Question

Mean of 20 observations was 63 but later it was found that the observations 69 was misread as 96.find the correct mean?

Answer 1

Answer:

answer 61.65

Step-by-step explanation:

20*63=1260

96-69=27

1260-27=1233

1233/20=61.65

Answer 2

Given:

The mean of 20 observations was 63. One of the terms 69 was misread as 96.

To Find:

The correct mean after correcting the term is?

Solution:

The given problem can be solved using the concept of averages.

1. Let X1, X2, X3,.., Xn be n terms. The average of the n terms is given by the formula,

=> Average = ( X1 + X2 + ... + Xn )/n,

2. In the given question,

=> Number of obersvations = 20,

=> Mean of the data = 63,

=> 63 = (X1 + X2 + .. + X20)/20,

=> X1 + X2 + .. + X20 = 1260.

3. Let the misread term be X1,

=> X1 = 96,

=> X2 + X3 + ... + X20 = 1260 - 96,

=> X2 + X3 + ... + X20 = 1164,

4. Now update the value of X1 as 69,

=> X2 + X3 + ... + X20 = 1174,

=> X1 + X2 + X3 + ... + X20 = 1164 + 69,

=> X1 + X2 + X3 + ... + X20 = 1233.

5. The Correct mean is,

=> Mean = ( X1 + X2 + X3 + ... + X20 )/20,

=> Mean = 1233/20,

=> Mean = 61.65

Therefore, the correct mean of the given data is 61.65