# Mean – Problems

## Mean – Problems

1. Mean of 9 observations is 100 and mean of 6 observations is 80, then the mean of 15 observations is

Solutions: 9 observations is 100

6 observations is 80

n₁ = 9 and n₂ = 6

x̄₁ = 100 and x̄₂ = 80

We know that

$$\bar{x}=\frac{{{n}_{1}}{{{\bar{x}}}_{1}}+{{n}_{2}}{{{\bar{x}}}_{2}}}{m+n}$$,

$$=\frac{9\times 100+6\times 80}{9+6}$$,

$$=\frac{1380}{15}=92$$.

2. Mean and made of the following data are respectively

 Class fᵢ 0 – 10 22 10 – 20 38 20 – 30 46 30 – 40 35 40 – 50 20

Solution:

 Class xᵢ fᵢ xᵢfᵢ 0 – 10 5 22 110 10 – 20 15 38 570 20 – 30 25 46 1150 30 – 40 35 35 1225 40 – 50 42 20 900 161 3955

Mean $$=\frac{\sum{{{f}_{i}}{{x}_{i}}}}{\sum{{{f}_{i}}}}=\frac{3955}{161}$$ = 24.56

Median = 24.26 (approximate)

Mean = 3 (median) – 2 (mean)

Mode = 3 (24.46) – 2 (24.46)

= 24.26.

3. Find the mean deviation about mean for the data in following table

 Income per Year Number of Persons 0 – 100 4 100 – 200 8 200 – 300 9 300 – 400 10 400 – 500 7 500 – 600 5 600 – 700 4 700 – 800 3

Solution:

 Income per Year Number of Persons Mid Value xᵢ $${{d}_{i}}={{A}_{i}}+\frac{\sum{{{f}_{i}}{{d}_{i}}}}{\sum{{{f}_{i}}}}\times h$$, A = 350 & h = 100 fᵢdᵢ |xᵢ – x̄| fᵢ |xᵢ – x̄| 0 – 100 4 50 -3 -12 308 1232 100 – 200 8 150 -2 -16 208 1664 200 – 300 9 250 -1 -9 108 972 300 – 400 10 350 0 0 8 80 400 – 500 7 450 1 7 92 644 500 – 600 5 550 2 10 192 960 600 – 700 4 650 3 12 292 1168 700 – 800 3 750 4 12 392 1176 ∑ fᵢ = 50 7896

Mean x̄ $$={{A}_{i}}+\frac{\sum{{{f}_{i}}{{d}_{i}}}}{\sum{{{f}_{i}}}}\times h$$,

$$=350+\frac{4}{50}\times 100=350+8$$,

x̄ = 358,

Mean deviation about the mean $$=\frac{\sum{{{f}_{i}}|{{x}_{i}}-\bar{x}|}}{\sum{{{f}_{i}}}}=\frac{7896}{50}=157.92$$.