Statistics – Mean, Median, Mode, Dispersion Quiz - ICSE Class 11 Mathematics

Free practice quiz: Statistics – Mean, Median, Mode, Dispersion (ICSE Class 11 Mathematics). 60 multiple-choice questions with answers and explanations. Play online, no sign-up needed.

This ICSE Class 11 Mathematics practice quiz has 60 multiple-choice questions on Statistics – Mean, Median, Mode, Dispersion, and 60 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 100 observations, the sum of deviations from the mean is always:

   1. Zero
   2. Equal to the mean
   3. Equal to the median
   4. Cannot be determined
   Show answer

   Answer: A. Zero

   The sum of deviations of individual observations from their arithmetic mean is always zero. This is a fundamental property of the mean.

2. Consider the dataset: {5, 15, 25, 35, 45}. If we add the value 55 to this dataset, how does the median change?

   1. It remains unchanged
   2. It increases by 5
   3. It increases by 10
   4. It decreases
   Show answer

   Answer: B. It increases by 5

   The original dataset is {5, 15, 25, 35, 45}. There are 5 observations. The median is the 3rd element, which is 25. When 55 is added, the dataset becomes {5, 15, 25, 35, 45, 55}. There are now 6 observations. The median is the average of the 3rd and 4th elements, which are 25 and 35. The new median is (25 + 35) / 2 = 60 / 2 = 30. The median has increased from 25 to 30, an increase of 5.

3. For a dataset, if Q1 = 10, Median (Q2) = 25, and Q3 = 40, what is the interquartile range (IQR)?

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

   Answer: C. 30

   The interquartile range (IQR) is the difference between the third quartile (Q3) and the first quartile (Q1). IQR = Q3 - Q1. Given Q1 = 10 and Q3 = 40, the IQR = 40 - 10 = 30.

4. What does the interquartile range measure?

   1. The total spread of the data
   2. The spread of the middle 50% of the data
   3. The average deviation from the mean
   4. The frequency of the most common value
   Show answer

   Answer: B. The spread of the middle 50% of the data

   The interquartile range (IQR) is the difference between the third quartile (Q3) and the first quartile (Q1). It represents the range of the middle half of the data, providing a measure of spread that is less affected by outliers than the total range.

5. If the mean of a dataset is 50 and the sum of deviations from the mean is 150, what is the number of observations?

   1. 15
   2. 5
   3. 10
   4. Cannot be determined
   Show answer

   Answer: D. Cannot be determined

   A fundamental property of the mean is that the sum of the deviations of each observation from the mean is always zero. If the sum of deviations is stated as 150, this implies an error in the premise of the question, as it contradicts a core statistical property. Therefore, the number of observations cannot be determined from this erroneous information.

More questions in this quiz

Answers and explanations are in the full quiz.

1. If all values in a dataset are multiplied by a constant 'k', how does the median change?
2. Which measure of central tendency is most affected by extreme values (outliers) in a dataset?
3. In a dataset, if the mean is 35, the median is 30, and the mode is 25, the distribution is:
4. The range of a dataset is calculated as:
5. If the variance of a dataset is 16, what is the standard deviation?
6. Which of the following is NOT a measure of dispersion?
7. For a dataset with an odd number of observations, the median is:
8. If the mode of a dataset is 50, it means that:
9. When a dataset is symmetric, the mean, median, and mode are:
10. Consider the dataset: {10, 20, 30, 40, 50}. If 10 is replaced by 100, how does the median change?
11. If a dataset has a standard deviation of 0, what can be concluded about the dataset?
12. Which measure of dispersion is most affected by the addition of a new data point at the extreme end of the dataset?
13. In a dataset of positive numbers, if the mean is 20 and the harmonic mean is 10, what can be said about the geometric mean?
14. If the interquartile range (IQR) of a dataset is 15, and the third quartile (Q3) is 40, what is the first quartile (Q1)?
15. Consider a dataset where the mode is 50 and the mean is 45. What is likely about the skewness of the distribution?
16. If you transform a dataset by adding 5 to each observation, which measure of dispersion remains unchanged?
17. What is the median of the following dataset: {7, 2, 5, 8, 1, 9, 4}?
18. If the mean of a dataset is 50 and its variance is 100, what is the coefficient of variation?
19. Which of the following statements about the mode is FALSE?
20. If the mean of a dataset is increased by 10, what happens to the median?
21. Which measure of central tendency is most affected by the presence of extreme values in a dataset?
22. The standard deviation of a dataset is 8. If each value in the dataset is divided by 2, what will be the new standard deviation?
23. If a dataset has a mean of 70 and a standard deviation of 10, and a specific data point is 90, how many standard deviations is this point away from the mean?
24. In a dataset, if the mean is 60, the median is 60, and the mode is 60, the distribution is:
25. The range of a dataset is 50. If the smallest value is 10, what is the largest value?
26. If all values in a dataset are increased by 7, how does the standard deviation change?
27. Which of the following statements is true about the median?
28. If a dataset has 15 values, and the 8th value in the ordered dataset is 45, what is the median?
29. In a dataset, the mean is 80 and the median is 75. The distribution is most likely:
30. If the variance of a dataset is 25, what is the variance of the dataset if each value is multiplied by 3?
31. Which measure of central tendency is NOT used to describe the center of a dataset?
32. If the standard deviation of a dataset is 12, what is the variance?
33. If the median of a dataset is 50 and the mode is 55, what can be inferred about the skewness?
34. If the mean of a dataset is 40, and the standard deviation is 10, what is the z-score of a data point with a value of 60?
35. If a dataset contains only one value, what is its standard deviation?
36. If a dataset is unimodal and symmetric, which of the following relationships holds?
37. Consider the dataset {2, 4, 6, 8, 10}. If each value is multiplied by 5, what is the new median?
38. If the mean of a dataset is 70 and the median is 70, and the distribution is skewed, which direction is the skewness likely towards?
39. The variance of a dataset is 36. If 4 is subtracted from each value, what is the new variance?
40. Which measure of dispersion is calculated as the average of the absolute differences between each data point and the mean?
41. If the mode of a dataset is 30, and the mean is 40, what can be inferred about the skewness?
42. Consider the dataset: {5, 10, 15, 20, 25}. If the value 25 is replaced by 100, how does the median change?
43. If the standard deviation of a dataset is doubled, what happens to the variance?
44. What is the mode of the dataset: {3, 5, 7, 5, 3, 5, 8, 9, 5}?
45. Which measure of dispersion is most robust to outliers?
46. If a dataset has mean 30 and median 30, what can be concluded about its skewness?
47. The sum of the squares of deviations of a dataset from its mean is 100, and the number of observations is 25. What is the variance?
48. If a dataset has a mode of 70 and a mean of 65, the distribution is most likely:
49. What is the median of the dataset {10, 30, 20, 50, 40}?
50. If the standard deviation of a dataset is 5, and each value is multiplied by -2, what is the new standard deviation?
51. If the variance of a dataset is 0, what is the coefficient of variation?
52. Which of the following is a measure of central tendency?
53. In a dataset, if the mean, median, and mode are all different, it indicates:
54. If the variance of a dataset is 64, what is the standard deviation?
55. Consider the dataset {1, 2, 3, 4, 5}. If 3 is removed, what happens to the median?

More quizzes

• Trigonometry – Unit Circle, Identities, Compound Angles, Solving Equations▶ Play
• Algebra – Mathematical Induction▶ Play
• Algebra – Permutations & Combinations▶ Play
• Algebra – Quadratic Equations▶ Play
• Algebra – Sequence & Series (AP, GP, Binomial Theorem)▶ Play
• Calculus – Limits & Derivatives▶ Play

Browse all Mathematics quizzes

More to play