Find the mean deviation about the mean for the data 38, 70, 48, 40, 42, 55, 63, 46, 54, 44.
Find the mean deviation about the mean for the data 38, 70, 48, 40, 42, 55, 63, 46, 54, 44.
Solution and Explanation
The given data is
38, 70, 48, 40, 42, 55, 63, 46, 54, 44
Mean of the given data,
\(\bar{x}=\frac{38+70+48+40+42+55+63+46+54+44}{10}=\frac{500}{10}=50\)
The deviations of the respective observations from the mean \(\bar{x},i.e.x_i-\bar{x}\) are
12, 20, 2, 10, 8, 5, 13, 4, 4, 6
The absolute values of the deviations, i.e. \(|x_i-\bar{x}|\), are
12, 20, 2, 10, 8, 5, 13, 4, 4, 6
The required mean deviation about the mean is \(M.D(\bar{x})=\frac{\sum_{i=1}^{8}|x_i-\bar{x}|}{10}\)
\(=\frac{12+20+2+10+8+5+13+4+4+6}{10}\)
\(=\frac{84}{10}\)
\(=8.4\)
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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