Dispersion – range, quartile deviation, standard deviation - Question Bank

1. Which statistical concept is crucial for understanding the reliability and precision of measurements in biological studies?
A) Central Tendency
B) Dispersion
C) Correlation
D) Regression
2. For a dataset with values {2, 4, 6, 8, 10}, the mean is 6. Calculate the variance (population).
A) 4
B) 5
C) 8
D) 10
3. Which of the following is a measure of relative dispersion?
A) Range
B) Variance
C) Standard Deviation
D) Coefficient of Variation
4. Compared to standard deviation, MAD is generally:
A) Larger
B) Smaller
C) Equal
D) Not comparable
5. The Mean Absolute Deviation (MAD) is calculated as:
A) Σ|x - mean| / n
B) Σ(x - mean)² / n
C) Σ|x - median| / n
D) Σ(x - median)² / n
6. Approximately what percentage of data falls within three standard deviations of the mean in a normal distribution?
A) 50%
B) 68%
C) 95%
D) 99.7%
7. Approximately what percentage of data falls within two standard deviations of the mean in a normal distribution?
A) 50%
B) 68%
C) 95%
D) 99.7%
8. Approximately what percentage of data falls within one standard deviation of the mean in a normal distribution?
A) 50%
B) 68%
C) 95%
D) 99.7%
9. The empirical rule (68-95-99.7 rule) applies to which type of distribution?
A) Uniform distribution
B) Skewed distribution
C) Normal distribution
D) Bimodal distribution
10. Which measure of dispersion is most affected by a single extreme value?
A) Standard Deviation
B) Quartile Deviation
C) Range
D) Interquartile Range
11. Calculate the Quartile Deviation for the dataset: 10, 20, 30, 40, 50, 60, 70, 80.
A) 10
B) 15
C) 20
D) 25
12. What is Q3 for the dataset: 10, 20, 30, 40, 50, 60, 70, 80?
A) 50
B) 60
C) 65
D) 70
13. What is Q1 for the dataset: 10, 20, 30, 40, 50, 60, 70, 80?
A) 20
B) 25
C) 30
D) 40
14. What is the median of the following dataset: 5, 10, 15, 20, 25?
A) 5
B) 15
C) 20
D) 25
15. If all values in a dataset are multiplied by a positive constant, the standard deviation will:
A) Remain the same
B) Be multiplied by that constant
C) Be divided by that constant
D) Increase by the constant
16. If all values in a dataset are increased by a constant, the standard deviation will:
A) Increase
B) Decrease
C) Remain the same
D) Become zero
17. Which measure of dispersion is expressed in the same units as the original data?
A) Variance
B) Standard Deviation
C) Range
D) All of the above
18. In a positively skewed distribution, which relationship generally holds true?
A) Mean > Median > Mode
B) Mode > Median > Mean
C) Mean < Median < Mode
D) Mode < Median < Mean
19. In a negatively skewed distribution, which relationship generally holds true?
A) Mean > Median > Mode
B) Mode > Median > Mean
C) Mean < Median < Mode
D) Mode < Median < Mean
20. If Q1 = 30, Q3 = 50, and the median (Q2) = 40, what is the Quartile Deviation?
A) 10
B) 20
C) 30
D) 40
21. Which measure of dispersion is robust against outliers?
A) Range
B) Standard Deviation
C) Interquartile Range
D) Variance
22. A dataset with a larger Coefficient of Variation has:
A) Less relative variability
B) More relative variability
C) A higher mean
D) A lower median
23. The Coefficient of Variation (CV) is calculated as:
A) (Standard Deviation / Mean) * 100
B) (Mean / Standard Deviation) * 100
C) (Variance / Mean) * 100
D) (Quartile Deviation / Median) * 100
24. Which measure of dispersion is used to compare variability between datasets with different means?
A) Standard Deviation
B) Quartile Deviation
C) Coefficient of Variation
D) Range
25. The formula for the sample variance (s²) is:
A) Σ(x - μ)² / N
B) Σ(x - x̄)² / (n-1)
C) Σ|x - x̄| / (n-1)
D) √(Σ(x - x̄)² / (n-1))
26. The formula for the population variance (σ²) is:
A) Σ(x - μ)² / N
B) Σ(x - x̄)² / (n-1)
C) Σ|x - μ| / N
D) √(Σ(x - μ)² / N)
27. What is the unit of variance compared to the original data?
A) The same unit
B) The unit squared
C) The square root of the unit
D) No unit
28. The variance is always:
A) Negative
B) Zero or positive
C) A whole number
D) Less than the standard deviation
29. If a dataset has values 5, 5, 5, 5, 5, what is the standard deviation?
A) 0
B) 1
C) 5
D) 25
30. The sum of the squared deviations from the mean is minimized for:
A) The Median
B) The Mode
C) The Mean
D) Any central value
31. Which measure of dispersion is calculated using deviations from the mean?
A) Range
B) Quartile Deviation
C) Standard Deviation
D) Median Absolute Deviation
32. In a symmetrical distribution, the mean, median, and mode are:
A) Far apart
B) Equal
C) Widely spread
D) Not related
33. Which measure of dispersion is sensitive to every value in the dataset?
A) Range
B) Quartile Deviation
C) Standard Deviation
D) Interquartile Range
34. If the interquartile range (IQR) is 15 and Q1 is 20, what is Q3?
A) 5
B) 27.5
C) 35
D) 40
35. Which of the following is NOT a measure of dispersion?
A) Range
B) Mean
C) Standard Deviation
D) Quartile Deviation
36. For a sample, the formula for standard deviation uses (n-1) in the denominator to:
A) Increase the value of the standard deviation
B) Decrease the value of the standard deviation
C) Provide a less biased estimate of the population standard deviation
D) Simplify the calculation
37. If the standard deviation of a dataset is 0, what does it imply?
A) The data has a wide spread
B) All data points are identical
C) The mean is equal to the median
D) The dataset is large
38. A higher standard deviation indicates:
A) Data points are clustered closely around the mean
B) Data points are more spread out from the mean
C) The median is higher than the mean
D) The dataset has no outliers
39. Standard deviation is the square root of:
A) Range
B) Mean Deviation
C) Variance
D) Quartile Deviation
40. What is the primary purpose of standard deviation?
A) To find the most frequent value
B) To measure the average distance of data points from the mean
C) To determine the highest and lowest values
D) To divide the data into four equal parts
41. Which measure of dispersion is less affected by extreme values compared to the range?
A) Standard Deviation
B) Quartile Deviation
C) Variance
D) Coefficient of Variation
42. Q1 represents the 25th percentile, and Q3 represents the:
A) 50th percentile
B) 60th percentile
C) 75th percentile
D) 90th percentile
43. The formula for Quartile Deviation is:
A) (Q3 - Q1) / 2
B) (Q3 + Q1) / 2
C) Q3 - Q1
D) (Q2 - Q1) / 2
44. Quartile Deviation (QD) is also known as:
A) Interquartile Range
B) Semi-Interquartile Range
C) Mean Deviation
D) Standard Deviation
45. Quartiles divide a dataset into how many equal parts?
A) Two
B) Three
C) Four
D) Five
46. In a dataset of scores: 10, 15, 12, 18, 20, what is the range?
A) 8
B) 10
C) 15
D) 20
47. What is a major limitation of using the range as a measure of dispersion?
A) It is difficult to calculate
B) It is not affected by outliers
C) It only considers the extreme values and ignores others
D) It requires a large dataset
48. The range of a dataset is defined as the difference between:
A) The mean and the median
B) The smallest and the largest values
C) The first and the third quartiles
D) The mode and the mean
49. Which measure of dispersion is the simplest to calculate?
A) Standard Deviation
B) Quartile Deviation
C) Range
D) Variance
50. What does 'dispersion' measure in statistics?
A) The central tendency of data
B) The spread or variability of data points
C) The correlation between two variables
D) The probability of an event occurring
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