Question:
The mean of $ 100 $ items was $ 60 $ . Later it was found that two items were misread as $ 69 $ and $ 96 $ instead of $ 66 $ and $ 99 $ respectively. The correct mean of the $ 100 $ items is
The mean of $ 100 $ items was $ 60 $ . Later it was found that two items were misread as $ 69 $ and $ 96 $ instead of $ 66 $ and $ 99 $ respectively. The correct mean of the $ 100 $ items is
Updated On: Jun 23, 2024
- $ 60 $
- $ 61 $
- $ 60.5 $
- $ 61.5 $
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The Correct Option is A
Solution and Explanation
Incorrect mean $= 60$,
Incorrect sum $= 6000$
$\therefore$ Correct sum $= 6000 -69 - 96 + 66 + 99$
$ = 6000$
$\therefore $ Correct mean $= \frac{6000}{100} =60$
Incorrect sum $= 6000$
$\therefore$ Correct sum $= 6000 -69 - 96 + 66 + 99$
$ = 6000$
$\therefore $ Correct mean $= \frac{6000}{100} =60$
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Concepts Used:
Mean Deviation
A statistical measure that is used to calculate the average deviation from the mean value of the given data set is called the mean deviation.
The Formula for Mean Deviation:
The mean deviation for the given data set is calculated as:
Mean Deviation = [Σ |X – µ|]/N
Where,
- Σ represents the addition of values
- X represents each value in the data set
- µ represents the mean of the data set
- N represents the number of data values
Grouping of data is very much possible in two ways:
- Discrete Frequency Distribution
- Continuous Frequency Distribution