Descriptive Statistics Practice Questions

Last Updated : 6 Jul, 2026

Descriptive Statistics is the branch of statistics that focuses on collecting, organizing, summarizing, and presenting data in a meaningful way.

Example 1: Calculate the Mean, Median, and Mode for the following series: {4, 8, 9, 10, 6, 12, 14, 4, 5, 3, 4}
Solution:

First, we are going to calculate the mean.

Mean = ÎĢx / n
= (4 + 8 + 9 + 10 + 6 + 12 + 14 + 4 + 5 + 3 + 4)/11
= 79 / 11
= 7.1818

Thus, the Mean is 7.1818.

Now, we are going to calculate the median.

Arrange the provided data collection in ascending order: 3, 4, 4, 4, 5, 6, 8, 9, 10, 12, 14

Median = [(n + 1) / 2]th term

= [(11 + 1) / 2]th term
= 6th term
= 6
Thus, the median is 6.

Now, we are going to calculate the mode.

Mode = The most repeated observation in the dataset
= 4

Thus, the mode is 4.

Example 2: Calculate the Range for the following series: {4, 8, 9, 10, 6, 12, 14, 4, 5, 3, 4}
Solution:

Arrange the provided data series in ascending order: 3, 4, 4, 4, 5, 6, 8, 9, 10, 12, 14
Range = H - L
= 14 - 3
= 11

So, the range is 11.

Example 3: Calculate the standard deviation and variance of the following data: {12, 24, 36, 48, 10, 18}
Solution:

First we are going to compute standard deviation. For standard deviation calculate the mean, deviation from mean and squared deviation.

Series

Deviation from Mean

Squared Deviation

12

12-24.66 = -12.66

160.28

24

24-24.66 = -0.66

0.436

36

36-24.66 = 11.34

128.595

48

48-24.66 = 23.34

544.76

10

10-24.66 = -14.66

214.92

18

18-24.66 = -6.66

44.36

Mean = 148/6 = 24.66

sum = 0

Sum = 1093.351

Dividing squared deviation with N-1 => 1093.351 / 5 = 218.67

√(218.67) = 14.79
So, the standard deviation is 14.79.

Now we are going to calculate the variance.
s = 14.79
s2 = 218.744

So, the variance is 218.744

Practice Problem Based on Descriptive Statistics

Question 1. What is the mean of the data set {4, 8, 9, 10, 6, 12, 14, 4, 5, 3, 4}?
Question 2. What is the median of the data set {4, 8, 9, 10, 6, 12, 14, 4, 5, 3, 4}?
Question 3. What is the mode of the data set {4, 8, 9, 10, 6, 12, 14, 4, 5, 3, 4}?
Question 4. What is the range of the data set {4, 8, 9, 10, 6, 12, 14, 4, 5, 3, 4}?
Question 5. What is the standard deviation of the data set {12, 24, 36, 48, 10, 18}?
Question 6. What is the variance of the data set {12, 24, 36, 48, 10, 18}?
Question 7. What is the quartile deviation formula in descriptive statistics?
Question 8. Write the formula that shows the relationship between the mean, median, and mode in a normal distribution.

Answer:-

  1. 7.18
  2. 6
  3. 4
  4. 11
  5. 14.79
  6. 218.74
  7. (Q3 - Q1 ) / 2
  8. Mean - Mode = 3(Mean - Median)
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