Question

The mean of a set of 20 observation is 19.3. The mean is reduced by 0.5 when new observation is added to the set .find the new mean.class inter.0-5........20-25.freq.10,15,12,20,9

Answer 1

Solution :-

Two questions are given but only the first one is clear. So, I have solved the first question only.

Given -

Mean of 20 observations = 19.3 

Mean = Sum of observations/Total number of observations

⇒ 19.3 = Sum of 20 observations/20

⇒ Sum of 20 observations = 20*19.3

Sum of 20 observations = 386

When a new observation is added then the new mean decreases by 0.5

Then,

Mean of 21 observations = Sum of 21 observations/21

⇒ 19.3 - 0.5 = Sum of 20 observations + 21st observation/21

⇒ 18.8 = 386 + 21st observation/21

⇒ 386 + 21st observation = 18.8*21

⇒ 386 + 21st observation = 394.8

⇒ 21st observation = 394.8 - 386

⇒ 21st observation = 8.8

So, 21st observation is 8.8

New mean = 394.8/21

New Mean = 18.8

Answer.