Question:
Find the mean deviation about the mean for the data
\(x_i\) 10 30 50 70 90 \(f_i\) 4 24 28 16 8
Find the mean deviation about the mean for the data
| \(x_i\) | 10 | 30 | 50 | 70 | 90 |
| \(f_i\) | 4 | 24 | 28 | 16 | 8 |
Updated On: Oct 20, 2023
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Solution and Explanation
| \(x_i\) | \(f_i\) | \(f_ix_i\) | \(|x_i-\bar{x}|\) | \(f_i|x_i-\bar{x}|\) |
| 10 | 4 | 40 | 40 | 160 |
| 30 | 24 | 720 | 20 | 480 |
| 50 | 28 | 1400 | 0 | 0 |
| 70 | 16 | 1120 | 20 | 320 |
| 90 | 8 | 720 | 40 | 320 |
| 80 | 4000 | 1280 |
\(N=\sum_{I=1}^{5}f_i=80\) \(\sum_{I=1}^{5}f_i=4000\)
∴ \(\bar{x}=\frac{1}{N}\sum_{I=1}^{5}f_ix_i=\frac{1}{80}X4000=50\)
\(MD(\bar{x})=\frac{1}{N}\sum_{i=1}^{5}f_i|x_i-\bar{x}|=\frac{1}{80}×1280= 16\)
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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