**Selina Concise Mathematics Class 10 ICSE Solutions Measures of Central Tendency (Mean, Median, Quartiles and Mode)**

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**Selina ICSE Solutions for Class 10 Maths Chapter 24 Measures of Central Tendency (Mean, Median, Quartiles and Mode)**

**Exercise 24(A)**

**Question 1.**

Find the mean of the following set of numbers:

(i) 6, 9, 11, 12 and 7

(ii) 11, 14, 23, 26, 10, 12, 18 and 6

**Solution:**

**Question 2.**

Marks obtained (in mathematics) by 9 student are given below:

60, 67, 52, 76, 50, 51, 74, 45 and 56

(a) find the arithmetic mean

(b) if marks of each student be increased by 4; what will be the new value of arithmetic mean.

**Solution:**

**Question 3.**

Find the mean of the natural numbers from 3 to 12.

**Solution:**

**Question 4.**

(a) Find the mean of 7, 11, 6, 5, and 6

(b) If each number given in (a) is diminished by 2, find the new value of mean.

**Solution:**

**Question 5.**

If the mean of 6, 4, 7, ‘a’ and 10 is 8. Find the value of ‘a’

**Solution:**

No. of terms = 5

Mean = 8

Sum of numbers = 8 x 5 = 40 .(i)

But, sum of numbers = 6+4+7+a+10 = 27+a ..(ii)

From (i) and (ii)

27+a = 40

a = 13

**Question 6.**

The mean of the number 6, ‘y’, 7, ‘x’ and 14 is 8. Express ‘y’ in terms of ‘x’.

**Solution:**

No. of terms = 5 and mean = 8

Sum of numbers = 5 x 8 = 40 ..(i)

but sum of numbers = 6+y+7+x+14 = 27+y+x .(ii)

from (i) and (ii)

27 + y + x = 40

x + y = 13

y = 13 – x

**Question 7.**

**Solution:**

**Question 8.**

If 69.5 is the mean of 72, 70, ‘x’, 62, 50, 71, 90, 64, 58 and 82, find the value of ‘x’.

**Solution:**

No. of terms = 10

Mean = 69.5

Sum of the numbers = 69.5 x 10 = 695 ……….(i)

But sum of numbers = 72+70+x+62+ 50+71+90+64+58+82

= 619 + x ……(ii)

from (i) and (ii)

619 + x = 695

x = 76

**Question 9.**

**Solution:**

**Question 10.**

**Solution:**

**Question 11.**

**Solution:**

**Solution 12.**

**Solution 13.**

**Solution 14.**

**Solution 15.**

**Exercise 24(B)**

**Question 1.**

**Solution:**

**Question 2.**

**Solution:**

**Question 3.**

**Solution:**

**Question 4.**

**Solution:**

**Question 5.**

**Solution:**

**Question 6.**

**Solution:**

**Question 7.**

**Solution:**

**Question 8.**

**Solution:**

**Question 9.**

**Solution:**

**Solution 10.**

**Solution 11.**

**Exercise 24(C)**

**Question 1.**

A student got the following marks in 9 questions of a question paper.

3, 5, 7, 3, 8, 0, 1, 4 and 6.

Find the median of these marks.

**Solution:**

Arranging the given data in descending order:

8, 7, 6, 5, 4, 3, 3, 1, 0

The middle term is 4 which is the 5th term.

Median = 4

**Question 2.**

The weights (in kg) of 10 students of a class are given below:

21, 28.5, 20.5, 24, 25.5, 22, 27.5, 28, 21 and 24.

Find the median of their weights.

**Solution:**

**Question 3.**

The marks obtained by 19 students of a class are given below:

27, 36, 22, 31, 25, 26, 33, 24, 37, 32, 29, 28, 36, 35, 27, 26, 32, 35 and 28. Find:

(i) median

(ii) lower quartile

(iii) upper quartile

(iv) interquartile range

**Solution:**

**Question 4.**

From the following data, find:

(i) Median

(ii) Upper quartile

(iii) Inter-quartile range

25, 10, 40, 88, 45, 60, 77, 36, 18, 95, 56, 65, 7, 0, 38 and 83

**Solution:**

**Question 5.**

**Solution:**

**Question 6.**

**Solution:**

**Question 7.**

**Solution:**

**Question 8.**

**Solution:**

**Question 9.**

**Solution:**

**Question 10.**

**Solution:**

**Question 11.**

**Solution:**

**Question 12.**

**Solution:**

**Exercise 24(D)**

**Question 1.**

Find the mode of the following data:

(i) 7, 9, 8, 7, 7, 6, 8, 10, 7 and 6

(ii) 9, 11, 8, 11, 16, 9, 11, 5, 3, 11, 17 and 8

**Solution:**

(i) Mode = 7

Since 7 occurs 4 times

(ii) Mode = 11

Since it occurs 4 times

**Question 2.**

**Solution:**

Mode is 122 cm because it occur maximum number of times. i.e. frequency is 18.

**Question 3.**

**Solution:**

**Question 4.**

**Solution:**

**Question 5.**

Find the median and mode for the set of numbers:

2, 2, 3, 5, 5, 5, 6, 8 and 9

**Solution:**

**Question 6.**

A boy scored following marks in various class tests during a term; each test being marked out of 20.

15, 17, 16, 7, 10, 12, 14, 16, 19, 12 and 16

(i) What are his modal marks?

(ii) What are his median marks?

(iii) What are his total marks?

(iv) What are his mean marks?

**Solution:**

**Question 7.**

Find the mean, median and mode of the following marks obtained by 16 students in a class test marked out of 10 marks.

0, 0, 2, 2, 3, 3, 3, 4, 5, 5, 5, 5, 6, 6, 7 and 8.

**Solution:**

**Question 8.**

**Solution:**

**Exercise 24(E)**

**Question 1.**

**Solution:**

**Question 2.**

**Solution:**

**Question 3.**

**Solution:**

**Question 4.**

The mean of 1, 7, 5, 3, 4 and 4 is m. The numbers 3, 2, 4, 2, 3, 3 and p have mean m-1 and median q. Find p and q.

**Solution:**

**Question 5.**

**Solution:**

**Question 6.**

**Solution:**

**Question 7.**

**Solution:**

**Question 8.**

The marks of 20 students in a test were as follows:

2, 6, 8, 9, 10, 11, 11, 12, 13, 13, 14, 14, 15, 15, 15, 16, 16, 18, 19 and 20.

Calculate:

(i) the mean (ii) the median (iii) the mode

**Solution:**

**Question 9.**

**Solution:**

**Question 10.**

**Solution:**

**Question 11.**

**Solution:**

**Question 12.**

For the following set of data, find the median:

10, 75, 3, 81, 17, 27, 4, 48, 12, 47, 9 and 15.

**Solution:**

**Question 13.**

**Solution:**

**Question 14.**

**Solution:**

**Question 15.**

**Solution:**

**Question 16.**

**Solution:**

**Question 17.**

**Solution:**

**Question 18.**

**Solution:**

**Question 19.**

**Solution:**

**Question 20.**

**Solution:**

**Question 21.**

**Solution:**

**Question 22.**

**Solution:**

**Solution 23.**

**Solution 24.**

**Solution 25.**

**Solution 26.**

**Solution 27.**

**Solution 28.**

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