Find the mean deviation about the mean for the data
Height in cms | 95-105 | 105-115 | 115-125 | 125-135 | 135-145 | 145-155 |
Number of boys | 9 | 13 | 26 | 30 | 12 | 10 |
The following table is formed.
Height in cms | Number of boys \(f_i\) | Mid-point \(x_i\) | \(f_ix_i\) | \(|x_i-\bar{x}\) | \(f_i|x_i-\bar{x}\)| |
95-105 | 9 | 100 | 900 | 25.3 | 227.7 |
100-200 | 13 | 110 | 1430 | 15.3 | 198.9 |
115-125 | 26 | 120 | 3120 | 5.3 | 137.8 |
125-135 | 30 | 130 | 3900 | 4.7 | 141 |
135-145 | 12 | 140 | 1680 | 14.7 | 176.4 |
145-155 | 10 | 150 | 1500 | 24.7 | 247 |
Here, \(\sum_{I=1}^{6}f_i=100\), \(\sum_{I=1}^{6}f_ix_i=12530\)
∴ \(\bar{x}\frac{1}{N}\frac{1}{N}\sum_{i=1}^{6}f_ix_i=\frac{1}{100}×12530=125.3\)
\(M.D.(\bar{x})=\frac{1}{N}\sum_{i=1}^{6}f_i|x_i-\bar{x}|=\frac{1}{100}×1128.8=11.28\)
Find the mean and variance for the following frequency distribution.
Classes | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 |
Frequencies | 5 | 8 | 15 | 16 | 6 |
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: