About Statistics (Mean, Median & Mode) — Class 10 ICSE

Compute mean, median, and mode for grouped frequency distributions and draw ogives. This topic is part of the ICSE Class 10 mathematics syllabus (chapter: Chapter 8). On this page you can practice 60 questions across three difficulty levels — 20 easy, 20 medium, and 20 hard — each with a visual step-by-step solution, plus a timed 10-question mastery test with a live leaderboard. Worked examples and sample questions from the topic are below.

Statistics (Mean, Median & Mode) — solved examples for Class 10 ICSE

Practice questions on Statistics (Mean, Median & Mode)

1. Q1.easy

   The mode of the data set $\{2, 3, 5, 3, 7, 3, 8\}$ is:

   1. A)$2$
   2. B)$3$
   3. C)$5$
   4. D)$7$
   Show answer

   Answer: $3$

   Hint: Mode is the value that appears most frequently.

2. Q2.easy

   The median of the data $\{4, 7, 2, 9, 5\}$ (when arranged in order) is:

   1. A)$4$
   2. B)$5$
   3. C)$7$
   4. D)$2$
   Show answer

   Answer: $5$

   Hint: First arrange in ascending order, then pick the middle value.

3. Q3.easy

   For a grouped frequency distribution, the mean is given by:

   1. A)$\bar{x} = \frac{\sum f_i x_i}{\sum f_i}$
   2. B)$\bar{x} = \frac{\sum f_i}{\sum x_i}$
   3. C)$\bar{x} = \sum f_i x_i$
   4. D)$\bar{x} = \frac{\sum x_i}{n}$
   Show answer

   Answer: $\bar{x} = \frac{\sum f_i x_i}{\sum f_i}$

   Hint: Mean = (sum of all fx) / (sum of all frequencies).

4. Q4.medium

   Find the mode of the following distribution:
   
   | Class | $10-20$ | $20-30$ | $30-40$ | $40-50$ | $50-60$ |
   |---|---|---|---|---|---|
   | $f$ | $5$ | $8$ | $12$ | $6$ | $4$ |
   
   Using the mode formula: $l + \frac{f_1 - f_0}{2f_1 - f_0 - f_2} \times h$

   1. A)$33.33$
   2. B)$34.17$
   3. C)$35$
   4. D)$36.25$
   Show answer

   Answer: $34.17$

   Hint: Modal class has highest frequency. Identify $f_0$, $f_1$, $f_2$ and use the formula.

5. Q5.medium

   Find the median from the following cumulative frequency distribution:
   
   | Less than | $10$ | $20$ | $30$ | $40$ | $50$ |
   |---|---|---|---|---|---|
   | cf | $3$ | $12$ | $27$ | $37$ | $40$ |
   

   1. A)$25$
   2. B)$26.67$
   3. C)$27.78$
   4. D)$28.5$
   Show answer

   Answer: $26.67$

   Hint: First find $\frac{n}{2}$, identify the median class, then apply the median formula.

6. Q6.medium

   Using the step deviation method with $A = 35$ and $h = 10$, find the mean of:
   
   | Class | $10-20$ | $20-30$ | $30-40$ | $40-50$ | $50-60$ |
   |---|---|---|---|---|---|
   | $f_i$ | $4$ | $8$ | $10$ | $12$ | $6$ |

   1. A)$35.5$
   2. B)$36$
   3. C)$37$
   4. D)$37.5$
   Show answer

   Answer: $37$

   Hint: Find $u_i = \frac{x_i - A}{h}$, then $\bar{x} = A + h \times \frac{\sum f_i u_i}{\sum f_i}$.

7. Q7.hard

   Three groups of students have means $40$, $50$, and $60$ with $20$, $30$, and $50$ students respectively. The combined mean of all $100$ students is:

   1. A)$50$
   2. B)$51$
   3. C)$52$
   4. D)$53$
   Show answer

   Answer: $52$

   Hint: Combined mean = (n1*mean1 + n2*mean2 + n3*mean3) / (n1 + n2 + n3).

8. Q8.hard

   In a distribution, the mean is $45$, variance is $100$. If each observation is first multiplied by $2$ and then $5$ is added, what is the new mean and variance?

   1. A)Mean $= 95$, Variance $= 400$
   2. B)Mean $= 95$, Variance $= 200$
   3. C)Mean $= 90$, Variance $= 400$
   4. D)Mean $= 95$, Variance $= 100$
   Show answer

   Answer: Mean $= 95$, Variance $= 400$

   Hint: If $y = ax + b$, then $\bar{y} = a\bar{x} + b$ and $\text{Var}(y) = a^2 \text{Var}(x)$.

9. Q9.hard

   The median of the following data is $32$. Find $x$ and $y$ if total frequency is $100$.
   
   | Class | $0-10$ | $10-20$ | $20-30$ | $30-40$ | $40-50$ | $50-60$ |
   |---|---|---|---|---|---|---|
   | $f$ | $10$ | $x$ | $25$ | $30$ | $y$ | $10$ |

   1. A)$x=9, y=16$
   2. B)$x=12, y=13$
   3. C)$x=15, y=10$
   4. D)$x=8, y=17$
   Show answer

   Answer: $x=9, y=16$

   Hint: Use two conditions: total frequency = 100, and median = 32 gives an equation from the median formula.

These are 9 of the 60 questions available for Statistics (Mean, Median & Mode). Start practicing above to unlock visual solutions, AI coaching, and the topic leaderboard — completely free.