Statistics – Measures of Dispersion (Range, Quartile, Standard, Mean Deviation, Coefficient of Variation) Quiz - ICSE Class 11 Economics

Free practice quiz: Statistics – Measures of Dispersion (Range, Quartile, Standard, Mean Deviation, Coefficient of Variation) (ICSE Class 11 Economics). 79 multiple-choice questions with answers and explanations. Play online, no sign-up needed.

This ICSE Class 11 Economics practice quiz has 79 multiple-choice questions on Statistics – Measures of Dispersion (Range, Quartile, Standard, Mean Deviation, Coefficient of Variation), and 79 of them come with an explanation. Try the 5 sample questions below (tap an option to check yourself), then play the full quiz online. No sign-up needed.

Sample questions

1. For a dataset with values {2, 5, 8, 10, 15}, calculate the range.

   1. 13
   2. 10
   3. 15
   4. 8
   Show answer

   Answer: A. 13

   The range is the difference between the maximum and minimum values in a dataset. Here, the maximum value is 15 and the minimum value is 2. Therefore, Range = 15 - 2 = 13.

2. If the range of a dataset is 30 and the minimum value is 5, what is the maximum value?

   1. 35
   2. 25
   3. 30
   4. 15
   Show answer

   Answer: A. 35

   The range is the difference between the maximum and minimum values. Range = Maximum Value - Minimum Value. Given Range = 30 and Minimum Value = 5, then 30 = Maximum Value - 5. Therefore, Maximum Value = 30 + 5 = 35.

3. Which of the following measures of dispersion is not affected by the addition of an outlier to the dataset?

   1. Range
   2. Standard Deviation
   3. Interquartile Range
   4. Mean Deviation
   Show answer

   Answer: C. Interquartile Range

   The Interquartile Range (IQR) is calculated from the first and third quartiles. Quartiles divide the data into four equal parts, making the IQR resistant to extreme values (outliers). Range, Standard Deviation, and Mean Deviation are all sensitive to outliers as they consider all data points or extreme values directly.

4. If a dataset has a mean of 50 and a standard deviation of 0, what are the values in the dataset?

   1. All values are 50.
   2. All values are 0.
   3. The values are spread around 0.
   4. The values are spread around 50.
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   Answer: A. All values are 50.

   A standard deviation of 0 indicates that there is no dispersion in the data. This means all data points are identical. If the mean is 50 and there is no dispersion, then all data points must be exactly 50.

5. For the dataset {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, calculate the Mean Deviation from the Mean.

   1. 2.5
   2. 3
   3. 1.5
   4. 2
   Show answer

   Answer: A. 2.5

   First, calculate the mean: (1+2+3+4+5+6+7+8+9+10)/10 = 55/10 = 5.5. Then calculate the absolute deviations from the mean: |1-5.5|=4.5, |2-5.5|=3.5, |3-5.5|=2.5, |4-5.5|=1.5, |5-5.5|=0.5, |6-5.5|=0.5, |7-5.5|=1.5, |8-5.5|=2.5, |9-5.5|=3.5, |10-5.5|=4.5. The sum of absolute deviations is 4.5+3.5+2.5+1.5+0.5+0.5+1.5+2.5+3.5+4.5 = 25. Mean Deviation = 25 / 10 = 2.5.

More questions in this quiz

Answers and explanations are in the full quiz.

1. If the first quartile (Q1) of a dataset is 20 and the third quartile (Q3) is 50, what is the Interquartile Range (IQR)?
2. Consider the dataset {3, 6, 9, 12, 15}. What is the Mean Deviation about the Mean (MD)?
3. If the variance of a dataset is 25, what is the Standard Deviation?
4. Two datasets, A and B, have the same mean. Dataset A has a Standard Deviation of 8 and Dataset B has a Standard Deviation of 12. Which dataset is more dispersed?
5. For a dataset with mean 50 and standard deviation 10, what is the Coefficient of Variation (CV)?
6. Which measure of dispersion is most affected by extreme values (outliers)?
7. If all values in a dataset are identical, what will be the value of Standard Deviation?
8. Which of the following is NOT a measure of dispersion?
9. The semi-interquartile range (SIQR) is calculated as:
10. If the mean deviation of a dataset is 5 and the mean is 20, what is the coefficient of mean deviation?
11. Which measure of dispersion is a relative measure and is useful for comparing the variability of datasets with different means?
12. For a symmetric distribution, which of the following relationships generally holds true?
13. If a dataset contains {10, 10, 10, 10, 10}, what is the Quartile Deviation?
14. Which measure of dispersion is calculated based on the deviations of each data point from the arithmetic mean, taking the absolute values of these deviations?
15. What does a standard deviation of 0 indicate about a dataset?
16. Consider the dataset {2, 4, 6, 8, 10}. What is the value of Q1 (First Quartile)?
17. If the Coefficient of Variation (CV) for two datasets is 25% and 35% respectively, with the same mean, which dataset shows greater relative dispersion?
18. Which measure of dispersion is sensitive to the squaring of deviations?
19. For the dataset {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, calculate the range.
20. If the Interquartile Range (IQR) of a dataset is 15, what can be said about the spread of the middle 50% of the data?
21. Calculate the mean deviation for the dataset {5, 10, 15, 20, 25}.
22. If a dataset has a variance of 100, what is its standard deviation?
23. Which measure of dispersion is calculated as (Q3 - Q1) / 2?
24. Two datasets have the same mean. Dataset X has a standard deviation of 5, and Dataset Y has a standard deviation of 10. Which dataset is more spread out relative to its mean?
25. If the mean of a dataset is 60 and the coefficient of variation is 25%, what is the standard deviation?
26. Which of the following statements about measures of dispersion is FALSE?
27. If the range of a dataset is 40 and the first quartile is 25 and the third quartile is 65, calculate the quartile deviation.
28. Consider the dataset {10, 12, 14, 16, 18}. What is the Mean Deviation from the Median?
29. If the standard deviation of a dataset is 7, what is the variance?
30. For a dataset {3, 3, 3, 3, 3}, what is the Coefficient of Variation?
31. If the mean of a dataset is 20 and the standard deviation is 5, and a new data point of 40 is added, how will the standard deviation likely change?
32. Which measure of dispersion is expressed in the same units as the data?
33. For the dataset {5, 8, 12, 15, 20, 22, 25}, what is the Range?
34. If a dataset has a median of 30 and its interquartile range (IQR) is 10, what can be inferred about the data?
35. Calculate the Variance for the dataset {2, 4, 6, 8, 10}.
36. If the Coefficient of Variation (CV) of two datasets are 20% and 30%, and they have the same mean, which dataset has more dispersion relative to its mean?
37. Which measure of dispersion is calculated using all data points and is sensitive to extreme values?
38. If the mean of a dataset is 50 and the standard deviation is 10, which of the following values is most likely to be considered an outlier?
39. Which of the following measures of dispersion is the least affected by outliers?
40. If a dataset contains {100, 100, 100}, what is the standard deviation?
41. What is the Coefficient of Variation for a dataset with a mean of 100 and a standard deviation of 20?
42. For the dataset {1, 3, 5, 7, 9}, what is the Median Absolute Deviation (MAD)?
43. If the third quartile (Q3) is 70 and the first quartile (Q1) is 30, what is the Interquartile Range (IQR)?
44. Which of the following is a measure of spread, not central tendency?
45. The difference between the highest and lowest values in a dataset is known as the:
46. If the mean of a dataset is 75 and the Coefficient of Variation is 10%, what is the standard deviation?
47. For the dataset {4, 6, 8, 10, 12}, what is the Mean Deviation about the Mean?
48. If the variance of a dataset is 81, what is its standard deviation?
49. The Interquartile Range (IQR) is a measure of dispersion for which part of the dataset?
50. If a dataset has a mean of 30 and a standard deviation of 15, what is its Coefficient of Variation?
51. Which measure of dispersion is most sensitive to outliers?
52. Consider the dataset {5, 10, 15, 20, 25}. What is the value of Q1 (First Quartile)?
53. What is the primary advantage of using the Coefficient of Variation (CV) over Standard Deviation when comparing variability?
54. If the mean deviation of a dataset is 6 and the standard deviation is 8, which statement is true?
55. Which measure of dispersion is derived from the squares of deviations from the mean?
56. For the dataset {10, 20, 30, 40, 50}, what is the Range?
57. If the mean of a dataset is 50 and the variance is 100, what is the standard deviation?
58. Which of the following statements is FALSE regarding the Interquartile Range (IQR)?
59. If the mean deviation of a dataset is 5 and its mean is 25, what is the coefficient of mean deviation?
60. If the mean of a dataset is 80 and the standard deviation is 16, what is the Coefficient of Variation?

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