Measures of central tendency, dispersion, skewness - Question Bank

1. A distribution where the mean is greater than the median, and the median is greater than the mode, is:
A) Symmetrical
B) Positively skewed
C) Negatively skewed
D) Bimodal
2. The formula for variance involves the sum of:
A) Absolute deviations from the mean
B) Squared deviations from the mean
C) Deviations from the median
D) Deviations from the mode
3. Which measure of central tendency is affected by the magnitude of each value?
A) Median
B) Mode
C) Mean
D) Range
4. Bowley's coefficient of skewness is calculated using:
A) Mean, Median, Mode
B) Quartiles
C) Standard Deviation
D) Range
5. What does a large interquartile range suggest?
A) The middle 50% of data is tightly clustered
B) The middle 50% of data is widely spread
C) The data is perfectly symmetrical
D) The data has no outliers
6. Which measure of central tendency is most appropriate for ordinal data?
A) Mean
B) Median
C) Mode
D) Geometric Mean
7. The standard deviation is always a:
A) Positive value
B) Negative value
C) Zero value
D) Non-negative value
8. Which of the following is a measure of dispersion?
A) Mean
B) Median
C) Mode
D) Quartile Deviation
9. If the mean, median, and mode are all equal, the distribution is:
A) Positively skewed
B) Negatively skewed
C) Symmetrical
D) Bimodal
10. A symmetrical distribution has a skewness value of:
A) Greater than 0
B) Less than 0
C) Equal to 0
D) 1
11. Which measure of dispersion is calculated using only the quartiles?
A) Standard Deviation
B) Variance
C) Range
D) Interquartile Range
12. The sum of deviations of individual data points from the mean is always:
A) Positive
B) Negative
C) Zero
D) Equal to the range
13. Which measure of central tendency is defined as the value that occurs most often?
A) Mean
B) Median
C) Mode
D) Geometric Mean
14. If a distribution is leptokurtic, it is:
A) Flatter than normal
B) More peaked than normal
C) Symmetrical
D) Positively skewed
15. What is the first quartile (Q1) also known as?
A) Median
B) Lower quartile
C) Upper quartile
D) Mode
16. A dataset with a mean of 100 and a standard deviation of 10 is considered more dispersed than a dataset with a mean of 100 and a standard deviation of:
A) 5
B) 15
C) 20
D) 100
17. Which measure of skewness is calculated as (Mean - Mode) / Standard Deviation?
A) Pearson's first coefficient of skewness
B) Pearson's second coefficient of skewness
C) Bowley's coefficient of skewness
D) Moment coefficient of skewness
18. The formula for the median of grouped data involves:
A) Sum of values and count
B) Mid-point of classes and cumulative frequencies
C) Highest and lowest frequencies
D) The most frequent class
19. If all values in a dataset are the same, what is the standard deviation?
A) Zero
B) One
C) The value itself
D) Undefined
20. Which of the following statistical measures is used to determine the concentration of data around a central point?
A) Range
B) Quartile Deviation
C) Standard Deviation
D) Skewness
21. In a negatively skewed distribution, the mode is typically:
A) Less than the median
B) Greater than the median
C) Equal to the median
D) Unrelated to the median
22. What is the primary advantage of using the median over the mean?
A) It is easier to calculate
B) It is not affected by extreme values
C) It is always a value present in the dataset
D) It is suitable for all types of data
23. For a dataset {1, 2, 3, 4, 5}, the mean is 3. What is the variance?
A) 1
B) 2
C) 2.5
D) 3
24. The coefficient of variation is a measure of:
A) Central tendency
B) Skewness
C) Relative dispersion
D) Absolute dispersion
25. Which measure of dispersion uses the absolute differences between each data point and the mean?
A) Standard Deviation
B) Variance
C) Range
D) Mean Deviation
26. Which of the following is NOT a measure of central tendency?
A) Mean
B) Median
C) Mode
D) Variance
27. What type of skewness is present if the mean is less than the median?
A) Positive skew
B) Negative skew
C) Zero skew
D) Symmetrical
28. The third quartile (Q3) is the value below which what percentage of data falls?
A) 25%
B) 50%
C) 75%
D) 100%
29. In a bimodal distribution, how many modes are there?
A) One
B) Two
C) Three
D) Multiple
30. Which measure of dispersion is sensitive to every value in the dataset?
A) Interquartile Range
B) Quartile Deviation
C) Range
D) Standard Deviation
31. If the mean of a dataset is 50 and the standard deviation is 5, what is the z-score of a value of 55?
A) -1
B) 0
C) 1
D) 2
32. The mode of the set {2, 3, 3, 4, 5, 5, 5, 6} is:
A) 3
B) 4
C) 5
D) 6
33. Which type of distribution has a bell shape and is symmetrical?
A) Skewed
B) Uniform
C) Normal
D) Bimodal
34. Variance is the average of the squared differences from the:
A) Median
B) Mode
C) Mean
D) Range
35. Which measure of central tendency is also known as the average?
A) Median
B) Mode
C) Mean
D) Range
36. The median is the value that divides the data into how many equal parts?
A) Two
B) Three
C) Four
D) Ten
37. Which formula is commonly used for calculating the Pearsonian coefficient of skewness?
A) (Mean - Mode) / Standard Deviation
B) (Q3 - Q1) / 2
C) Standard Deviation / Mean
D) (Median - Mode) / Standard Deviation
38. If a distribution is perfectly symmetrical, what is its skewness value?
A) Positive
B) Negative
C) Zero
D) One
39. What does a negative skewness value indicate?
A) The tail is longer on the right side
B) The tail is longer on the left side
C) The distribution is perfectly symmetrical
D) The mode is the highest value
40. In a positively skewed distribution, which relationship between mean, median, and mode is typically observed?
A) Mean < Median < Mode
B) Mean > Median > Mode
C) Mean = Median = Mode
D) Mode > Mean > Median
41. What is skewness a measure of?
A) The peakedness of a distribution
B) The symmetry of a distribution
C) The average value of a dataset
D) The spread of data points
42. Which measure of dispersion is less affected by outliers than the range?
A) Standard Deviation
B) Variance
C) Interquartile Range
D) Mean Deviation
43. The interquartile range (IQR) is the difference between which two quartiles?
A) Q1 and Q2
B) Q2 and Q3
C) Q1 and Q3
D) Q3 and Q4
44. What does a small standard deviation indicate about a dataset?
A) The data points are widely spread out
B) The data points are clustered closely around the mean
C) The data is skewed
D) The mean is not representative
45. Which measure of dispersion is calculated as the square root of the variance?
A) Interquartile Range
B) Mean Deviation
C) Standard Deviation
D) Variance
46. What does the range of a dataset measure?
A) The average spread of data
B) The difference between the maximum and minimum values
C) The most frequent value
D) The middle value
47. Which of the following is a measure of dispersion?
A) Mean
B) Median
C) Standard Deviation
D) Mode
48. If a dataset has an even number of observations, how is the median calculated?
A) It is the average of the two middle values
B) It is the first of the two middle values
C) It is the second of the two middle values
D) It is the mode of the two middle values
49. Which measure of central tendency is used for categorical data?
A) Mean
B) Median
C) Range
D) Mode
50. What does the median represent in a dataset?
A) The most frequent value
B) The average of all values
C) The middle value when data is ordered
D) The difference between the highest and lowest values