Question:
The average weight of $25$ boys was calculated to be $78.4\, kg$. It was later discovered that one weight was misread as $69$ kg instead of $96 \,kg$. The correct average is
The average weight of $25$ boys was calculated to be $78.4\, kg$. It was later discovered that one weight was misread as $69$ kg instead of $96 \,kg$. The correct average is
Updated On: Jun 23, 2023
- $79\, kg$
- $79.48 \,kg$
- $81.32 \,kg$
- $80.04 \,kg$
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The Correct Option is B
Solution and Explanation
Incorrect sum of all items $= 78.4 \times 25 = 1960\, kg$
$\therefore$ Correct sum $= 1960 - 69 + 96 = 1987 \,kg$
$\therefore$ Correct average $= \frac{1987}{25} = 79.48\,kg$.
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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