TRB PG Assistant - Dispersion – range, quartile deviation, standard deviation Online Test (MCQ Quiz)

1. 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

2. Which measure of dispersion is the simplest to calculate?

A) Standard Deviation B) Quartile Deviation C) Range D) Variance

3. 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

4. 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

5. In a dataset of scores: 10, 15, 12, 18, 20, what is the range?

A) 8 B) 10 C) 15 D) 20

6. Quartiles divide a dataset into how many equal parts?

A) Two B) Three C) Four D) Five

7. Quartile Deviation (QD) is also known as:

A) Interquartile Range B) Semi-Interquartile Range C) Mean Deviation D) Standard Deviation

8. The formula for Quartile Deviation is:

A) (Q3 - Q1) / 2 B) (Q3 + Q1) / 2 C) Q3 - Q1 D) (Q2 - Q1) / 2

9. Q1 represents the 25th percentile, and Q3 represents the:

A) 50th percentile B) 60th percentile C) 75th percentile D) 90th percentile

10. 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

11. 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

12. Standard deviation is the square root of:

A) Range B) Mean Deviation C) Variance D) Quartile Deviation

13. 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

14. 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

15. 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

16. Which of the following is NOT a measure of dispersion?

A) Range B) Mean C) Standard Deviation D) Quartile Deviation

17. If the interquartile range (IQR) is 15 and Q1 is 20, what is Q3?

A) 5 B) 27.5 C) 35 D) 40

18. Which measure of dispersion is sensitive to every value in the dataset?

A) Range B) Quartile Deviation C) Standard Deviation D) Interquartile Range

19. In a symmetrical distribution, the mean, median, and mode are:

A) Far apart B) Equal C) Widely spread D) Not related

20. Which measure of dispersion is calculated using deviations from the mean?

A) Range B) Quartile Deviation C) Standard Deviation D) Median Absolute Deviation

21. 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

22. If a dataset has values 5, 5, 5, 5, 5, what is the standard deviation?

A) 0 B) 1 C) 5 D) 25

23. The variance is always:

A) Negative B) Zero or positive C) A whole number D) Less than the standard deviation

24. 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

25. 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)

26. 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))

27. 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

28. 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

29. 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

30. Which measure of dispersion is robust against outliers?

A) Range B) Standard Deviation C) Interquartile Range D) Variance

31. If Q1 = 30, Q3 = 50, and the median (Q2) = 40, what is the Quartile Deviation?

A) 10 B) 20 C) 30 D) 40

32. 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

33. 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

34. 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

35. 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

36. 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

37. What is the median of the following dataset: 5, 10, 15, 20, 25?

A) 5 B) 15 C) 20 D) 25

38. What is Q1 for the dataset: 10, 20, 30, 40, 50, 60, 70, 80?

A) 20 B) 25 C) 30 D) 40

39. What is Q3 for the dataset: 10, 20, 30, 40, 50, 60, 70, 80?

A) 50 B) 60 C) 65 D) 70

40. Calculate the Quartile Deviation for the dataset: 10, 20, 30, 40, 50, 60, 70, 80.

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

41. Which measure of dispersion is most affected by a single extreme value?

A) Standard Deviation B) Quartile Deviation C) Range D) Interquartile Range

42. 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

43. 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%

44. 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%

45. 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%

46. 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

47. Compared to standard deviation, MAD is generally:

A) Larger B) Smaller C) Equal D) Not comparable

48. Which of the following is a measure of relative dispersion?

A) Range B) Variance C) Standard Deviation D) Coefficient of Variation

49. 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

50. 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

Dispersion – range, quartile deviation, standard deviation - Online Test

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