Question

Arithmetic mean of 15 observations was calculated as 85. In doing so an observation
was wrongly taken as 73 for 28. What would be correct mean?​

Answer 1

Answer:

No of observations=15

Arithematic mean=85

Sum of observations/No of observations =85

Sum of observations/15=85

Sum of observations =15×85

Sum of observations =1275

New sum of observations =1275-73+28=1230

New arithematic mean=New sum of observations/No of observations =1230/15=82

Answer 2

The corrected mean is 82

Step-by-step explanation:

• Given that Arithmetic mean of 15 observations was calculated as 85
• That is Arithmetic mean=85 and No. of observations=15
• $Arithmetic mean=\frac{Sum of observations}{No. of observations}=85$
• $\frac{Sum of observations}{15}=85$

• $Sum of observations=15\times 85$

Therefore $Sum of observations=1275$

• For  an observation  was wrongly taken as 73 for 28.
• So that the New sum of observations=1275-73+28

Therefore New sum of observations=1230

• $New arithmetic mean=\frac{New sum of observations}{No. of observations}$
• $=\frac{1230}{15}$
• $=82$
• Therefore $New arithmetic mean=82$.

Therefore the corrected mean is 82