Find the mean deviation about median for the following data
Marks | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 |
Number of Girls | 6 | 8 | 14 | 16 | 4 | 2 |
The following table is formed.
Marks | Number of boys \(f_i\) | Cumulative frequency \(c.f\) | Mid point \(x_i\) | \(|x_i-Med.|\) | \(f_i|x_i-Med.|\) |
0-10 | 6 | 6 | 5 | 22.85 | 137.1 |
10-20 | 8 | 14 | 15 | 12.85 | 102.8 |
20-30 | 14 | 28 | 25 | 2.85 | 39.9 |
30-40 | 16 | 44 | 35 | 7.15 | 114.4 |
40-50 | 4 | 48 | 45 | 17.15 | 68.6 |
50-60 | 2 | 50 | 55 | 27.15 | 54.3 |
- | 50 | - | - | - | 517.1 |
The class interval containing the \((\frac{N}{2})^{th}\) or 25th item is 20 – 30.
Therefore, 20 – 30 is the median class.
It is known that,
Median= \(I+\frac{\frac{N}{2}-c}{f}h\)
Here, l = 20, C = 14, f = 14, h = 10, and N = 50
∴ Median \(=20+\frac{25-14}{14}×10=20+\frac{110}{14}=20+7.85=27.85\)
Thus, mean deviation about the median is given by,
\(M.D.(M)=\frac{1}{N}\sum_{i=1}^{6}f_i|x_i-M|=\frac{1}{50}×517.1=10.34\)
take on sth: | to begin to have a particular quality or appearance; to assume sth |
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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 mean deviation for the given data set is calculated as:
Mean Deviation = [Σ |X – µ|]/N
Where,
Grouping of data is very much possible in two ways: