Question

If there are two groups containing 30 and 20 observations and having 50 and 60 as arithmetic means, then the combined arithmetic mean is

Answer 1

Answer:

The combined arithmetic mean = 54

Step-by-step explanation:

Given,

Mean of 30 observations = 50

Mean of 20 observations = 60

Required to find,

The combined mean of 50 observations.

We Know,

Mean = $\frac{Sum\ of\ observations}{Total\ number\ of\ observations}$

Since the mean of 30 observations is  50.

Then we have, 50 = $\frac{Sum \ of\ observations}{30}$

Sum of 30 Observations = 50 x 30 = 1500

Again since the mean of 20 observations is 60.

Then we have, 60 = $\frac{Sum \ of\ observations}{20}$

Sum of 20 observations = 60 x 20 = 1200

Then, the Sum of all the 50 observations = 1500 + 1200 =2700

So, the combined mean of all the 50 observations = $\frac{Sum\ of\ 50\ Observations}{50}$

= $\frac{2700}{50}$

= 54

Hence, the combined arithmetic mean = 54