Solution:
The Data set is , 87,46, 90, 78, 89.
Number of Observation = 5
Mean=[tex]\frac{\text{Sum of all the observation}}{\text{Total number of observation}}[/tex] = [tex]\frac{87 + 46+90+78+89}{5}=\frac{390}{5}= 78[/tex]
To find the Variance :
1. We have calculated mean.
2nd Step : From each Data set subtract mean in this way:
87 - 78 = 9, 46 -78 = -32, 90 - 78 = 12, 78 - 78 = 0, 89 - 78 = 11
3. Square the difference of Data and Mean.
(9)² = 81, (-32)²= 1024, (12)² = 144, 0² =0, (11)² = 121
4. Sum of all the Squared Data
81 + 1024 + 144 +0 + 121= 1370
5. Divide Sum of squared observation by 5.
We get = [tex]\frac{1370}{5} =274[/tex]
6. Variance = √274 = 16.55 (approx)
Now the value of 89 - 78 is not given .So we can't say she had made the error or not.
As we have to divide the sum of squared observations by N , not N-1.This is the first error.
