Mean Deviation

Mean deviation is defined as the average of the absolute values of the deviation of each item from mean, median or mode. It is also known as average deviation.

Mean deviation is an absolute measure. So to compare two or more series having different units, the relative measure corresponding to mean deviation is used, which is called the coefficient of mean deviation.

The formula to find the mean deviation (MD) from mean is:
MD = $\frac{\sum f \vert D \vert}{N}$
Where, D = m - X̅; X̅ = mean of the class, m = mid value
f = frequency of the corresponding term, N = $\sum f$ = total of the frequency

The formula to calculate coefficient of mean deviation from mean is:
Coefficient of mean deviation = $\frac{\text{M.D. from mean}}{\text{Mean}}$

The formula to find the mean deviation (MD) from median is:
MD = $\frac{\sum f \vert D \vert}{N}$
Where, D = m - M_d; M_d = median value of the class, m = mid value
f = frequency of the corresponding term, N = $\sum f$ = total of the frequency

The formula to calculate coefficient of mean deviation from median is:
Coefficient of mean deviation = $\frac{\text{M.D. from median}}{\text{Median}}$

Mean deviation and its coefficient can be calculated from mean and median.
Calculation from mean is best because median doesn't depend on all the values in the dataset, its value is just the middle value of the dataset but mean is the average value of dataset.

Here,
∑fm = 1000
N = 50
∑f|𝑚 - X̅| = 308
Mean deviation(MD) = ?
Coefficient of mean deviation = ?

Now, We have,
MD = $\frac{\sum f \vert 𝑚 \, - \, \overline{X} \vert}{N}$ = $\frac{308}{50}$ = 6.16

Mean = $\frac{∑fm}{N}$ = $\frac{1000}{50}$ = 20

Coefficient of MD = $\frac{\text{M.D. from mean}}{\text{Mean}}$ = $\frac{6.16}{20}$ = 0.31

Here,
∑f|𝑚 - X̅| = 680
Mean deviation (MD) = 17
N = ∑f = ?

Now, We have, MD = $\frac{\sum f \vert 𝑚 \, - \, \overline{X} \vert}{N}$ or, 17 = $\frac{680}{N}$
∴ N = ∑f = 40.

Here,
∑f|m - M_d| = 530
Median (Md) = 40
∑f = N = 50
Mean deviation from median (MD) = ?
Coefficient of mean deviation = ?

Now, We have,
MD = $\frac{\sum f \vert 𝑚 \, - \, M_d \vert}{N}$ = $\frac{530}{50}$ = 10.6

Coefficient of MD = $\frac{\text{M.D. from median}}{\text{Median}}$ = $\frac{10.6}{40}$ = 0.265

Here,
Coefficient of mean deviation = 0.5
Median = 40
Mean deviation (MD) = ?

Now, We have, Coefficient of MD = $\frac{\text{MD}}{\text{Median}}$ or, 0.5 = $\frac{MD}{40}$
∴ Median deviation = 20