Question

An additional observation 15 is included in a series of 11 observations and its mean remains unaffected . The mean of the series was

Answer 1

Let, mean=x

The sum of observations=11x

According to the question,

(11x+15)/12=x

x=15

Therefore, the mean of the series was 15

Answer 2

Answer:

The mean of series was 15

Step-by-step explanation:

Let the mean of series = x

Since we know,

Mean = Sum of all observations / Total Number of observations

According to question ,

15 is included in a series of 11 observations

So,

Total number of observations = 11

Putting the value in formula we get ,

Mean = Sum of all observations / 11

x = Sum of all observations / 11

Sum of all observations = 11x

Now,

15 is included so,

Sum of all observations = 11x + 15

Total number of observations will now increase by 11, that is ,

11 + 1 = 12

Mean remains the same = x

So now,

x = $\frac{11x+15}{12}$

12 x = 11x + 15

x = 15

Hence,

The mean of series was 15