Question

"A clerk calculated arithmetic mean of 50
values as 39.2. However, it was found that
instead of taking two values as 25 and 32,
he took them as 52 and 23. Find the
corrected arithmetic mean."​

Answer 1

Given:-

→Arithmetic mean of the obsevations

(incorrect) = 39.2

→Number of observations = 50

→Incorrect values = 52, 23

→Correct values = 25, 32

To find:-

→Correct arithmetic mean

Solution:-

Firstly, let's calculate the sum of observations (incorrect).

Let the incorrect sum be x.

Mean:-

Sum of observations/No of observations

=> x/50 = 39.2

=> x = 50(39.2)

=> x = 1960

Hence, the incorrect sum was 1960.

So, the correct sum will be:-

= 1960-52+25-23+32

= 1942

Thus, correct sum is 1942.

Now, correct mean:-

= 1942/50

= 38.84

Thus, the correct arithmetic mean

is 38.84.

Answer 2

Answer:

38.84..........................