Find the mean deviation about the mean for the given data.
\(x_i\) 5 10 15 20 25 \(f_i\) 7 4 6 3 5
Find the mean deviation about the mean for the given data.
| \(x_i\) | 5 | 10 | 15 | 20 | 25 |
| \(f_i\) | 7 | 4 | 6 | 3 | 5 |
Solution and Explanation
| \(x_i\) | \(f_i\) | \(f_ix_i\) | \(|x_i-\bar{x}|\) | \(f_i|x_i-\bar{x}|\) |
| 5 | 7 | 35 | 9 | 63 |
| 10 | 4 | 40 | 4 | 16 |
| 15 | 6 | 90 | 1 | 6 |
| 20 | 3 | 60 | 6 | 18 |
| 25 | 5 | 125 | 11 | 55 |
| 25 | 350 | 158 |
\(N=\sum_{I=1}^{5}f_i=25\)
\(N=\sum_{I=1}^{5}f_ix_i=350\)
∴ \(\bar{x}=\frac{1}{N}\sum_{I=1}^{5}f_ix_i=\frac{1}{25}×350=14\)
∴ \(=MD\bar{(x)}=\frac{1}{N}\sum_{i=1}^{5}f_i|x_i-\bar{x}|=\frac{1}{25}×158=6.32\)
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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