The mean and standard deviation of 20 items are found to be 10 and 2 respectively. At the time of checking it was found that an item 12 was wrongly entered as 8. Calculate the correct mean and standard deviation.
Mean of 20 items 
= 10
SD of 10 items = 2
Wrong Value = 8
Correct Value = 12
To find Mean:
Formula for 
= 10 = 
Sum of all the items 
200
This value is wrong since item 12 was wrongly entered as 8.
Let 
be the corrected sum
200 + (Correct Value) - (Wrong Value)
= 200 + 12 - 8 = 204
Corrected mean will be 
= 
10.2
To find SD:
SD2 = 
4 = 
= 2080
This value is wrong since item 12 was wrongly entered as 8.
Let 
be the corrected sum of squares.
= 2080 + (Correct Value)2 - (Wrong Value)2
= 2080 + 122 - 82
= 2160
Corrected SD:
SD2 = 
SD2 = 
SD = 1.99
The corrected mean is 10.2, corrected SD is 1.99
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