Question

If there are two groups with 50 observations each and with 25 and 35 as
values of their arithmetic mean, the combined arithmetic mean of 100
observations is​

Answer 1

Step-by-step explanation:

Arithmetic mean of 12 observations is 15.

Thus, sum of 12 observations = 180

After removing 25 and 20 from the series, sum of 10 observations = 180−25−20=135

Thus, mean =

number

sum

=

10

135

=13.5

Answer 2

The combined arithmetic mean of 100 observations is 30

Given :

There are two groups with 50 observations each and with 25 and 35 as values of their arithmetic mean

To find :

The combined arithmetic mean of 100 observations

Solution :

Step 1 of 3 :

Find sum of the first 50 observations

Here it is given that the Arithmetic mean of 50 observations is 25

So sum of first 50 observations

= 50 × 25

= 1250

Step 2 of 3 :

Find sum of the last 50 observations

Here it is given that the Arithmetic mean of 50 observations is 35

So sum of last 50 observations

= 50 × 35

= 1750

Step 3 of 3 :

Find combined arithmetic mean of 100 observations

Sum of combined 100 observations

= 1250 + 1750

= 3000

Hence the required arithmetic mean

$\displaystyle \sf{ = \frac{3000}{100} }$

$\displaystyle \sf{ = 30}$

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