Question

the mean of 40 observations of a data was calculated as 16.5 .later it was noted that the value 20.4 was only read as 16.4 .Find the correct value

Answer 1

Hi there!
Here's the answer:

•°•°•°•°•°<><><<><>><><>°•°•°•°•°•

Given,
Mean of 40 Observations = 16.5

=> $\frac{Sum\: of\: Observations}{No.\: of\: Observations} = 16.5$

=> $\frac{Sum\: of\: Observations}{40} = 16.5$

=> Sum of 40 Observations = 40×16.5 = 660

Given,
An observation 20.4 was read as 16.4

Actual sum = Sum of 40 observations + Correct observation - Incorrect observation

=> Actual Sum = 660 + 20.4 - 16.4
=> Actual sum = 664

Now,

Correct Mean = $\frac{Actual\: Sum\: of\: 40\: Observations}{40}$

= $\frac{664}{40}$

= 16.6

•°•°•°•°•°<><><<><>><><>°•°•°•°•°•

Answer 2

Answer:

The correct mean = 16.6

Step-by-step explanation:

Given,

The mean of 40 observations of a data = 16.5

The value 16.4 is wrongly taken in place of 20.4

To find,

The corrected mean of the data

Solution:

Recall the formula

Mean = $\frac{Sum \ of \ observations}{Total \ number \ of \ observations}$

Since the mean of 40 observations of a data is 16.5, we have

16.5 = $\frac{Sum \ of \ observations}{40}$

Sum of observations = 16.5 × 40 = 660

Since the value 16.4 is wrongly taken in place of 20.4, the sum of observations including 20.4 and excluding 16.4 we get

Sum of observations = 660 - 16.4 +20.4

= 664

Total number of observations = 40

Mean = $\frac{Sum \ of \ observations}{Total \ number \ of \ observations}$ = $\frac{664}{40}$ = 16.6

∴ The correct mean = 16.6

#SPJ2