Question

The second of the two samples has 50 items with mean 15. if the whole group has 150 items with mean 16, find the mean of first sample?

Answer 1

Given :

No of items in 2nd sample = 50

Mean of 2nd sample = 15

Total no of items = 150

To Find :

Mean of 1st sample = ?

Solution :

No of items in 1st sample = 150 - 50 = 100

Let mean of 1st sample be = x

So , the sum of 1st sample will be :

$S_1 = 100 \times x$

And the sum of 2nd sample will be :

$S_2 = 50 \times 150$

Now the mean of the two samples will be given as :

$M_{tot} = \frac{S_1+S_2}{150}$

Or, $16 = \frac{100x + 15 \times 50}{150}$

Or, $16 \times 15 = 10x + 15 \times 5$

Or, $16 \times 3 = 2x + 15$

Or, $2x = 48 - 15$

Or, $x = \frac{33}{2}$

So, x =16 . 5

Hence , the mean of 1st sample is 16 .5