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

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 –

X₁, x₂, x₃, x₄, x₅, and, x₆.

X₁ + x₂ + x₃ + x₄ + x₅ + x₆/6 = 42

X₁ + x₂ + x₃ + x₄ + x₅ + x₆ = 42 × 6

X₁ + x₂ + x₃ + x₄ + x₅ + x₆ = 252 —-(i)

Now,

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

X₁ + x₂ + x₃ + x₄ + x₅/5 = 45

X₁ + x₂ + x₃ + x₄ + x₅ = 45 × 5

X₁ + x₂ + x₃ + x₄ + x₅ = 225 —– (ii)

from equation (i) and (ii),

(x₁ + x₂ + x₃ + x₄ + x₅) + x₆ = 252

225 + x₆ = 252

X₆ = 252 – 225

X₆ = 27

∴ The excluded number x₆ = 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.

x̄₁₀ = 24

x₁ + x₂ + ——- + x₁₀/ 10 = 24

x₁ + x₂ + ——- + x₁₀ = 24 × 10

x₁ + x₂ + —- + x₁₀ = 240 — (i)

Also,

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

x̄₁₁ = 25

x₁ + x₂ + x₃ + ——— + x₁₀ + x₁₁ / 11 = 25

x₁ + x₂ + x₃ + ———- + x₁₀ + x₁₁ = 25 × 11

x₁ + x₂ + x₃ + ———- + x₁₀ + x₁₁ = 275 —- (ii)

from equation (i) and (ii),

(x₁ + x₂ + ——– + x₁₀) + x₁₁ = 275

240 + x₁₁ = 275

x₁₁ = 275 – 240

x₁₁ = 35

∴ The included number is x₁₁ = 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.