Question

The average of 8 observations was 25.5. it was noticed later that two of those observations were wrongly taken. one observation was 14 more than the original value and the other observation was wrongly taken as 31 instead of 13. what will be the correct average of those 8 observations ?

Answer 1

Answer:   ((21.5))

Step-by-step explanation:

total value: 8* 25.5 = 204.

one observation was 14 more : 204 - 14 = 190

another was 31 instead of 13 so (31-13=18).

so minus 18 :  190 - 18 = 172.

the correct avg is :   172/8 = 21.5

Answer 2

Correct average of those 8 observations is 21.5 if The average of 8 observations was 25.5 and one observation was 14 more than the original value and the other observation was wrongly taken as 31 instead of 13.

Given:

• The average of 8 observations was 25.5
• Two of those observations were wrongly taken.
• one observation was 14 more than the original value
• other observation was wrongly taken as 31 instead of 13

To Find:

• The correct average of those 8 observations

Solution:

• $\text{Mean}=\dfrac{\text{sum of all the obervations}}{\text{number of the observations}}$

Step 1:

Find sum of all the observation

Sum =Average * Number of observations

=> Sum = 25.5 * 8

=> Sum = 204

Step 2:

Assume that original value = x which was observed 14 more

Hence observed value = x + 14

Step 3:

Find the correct sum by Subtracting wrong observed values and adding original value

Correct Sum = 204 - (x + 14 + 31)  + (x + 13)

= 172

Step 4:

Find correct average

172/8

= 21.5

correct average of those 8 observations is 21.5