring value
D) The sum of all values divided by the total number of observations

Correct Answer: (B) The middle value that divides the dataset into two equal halves

104. If the mean of a dataset is greater than the median, what can be inferred about the distribution?

A) It is symmetrical.
B) It is negatively skewed.
C) It is positively skewed.
D) It has no outliers.

Correct Answer: (C) It is positively skewed.

105. In a dataset with the following values: 3, 7, 7, 8, 9, 10, 10, 10, 11, what are the mean, median, and mode?

A) Mean: 8.6, Median: 9, Mode: 10
B) Mean: 9, Median: 9, Mode: 10
C) Mean: 8, Median: 9, Mode: 10
D) Mean: 9.5, Median: 9, Mode: 7

Correct Answer: (A) Mean: 8.6, Median: 9, Mode: 10

106. If a dataset has a mode but no median, what can be inferred about the data?

A) The data is continuous and normally distributed.
B) The data is categorical and does not have numerical values.
C) The data contains only one unique value.
D) The data is symmetric.

Correct Answer: (B) The data is categorical and does not have numerical values.

107. Which of the following distributions would likely have a mode that differs significantly from the mean?

A) Normal Distribution
B) Uniform Distribution
C) Skewed Distribution
D) Bimodal Distribution

Correct Answer: (C) Skewed Distribution

108. In a perfectly symmetrical bell curve, what would the values of the mean, median, and mode be?

A) Mean < Median < Mode
B) Mean = Median > Mode
C) Mean = Median = Mode
D) Mode < Median < Mean

Correct Answer: (C) Mean = Median = Mode

109. Which measure of central tendency is most appropriate for ordinal data?

A) Mean
B) Median
C) Mode
D) None of the above

Correct Answer: (B) Median

110. If the mode is greater than the median, what can be inferred about the distribution?

A) The distribution is positively skewed.
B) The distribution is negatively skewed.
C) The distribution is symmetrical.
D) The distribution has no mode.

Correct Answer: (B) The distribution is negatively skewed.

111. Which measure is considered the best representation of central tendency in a skewed distribution?

A) Mean
B) Median
C) Mode
D) All are equally valid

Correct Answer: (B) Median

112. If a dataset has multiple modes, it is termed as:

A) Unimodal
B) Bimodal
C) Multimodal
D) None of the above

Correct Answer: (C) Multimodal

113. In which scenario would the mean be considered the least useful measure of central tendency?

A) In a dataset with one extreme value
B) In a dataset with a normal distribution
C) In a small dataset
D) In categorical data

Correct Answer: (A) In a dataset with one extreme value

114. Which of the following measures can be affected by outliers?

A) Mean
B) Median
C) Mode
D) Both B and C

Correct Answer: (A) Mean

115. In a data set with equal frequencies, which measure of central tendency would be the most reliable?

A) Mean
B) Median
C) Mode
D) None of the above

Correct Answer: (B) Median

116. What is the mode of the dataset: 2, 3, 4, 4, 5, 5, 5, 6, 7?

A) 4
B) 5
C) 6
D) 7

Correct Answer: (B) 5

117. Which measure is not affected by the order of values in the dataset?

A) Mean
B) Median
C) Mode
D) All of the above

Correct Answer: (C) Mode

118. What can be said about the mean, median, and mode in a negatively skewed distribution?

A) Mean > Median > Mode
B) Mean < Median < Mode
C) Mean = Median = Mode
D) Mode > Median > Mean

Correct Answer: (B) Mean < Median < Mode

119. In a dataset containing the numbers 1, 1, 2, 2, 3, 3, 4, what is the median?

A) 1
B) 2
C) 3
D) 2.5

Correct Answer: (D) 2.5

120. If the dataset is: 10, 20, 30, 40, 50, what is the mean?

A) 30
B) 35
C) 40
D) 45

Correct Answer: (A) 30

121. In a normal distribution, how do the mean, median, and mode compare?

A) Mean < Median < Mode
B) Mean = Median = Mode
C) Mean > Median > Mode
D) Median < Mode < Mean

Correct Answer: (B) Mean = Median = Mode

122. Which of the following measures can be used to describe a categorical dataset?

A) Mean
B) Median
C) Mode
D) None of the above

Correct Answer: (C) Mode

123. In which case would the median and mean be significantly different?

A) In a symmetrical distribution
B) In a dataset with outliers
C) In a small dataset
D) In a uniform distribution

Correct Answer: (B) In a dataset with outliers

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Interactive MCQs Quiz

1. What is the mean of a set of numbers?

2. In the example provided, what is the mean of the numbers 2, 5, 8, 3, and 9?

3. What does the formula for arithmetic mean indicate?

4. What is the first property of the arithmetic mean?

5. If every value of a variable is increased by a constant 𝑎, what happens to the arithmetic mean?

6. What does it mean for the arithmetic mean to be dependent on the change of origin and scale?

7. What is the minimum property of the sum of the squares of the deviations about the mean?

8. How do you find the arithmetic mean of the first 𝑛 natural numbers?

9. If 8 is the average of six variates and five of them are 8, 15, 0, 6, and 11, how can the sixth variate be determined?

10. If the first five variates are 8, 15, 0, 6, and 11, what is the total sum required to find the sixth variate?

11. What does the value of 𝑁 N represent in a discrete frequency distribution?

12. In a discrete series, if the value 𝑥1 occurs 𝑓1 times and 𝑥2 occurs 𝑓2 times, what is the total frequency represented as?

13. Which of the following is NOT one of the methods for calculating the arithmetic mean?

14. The arithmetic mean is applicable to which type of series?

15. What is the value of the mean (𝑋) as provided in the information?

16. In a discrete frequency distribution, if the frequencies are provided for various variable values, what is this type of data called?

17. What is the purpose of calculating the arithmetic mean in a data set?

18. Which method would be most appropriate for quickly calculating the arithmetic mean when dealing with large sets of data?

19. If the total frequency 𝑁 N equals the sum of individual frequencies Σ 𝑓𝑖, what can be inferred?

20. In a continuous series, what replaces the class intervals for calculating the mean?

21. How is the arithmetic mean of a continuous series calculated?

22. What is the primary difference between a continuous series and a discrete series?

23. Which of the following is an example of a continuous series?

24. Which method is NOT used to find the arithmetic mean of a continuous series?

25. What is the formula used in the direct method to find the mean in a continuous series?

26. What does the shortcut method for finding the mean involve?

27. In the step deviation method, what role does the class interval width play?

28. What is the purpose of the step deviation method?

29. What is an important step in the step deviation method?

30. Which method requires the use of an assumed mean for calculating the arithmetic mean?

31. In the given example of a continuous series, how many students scored between 50 and 60?

32. How is the mean calculated in the step deviation method?

33. What is the assumed mean used for in the shortcut and step deviation methods?

34. What is the geometric mean of a dataset?

35. How is the geometric mean of two numbers (a) and (b) calculated?

36. What is the geometric mean of 4 and 16?

37. Which of the following statements is true regarding the relationship between the arithmetic mean (AM) and geometric mean (GM)?

38. According to the geometric mean theorem, what is the relationship between segments (a), (b), and the altitude (h) in a right triangle?

39. Which of the following is NOT a property of the geometric mean?

40. In what fields is the geometric mean commonly used?

41. How do you find the geometric mean of the numbers 2, 4, 6, 8, 10, and 12?

42. What is the product (P) of the numbers 2, 4, 6, 8, 10, and 12?

43. How is the geometric mean applied in biological processes?

44. What is the definition of the median in a dataset?

45. What does it mean when it is stated that fifty percent of the goods are above and fifty percent are below their worth?

46. How do you determine the median when the number of observations is even?

47. What are the first steps to compute the median of ungrouped data?

48. What does 'n' represent in the context of median calculation?

49. Why is sorting the data important when calculating the median?

50. In the provided example, how many observations are there in the dataset of heights?

51. What is the correct order of the heights when arranged in ascending order?

52. How is the median related to the concept of central tendency?

53. What is the formula to find the position of the median in an ordered dataset?

54. What does the median represent in a discrete series?

55. In a discrete series, what does 'N' represent?

56. How is the cumulative frequency defined in a discrete series?

57. What are the first steps to calculate the median of a discrete series?

58. When calculating the median item, what does the formula \( \text{Median} = \text{Size of the } \frac{N}{2} \text{ th item} \) indicate?

59. In the example given, how many students received 60 marks?

60. What is the cumulative frequency if three students receive 60 marks, nine students receive 70 marks, five students receive 80 marks, and two students receive 90 marks?

61. If the median of a discrete series is given as 12, what does this imply about the dataset?

62. How do you identify the missing frequency in a given series when the median is known?

63. What is the missing frequency value in the example where the median is 12?

64. What is the definition of the median in the context of continuous data?

65. How is the median calculated in a continuous series?

66. What is the first step in calculating the median of continuous data?

67. In continuous data, how is the class interval related to the calculation of the median?

68. What is the formula for finding the median in a continuous frequency distribution?

69. In the median formula \( L + \left( \frac{N}{2} - CF \right) \times h \), what does 'L' represent?

70. What does 'CF' stand for in the median formula?

71. How do you determine the median class in a continuous frequency distribution?

72. If the total number of observations (N) is 50, at what cumulative frequency should the median be located?

73. Why is the median a preferred measure of central tendency for continuous data?

74. What is the mode in a dataset?

75. In a dataset, if there are two values that occur with the highest frequency, what is it called?

76. How do you identify the mode in ungrouped data?

77. What is the mode of the following dataset: 4, 1, 2, 2, 3, 4, 4, 5?

12. In a discrete series, if the value 𝑥₁ occurs 𝑓₁ times and 𝑥₂ occurs 𝑓₂ times, what is the total frequency represented as?

19. If the total frequency 𝑁 N equals the sum of individual frequencies Σ 𝑓_𝑖, what can be inferred?