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

**Exercise 19C**

**(1) Find the mean of 8, 12, 16, 22 and 4. Find the resulting if each of the observations. given above be:**

**(i) multiplied by 3**

**(ii) Divided by 2**

**(iii) multiplied by 3 and then divides by 2**

**(iv) Increased by 25%**

**(v) Decreased by 40%**

**Solution:**

Given numbers are-

8, 12, 16, 22, 10 and 4.

Mean x̄ = 8 + 12 + 16 + 22 + 10 + 4/6

= 72/6

x̄ = 12

(i) New mean x̄ = 12 × 3 = 36

(ii) New mean x̄ = 12/2

x̄ = 6

(iii) New mean x̄ = 12 × 3/2

= 36 / 2

x̄ = 18

(iv) New mean x̄ = 12 + 12 × 25/100

= 12 + 12 × 1/4

= 12 + 3

x̄ = 15

(v) New mean x̄ = 12 – 12 × 40 / 100

= 12 – 12 × 2/ 5

= 12 – 24/ 5

= 60 – 24/ 5

= 36/5

x̄ = 7.2

**(2) The mean of 18, 24, 15, 2x + 2 and 12 is 21. Find the value of x.**

**Solution:**

Given numbers are –

18, 24, 15, 2x + 1 and 12.

21 × 5 = 70 + 2x

105 = 70 + 2x

105 – 70 = 2x

35 = 2x

35/2 = x

17.5 = x

**(3) The mean of 6 numbers is 42. If one number is excluded, the mean of remaining number is 45. Find the excluded number.**

**Solution:**

Let the 6 numbers are –

X_{1}, x_{2}, x_{3}, x_{4}, x_{5}, and, x_{6}.

X_{1} + x_{2} + x_{3} + x_{4} + x_{5} + x_{6}/6 = 42

X_{1} + x_{2} + x_{3} + x_{4} + x_{5} + x_{6} = 42 × 6

X_{1} + x_{2} + x_{3} + x_{4} + x_{5} + x_{6 }= 252 —-(i)

Now,

If one number is excluded, the mean of remaining number is 45.

X_{1 }+ x_{2} + x_{3} + x_{4} + x_{5}/5 = 45

X_{1 }+ x_{2} + x_{3} + x_{4} + x_{5} = 45 × 5

X_{1} + x_{2} + x_{3} + x_{4} + x_{5} = 225 —– (ii)

from equation (i) and (ii),

(x_{1} + x_{2} + x_{3} + x_{4} + x_{5}) + x_{6} = 252

225 + x_{6} = 252

X_{6} = 252 – 225

X_{6} = 27

**∴ **The excluded number x_{6 }= 27.

**(4) The mean of 10 numbers is 24. If one more number is included the new mean is 25. Find the included number.**

**Solution:**

Given: The mean of 10 numbers is 24.

x̄_{10} = 24

x_{1} + x_{2} + ——- + x_{10}/ 10 = 24

x_{1} + x_{2} + ——- + x_{10} = 24 × 10

x_{1} + x_{2} + —- + x_{10} = 240 — (i)

Also,

If one more number is included the new mean is 25.

x̄_{11} = 25

x_{1} + x_{2} + x_{3} + ——— + x_{10} + x_{11} / 11 = 25

x_{1} + x_{2} + x_{3} + ———- + x_{10} + x_{11} = 25 × 11

x_{1} + x_{2} + x_{3} + ———- + x_{10} + x_{11} = 275 —- (ii)

from equation (i) and (ii),

(x_{1} + x_{2} + ——– + x_{10}) + x_{11} = 275

240 + x_{11} = 275

x_{11} = 275 – 240

x_{11} = 35

**∴ **The included number is x_{11} = 35.

**(5) The following observations have been arranged in ascending order. If the median of the data is 78, find the value of x.**

44, 47, 63 65, x + 13, 87, 93, 99, 110

N = 9 (odd)

78 = x + 13

78 – 13 = x

65 = x

**∴ **x = 65

**∴ **The value of x = 65.