The first of the two samples in a group has 100 items with mean 15 and standard deviation …

Question

The first of the two samples in a group has 100 items with mean 15 and standard deviation 3. If the whole group has 250 items with mean 15.6 and standard deviation $\sqrt{13.44}$, then the standard deviation of the second sample is

Accepted Answer

n1 = 100

m = 250

$$\overline X $$1 = 15

$$\overline X $$ = 15.6

V1(x) = 9

Var(x) = 13.44

$${\sigma ^2} = {{{n_1}\sigma _1^2 + {n_2}\sigma _2^2} \over {{n_1} + {n_2}}} + {{{n_1}{n_2}} \over {{{({n_1} + {n_2})}^2}}}{({\overline x _1} - {\overline x _2})^2}$$

n2 = 150, $${\overline x _2}$$ = 16, V2(x) = $$\sigma$$2

$$13.44 = {{100 \times 9 + 150 \times \sigma _2^2} \over {250}} + {{100 \times 150} \over {{{(250)}^2}}} \times 1$$

$$\Rightarrow$$ $${\sigma _2}^2$$ = 16 $$\Rightarrow$$ $$\sigma$$2 = 4

Solutions · 1