SSC Mean, Median and Mode Questions with Solutions (Statistics)

Statistics questions on mean, median and mode are asked in SSC CGL Tier 1, Tier 2 and many other exams. The formulas are short, and the questions are easy if you sort the data and take care with even and odd numbers of values. This practice paper gives you 21 questions with answers and quick solutions.

Practice Paper at a Glance

What Are Mean, Median and Mode?

These are three ways to describe the centre of a set of data.

• Mean (average) = sum of all values / number of values.
• Median is the middle value when the data is arranged in order. For an even number of values, it is the average of the two middle values.
• Mode is the value that occurs most often. A data set can have more than one mode.
• Range = largest value - smallest value.

Formulas and Shortcut Tricks

• Mode = 3 x Median - 2 x Mean (empirical relation for moderately skewed data).
• Grouped data: mean = sum of (f x value) / sum of f.
• Weighted mean = (n1 x m1 + n2 x m2) / (n1 + n2).
• Adding a constant to every value adds the same constant to the mean and median. Multiplying every value multiplies the mean and median.
• Variance = average of the squares of the deviations from the mean. Standard deviation = square root of the variance.
• Always sort the data before finding the median.

Set 1: Basic Questions (Q1–Q7)

Q1. Find the mean of 4, 8, 12, 16 and 20.
Answer: 12
Solution: Sum = 60 and n = 5, so mean = 12.

Q2. Find the median of 7, 3, 9, 1 and 5.
Answer: 5
Solution: Sorted: 1, 3, 5, 7, 9. The middle value is 5.

Q3. Find the median of 12, 4, 8 and 6.
Answer: 7
Solution: Sorted: 4, 6, 8, 12. Median = (6 + 8) / 2 = 7.

Q4. Find the mode of 2, 3, 3, 4, 5, 3, 6, 2.
Answer: 3
Solution: The value 3 occurs three times.

Q5. Find the range of 15, 22, 9, 31 and 18.
Answer: 22
Solution: Range = 31 - 9 = 22.

Q6. The mean of 5 numbers is 20. Four of them are 18, 22, 19 and 21. Find the fifth number.
Answer: 20
Solution: Total = 100. Four numbers add up to 80, so the fifth = 20.

Q7. Find the mean of the first 10 natural numbers.
Answer: 5.5
Solution: Mean = (n + 1) / 2 = 5.5.

Set 2: Relations and Grouped Data (Q8–Q14)

Q8. If the mean is 12 and the median is 11, find the mode.
Answer: 9
Trick: Mode = 3 x 11 - 2 x 12 = 33 - 24 = 9.

Q9. If the mean is 20 and the mode is 14, find the median.
Answer: 18
Trick: Median = (Mode + 2 x Mean) / 3 = (14 + 40) / 3 = 18.

Q10. Find the median of 3, 7, 2, 9, 10 and 5.
Answer: 6
Solution: Sorted: 2, 3, 5, 7, 9, 10. Median = (5 + 7) / 2 = 6.

Q11. The mean of 5 numbers is 8. Each number is multiplied by 3 and then 2 is added. Find the new mean.
Answer: 26
Solution: New mean = 8 x 3 + 2 = 26.

Q12. The marks 10, 20 and 30 have frequencies 2, 3 and 5. Find the mean.
Answer: 23
Solution: Sum = 20 + 60 + 150 = 230 and total frequency = 10, so mean = 23.

Q13. The mean of 10 numbers is 12. If one number 22 is replaced by 32, find the new mean.
Answer: 13
Solution: The total increases by 10, so the mean increases by 1.

Q14. The mean of 5 numbers is 30. When one number is removed, the mean of the rest is 28. Find the removed number.
Answer: 38
Solution: Total = 150 and the rest = 112, so removed number = 38.

Set 3: Exam-Level Questions (Q15–Q21)

Q15. Find the median of 2, 5, 8, 11, 14, 17 and 20.
Answer: 11
Solution: There are 7 values and the 4th value is 11.

Q16. Find the mode of 5, 7, 7, 9, 9 and 10.
Answer: 7 and 9 (bimodal)
Solution: Both 7 and 9 occur twice.

Q17. The mean marks of 30 students is 60 and of 20 students is 70. Find the combined mean.
Answer: 64
Trick: (30 x 60 + 20 x 70) / 50 = 3,200 / 50 = 64.

Q18. Find the median of the first 9 odd numbers.
Answer: 9
Solution: The numbers are 1, 3, 5, ..., 17 and the 5th number is 9.

Q19. The mean of 6 numbers is 15. A seventh number 29 is added. Find the new mean.
Answer: 17
Solution: New total = 90 + 29 = 119 and 119 / 7 = 17.

Q20. Find the mean of 2, 4, 6, ..., 20.
Answer: 11
Solution: Sum = 110 and n = 10, so mean = 11.

Q21. Find the variance of 1, 2, 3, 4 and 5.
Answer: 2
Solution: Mean = 3. Squared deviations: 4, 1, 0, 1, 4 = 10, so variance = 10 / 5 = 2.

Common Mistakes in Statistics Questions

• Finding the median without sorting the data.
• Forgetting to average the two middle values for an even number of values.
• Using Mode = 3 Median - 2 Mean in the wrong order.
• Dividing by the number of groups instead of the total frequency in grouped data.
• Confusing range with the mean.
• Ignoring that a data set can have more than one mode.

How to Practice These 21 Questions

1. Memorise the four formulas and the empirical relation.
2. Practise sorting small data sets quickly.
3. Solve each set in 7 to 8 minutes.
4. Check your answers by calculating the mean again.
5. Revise the mistakes after one day.

Related Topics to Study Next

• SSC Percentage Questions with Shortcut Tricks
• SSC Simplification Questions
• Fractions and Decimals Questions
• SSC Algebra Questions

Frequently Asked Questions

What is the mean in statistics?

The mean is the sum of all values divided by the number of values. It is also called the average.

What is the median?

The median is the middle value of the data after arranging it in order. For an even count, it is the average of the two middle values.

What is the mode?

The mode is the value that occurs most often in the data.

What is the relation between mean, median and mode?

The empirical relation is Mode = 3 x Median - 2 x Mean.

How do you find the mean of grouped data?

Multiply each value by its frequency, add the products and divide by the total frequency.

What is the range of data?

The range is the difference between the largest and the smallest value.

How do you find the combined mean of two groups?

Use the weighted mean: (n1 x m1 + n2 x m2) / (n1 + n2).

What is variance and standard deviation?

Variance is the average of the squared deviations from the mean. Standard deviation is the square root of the variance.

What happens to the mean if every value is increased by 5?

The mean increases by 5. The median and mode also increase by 5.

Can a data set have no mode?

Yes. If all values occur only once, there is no mode.

How many statistics questions come in SSC exams?

One or two questions come in CGL Tier 1 and Tier 2 on mean, median, mode or related topics.

How should I prepare statistics for SSC exams?

Learn the formulas, practise sorting and grouped data questions, and solve previous year questions.