**Selina Concise Class 9 Maths Chapter 19 ****Mean and Median**** Exercise 19B Solutions**

**EXERCISE – 19B**

**(1) Find the median of:**

**(i) 25, 16, 26, 16, 32, 31, 19, 28 and 35**

**Solution:**

First we will arrange given numbers in ascending order

16, 16, 19, 25, 26, 28, 31, 32 and 35

Total numbers are 9.

And 9 is the odd number

∴ n = 9 (odd)

So, we will use the formula,

M = (n +1/2)^{th} term

= (9 + 1/2)^{th} term

M = (10/2)^{th} term

Median = 5^{th} term.

Median = 26

**(ii) 241, 243, 347, 350, 327, 299, 261, 292, 271, 258, and 257.**

**Solution:**

First we will arrange given number in ascending order.

241, 243, 257, 258, 261, 271, 292, 299, 327, 347, 350.

Total numbers are 11 and 11 is the odd number.

∴ n = 11 (odd)

So, we will use the formula,

M = (n +1/2)^{th} term

M = (11 + 1/2)^{th} term

= (12/2)^{th} term

= 6^{th} term

Median = 271

**(iii) 63, 17, 50, 9, 25, 43, 21, 50, 14, and 34.**

**Solution:**

First we will arrange given numbers in ascending order

9, 14, 17, 21, 25, 34, 43, 50, 50, 63

Total numbers are 10 and 10 is the even number

∴ n = 10 (even)

So, we will use the formula,

M = 25 + 34/2

M = 59/2

Median = 29.5

**(iv) 233, 173, 189, 208, 194, 194, 185, 200 and 220.**

**Solution:**

First we will arrange given numbers in ascending order.

173, 185, 189, 194, 194, 200, 204, 208, 220, 223.

Total numbers are 10 and 10 is the even number.

∴ n = 10 (even)

So, we will use the formula,

Median = 194 + 200/2

Median = 394/2

Median = 197

**(2) The following data have been arranged in ascending order. If their median is 63, find the value of x.**

**34, 37, 53, 55, x, x + 2, 77, 83, 89 and 100.**

**Solution:**

The given numbers are –

34, 37, 53, 55, x, x + 2, 77, 83, 89 and 100.

Total numbers are 10 and 10 is the even number.

∴ n = 10 (even)

Now,

We will use the formula,

Median = 2x + 2/2

= 2 ( x + 1)/2

Median = x + 1

63 = x + 1

63 – 1 = x

62 = x

∴ x = 62

**(3) In 10 numbers, arranged in increasing order, the 7 ^{th} number is increased by 8, how much will the median be changed?**

**Solution:**

Let 10 numbers are –

X_{1}, x_{2}, x_{3}, ——— x_{10}

The 7^{th} number is increased by 8.

X_{1}, x_{2}, x_{3}, ———– (x_{7} + 8), x_{8}, x_{9}, x_{10}.

Median = x5 + x6/ 2

∴ Median remains Same.

Median will not changed.

**(4) out of 10 students, who ****appears ****in a test, three secured less than 30 marks and 3 secured more than 75 marks, The marks secured by the remaining 4 Students are 35, 48, 66 and 40. Find the median score of the whole group.**

**Solution:**

Let, The 10 students are

X_{1}, x_{2}, x_{3}, x_{4}, x_{5}, x_{6}, x_{7}, x_{8}, x_{9} and x_{10}.

∴ The three students Secured less than 30 marks

X_{1}, x_{2}, x_{3} = 30.

∴ The 3 Students secured more than 75 marks.

X_{8}, x_{9}, x_{10} = 75.

And remaining 4 students Secured 35, 48, 66 and 40 marks.

X_{4}, x_{5}, x_{6}, x_{7} = 35, 48, 66, and 40.

∴ n = 10 (even)

Now,

Median = 40 + 48/2

= 88/2

Median = 44

**(5) The median of observations 10, 11, 13, 17, x + 5, 20, 22, 24 and 53 ( arranged in ascending order) is 18; find the value of x.**

**Solution:**

Given numbers are –

10, 11, 13, 17, x + s, 20, 22, 24 and 53.

∴ n = 9 (odd)

**Here is your solution of Selina Concise Class 9 Maths Chapter 19 Mean and Median Exercise 19B**

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