1. Which of the following is not a measure of variability?
A. Range
B. Median
C. Standard Deviation
D. Quartile Deviation
Answer: B. Median
Explanation: Median is a measure of central tendency, not variability. Measures of variability include range, standard deviation, quartile deviation, and mean deviation.
2. The simplest measure of variability is:
A. Standard Deviation
B. Range
C. Mean Deviation
D. Quartile Deviation
Answer: B. Range
Explanation: Range is the simplest measure, calculated as the difference between the highest and lowest values in a dataset.
3. The interquartile range (IQR) is calculated as:
A. Q3 + Q1
B. Q3 − Q1
C. Q1 − Q3
D. Q1 × Q3
Answer: B. Q3 − Q1
Explanation: IQR = Q3 − Q1. It measures the spread of the middle 50% of the data and is a robust measure of variability.
4. Which measure of variability is most affected by extreme scores?
A. Mean Deviation
B. Standard Deviation
C. Range
D. Quartile Deviation
Answer: C. Range
Explanation: Range is highly sensitive to outliers because it only considers the two extreme values.
5. Which measure of variability is considered the most reliable?
A. Range
B. Quartile Deviation
C. Standard Deviation
D. Mean Deviation
Answer: C. Standard Deviation
Explanation: Standard deviation is the most commonly used and reliable measure of variability because it considers all values in the dataset.
6. If all values in a dataset are the same, the standard deviation is:
A. 1
B. 0
C. Undefined
D. Cannot say
Answer: B. 0
Explanation: When there is no variability among data points, standard deviation equals zero.
7. Quartile Deviation is also known as:
A. Semi-standard deviation
B. Semi-range
C. Semi-interquartile range
D. None of the above
Answer: C. Semi-interquartile range
Explanation: Quartile deviation = (Q3 − Q1)/2, hence also called the semi-interquartile range.
8. In a symmetrical distribution, the mean deviation is minimum when calculated from:
A. Mean
B. Median
C. Mode
D. Any of the three
Answer: B. Median
Explanation: Mean deviation is least when measured from the median in a symmetrical distribution.
9. Which measure of variability is not based on all values in a distribution?
A. Standard Deviation
B. Range
C. Mean Deviation
D. None
Answer: B. Range
Explanation: Range only uses the highest and lowest scores, ignoring the rest.
10. Mean Deviation is:
A. Arithmetic average of deviations from mean
B. Average of squared deviations
C. Average of absolute deviations
D. None of the above
Answer: C. Average of absolute deviations
Explanation: Mean deviation is the average of the absolute deviations from the mean or median.
11. When the variability in a dataset is high, the standard deviation will be:
A. Zero
B. Small
C. Large
D. Negative
Answer: C. Large
Explanation: More spread in data → higher standard deviation.
12. The standard deviation is always:
A. Negative
B. Zero
C. Non-negative
D. Positive
Answer: C. Non-negative
Explanation: Because it is derived from a square root of squared differences, SD is never negative.
13. Which of the following statements is TRUE?
A. Standard deviation is less reliable than range.
B. Mean deviation uses all scores.
C. Quartile deviation uses the entire dataset.
D. Range uses all scores.
Answer: B. Mean deviation uses all scores.
Explanation: Mean deviation considers every value by calculating their deviation from mean or median.
14. Variability gives information about:
A. Location of data
B. Shape of data
C. Spread of data
D. Frequency
Answer: C. Spread of data
Explanation: Measures of variability help understand the degree to which data values deviate from each other.
15. Which measure of variability is most appropriate when comparing two distributions with different units?
A. Standard Deviation
B. Coefficient of Variation
C. Range
D. Mean Deviation
Answer: B. Coefficient of Variation
Explanation: CV = (Standard Deviation / Mean) × 100; it expresses variability in relative terms, making it unit-free.
16. The unit of standard deviation is:
A. Same as mean
B. Square of mean
C. Root of mean
D. No unit
Answer: A. Same as mean
Explanation: Both mean and standard deviation are expressed in the same unit as the original data.
17. Quartile Deviation is used when:
A. Extreme scores are included
B. Distribution is skewed
C. Distribution is normal
D. Mean is used
Answer: B. Distribution is skewed
Explanation: Quartile Deviation is robust and preferred when data has extreme values or skewness.
18. Which measure of dispersion is best when comparing consistency of two players?
A. Mean Deviation
B. Range
C. Standard Deviation
D. Coefficient of Variation
Answer: D. Coefficient of Variation
Explanation: CV gives a relative measure of consistency regardless of mean scores.
19. If range is 20 and the smallest value is 5, the largest value is:
A. 15
B. 25
C. 30
D. Cannot be determined
Answer: B. 25
Explanation: Range = Largest − Smallest → 20 = L − 5 → L = 25
20. Which of the following is the most stable measure of variability?
A. Range
B. Mean Deviation
C. Standard Deviation
D. Quartile Deviation
Answer: C. Standard Deviation
Explanation: Standard deviation considers all data points and their squared deviations from the mean, making it the most stable and accurate measure.
21. In a normal distribution, the relationship between mean deviation and standard deviation is approximately:
A. MD = SD
B. MD = 2 × SD
C. MD = 0.8 × SD
D. MD = 1.25 × SD
Answer: C. MD = 0.8 × SD
Explanation: In a normal distribution, the mean deviation is roughly 4/5 (0.8) of the standard deviation.
22. Which measure of dispersion is appropriate when the data is ordinal?
A. Standard Deviation
B. Mean Deviation
C. Quartile Deviation
D. Range
Answer: C. Quartile Deviation
Explanation: Quartile Deviation is preferred for ordinal data because it does not assume equal intervals between values.
23. The coefficient of range is given by:
A. (H − L) / (H + L)
B. (H + L) / 2
C. H − L
D. (Q3 − Q1)/2
Answer: A. (H − L) / (H + L)
Explanation: This formula gives the relative measure of range, useful for comparing variability across datasets.
24. A distribution with low variability is considered:
A. Scattered
B. Skewed
C. Consistent
D. Unreliable
Answer: C. Consistent
Explanation: Low variability means that data points are close to the mean, implying consistency or stability.
25. The main drawback of range is:
A. It is difficult to calculate
B. It requires grouping
C. It is based on only two values
D. It cannot be used for continuous data
Answer: C. It is based on only two values
Explanation: Range ignores the distribution of all other data points between the extremes.
26. The square of standard deviation is known as:
A. Mean
B. Quartile Deviation
C. Range
D. Variance
Answer: D. Variance
Explanation: Variance = (Standard Deviation)²; it represents the average squared deviation from the mean.
27. A smaller standard deviation indicates:
A. Greater dispersion
B. Less consistency
C. High variability
D. More consistency
Answer: D. More consistency
Explanation: A smaller standard deviation means data points are closer to the mean.
28. If the standard deviation is zero, it means:
A. The distribution is normal
B. All values are different
C. All values are the same
D. Mean is zero
Answer: C. All values are the same
Explanation: No deviation among values implies no variability—hence, SD = 0.
29. Which measure of variability is calculated using absolute deviations?
A. Range
B. Mean Deviation
C. Standard Deviation
D. Variance
Answer: B. Mean Deviation
Explanation: Mean deviation uses the absolute values of deviations from mean or median.
30. Which measure of variability can never be negative?
A. Standard Deviation
B. Variance
C. Mean Deviation
D. All of the above
Answer: D. All of the above
Explanation: Variability measures are always ≥ 0 since they represent distances, squared or absolute.
31. Coefficient of variation is helpful in:
A. Finding mode
B. Comparing variability between two datasets
C. Identifying mean
D. Finding median
Answer: B. Comparing variability between two datasets
Explanation: Coefficient of Variation expresses variability relative to the mean, allowing meaningful comparisons.
32. In a normal distribution, about 68% of the data falls within:
A. ±1 SD
B. ±2 SD
C. ±3 SD
D. ±4 SD
Answer: A. ±1 SD
Explanation: In a normal distribution:
- 68% falls within ±1 SD
- 95% within ±2 SD
- 99.7% within ±3 SD
33. The mean deviation about mean is always:
A. Zero
B. Greater than zero
C. Less than zero
D. Cannot be negative or zero
Answer: B. Greater than zero
Explanation: Because it is calculated using absolute values, mean deviation cannot be zero (unless all values are the same).
34. Which of the following is most affected by the presence of extreme scores?
A. Quartile Deviation
B. Mean Deviation
C. Standard Deviation
D. Range
Answer: D. Range
Explanation: Since range uses only the highest and lowest values, it is most influenced by outliers.
35. If the range of a dataset is 0, then:
A. Mean is also 0
B. Median is 0
C. All values are equal
D. SD is maximum
Answer: C. All values are equal
Explanation: A range of zero means maximum and minimum are equal → no variability.
36. If a dataset has a high standard deviation, then the scores are:
A. Similar
B. Very close to the mean
C. Spread out widely
D. Positively skewed
Answer: C. Spread out widely
Explanation: A higher SD means more dispersion of scores from the mean.
37. Which measure of variability is used when calculating the z-score?
A. Mean
B. Range
C. Standard Deviation
D. Quartile Deviation
Answer: C. Standard Deviation
Explanation: Z-score = (X − Mean)/SD. It expresses how far a score is from the mean in SD units.
38. The inter-decile range includes which percent of data?
A. 100%
B. 80%
C. 50%
D. 25%
Answer: B. 80%
Explanation: Inter-decile range = D9 − D1, which includes the middle 80% of the data (excluding lowest 10% and highest 10%).
39. If the variance is 16, then the standard deviation is:
A. 8
B. 4
C. 2
D. 16
Answer: B. 4
Explanation: Standard deviation = √Variance → √16 = 4
40. Which of the following is a relative measure of variability?
A. Variance
B. Standard Deviation
C. Coefficient of Variation
D. Range
Answer: C. Coefficient of Variation
Explanation: Coefficient of Variation (CV) is unit-free and expressed as a percentage, making it a relative measure.
41. Variability is important in educational testing because it shows:
A. Students’ creativity
B. The difference between age groups
C. How much scores differ from each other
D. The reliability of median
Answer: C. How much scores differ from each other
Explanation: Variability reveals the spread or dispersion of test scores, indicating consistency or differences in performance.
42. Which measure of variability is the square root of variance?
A. Mean Deviation
B. Standard Deviation
C. Quartile Deviation
D. Range
Answer: B. Standard Deviation
Explanation: Standard deviation is defined as the square root of variance.
43. Which of the following is least affected by extreme scores?
A. Standard Deviation
B. Range
C. Mean Deviation
D. Quartile Deviation
Answer: D. Quartile Deviation
Explanation: Quartile Deviation only considers the middle 50% of the data (Q1 to Q3), hence is less affected by outliers.
44. If SD = 0, CV (coefficient of variation) will be:
A. 1
B. 100
C. 0
D. Infinite
Answer: C. 0
Explanation: CV = (SD / Mean) × 100. If SD = 0, then CV = 0, indicating no variation.
45. The average absolute deviation from the median is called:
A. Quartile Deviation
B. Standard Deviation
C. Mean Deviation
D. Range
Answer: C. Mean Deviation
Explanation: Mean Deviation can be calculated from either mean or median, but it is minimized when taken from the median.
46. If all values in a dataset are multiplied by a constant, the standard deviation:
A. Remains unchanged
B. Multiplied by the same constant
C. Divided by that constant
D. Becomes zero
Answer: B. Multiplied by the same constant
Explanation: Scaling all data by a constant scales the SD by the same constant.
47. When comparing test scores in two subjects with different means and standard deviations, which measure is best?
A. Mean
B. Range
C. Raw score
D. Coefficient of Variation
Answer: D. Coefficient of Variation
Explanation: CV helps compare the relative variability regardless of units or mean differences.
48. Which of the following pairs is correctly matched?
A. Mean deviation – Square of deviation
B. Standard deviation – Square root of variance
C. Quartile Deviation – Absolute deviation from mean
D. Variance – Median of data
Answer: B. Standard deviation – Square root of variance
Explanation: SD is the square root of the variance.
49. A student scored 80 in Math (mean = 70, SD = 5). His z-score is:
A. 2
B. −2
C. 1
D. −1
Answer: C. 2
Explanation: z = (X − Mean)/SD = (80 − 70)/5 = 10/5 = 2
50. The more the spread in a dataset, the ______ the standard deviation.
A. Smaller
B. Larger
C. Equal
D. Zero
Answer: B. Larger
Explanation: Greater spread means more deviation from the mean, hence a higher SD.
51. The formula for population variance is:
A. Σ (x − x̄)/N
B. Σ (x − x̄) ²/N
C. Σx/N
D. Σ (x + x̄) ²/N
Answer: B. Σ (x − x̄) ²/N
Explanation: This formula calculates the population variance.
52. The difference between the highest and lowest observation is known as:
A. Range
B. Interquartile Range
C. Standard Deviation
D. Quartile Deviation
Answer: A. Range
Explanation: Range = Maximum value − Minimum value.
53. Mean deviation is more accurate than range because:
A. It is easier to compute
B. It uses more data points
C. It considers only extremes
D. It ignores central tendency
Answer: B. It uses more data points
Explanation: Mean deviation involves all data points, unlike range which uses only two.
54. Which measure of dispersion is not suitable for open-ended distributions?
A. Mean Deviation
B. Quartile Deviation
C. Standard Deviation
D. Range
Answer: C. Standard Deviation
Explanation: SD requires exact values for accurate computation, which open-ended classes do not provide.
55. A smaller value of coefficient of variation indicates:
A. Higher variability
B. Higher consistency
C. More skewness
D. More central tendency
Answer: B. Higher consistency
Explanation: Smaller CV means lesser variability relative to mean, indicating consistency.
56. The sum of deviations from the mean is always:
A. Positive
B. Negative
C. One
D. Zero
Answer: D. Zero
Explanation: The algebraic sum of deviations from the mean is always zero.
57. The standard deviation is useful in calculating:
A. Percentiles
B. Z-scores
C. Median
D. Range
Answer: B. Z-scores
Explanation: Z-score = (Score − Mean)/SD; hence, SD is essential in standardization.
58. In grouped data, the standard deviation is calculated by:
A. Ignoring frequencies
B. Using class midpoints and frequencies
C. Using only class width
D. Using only the highest score
Answer: B. Using class midpoints and frequencies
Explanation: Midpoints represent the class and frequencies represent data weight.
59. Which of the following is best used to describe consistency in performance?
A. Mean
B. Standard Deviation
C. Mode
D. Range
Answer: B. Standard Deviation
Explanation: SD reveals how consistently values cluster around the mean; lower SD = higher consistency.