# Mean Deviation

Define 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.

What do you mean by coefficient of mean 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.

Write the formula to find the mean deviation and its coefficient from the mean.

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 = $\frac{\text{M.D. from mean}}{\text{Mean}}$

Write the formula to calculate mean deviation and its coefficient from median.

The formula to find the mean deviation (MD) from median is:
MD = $\frac{\sum f \vert D \vert}{N}$
Where, D = m - Md; Md = 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 = $\frac{\text{M.D. from median}}{\text{Median}}$

What are the methods to find the mean deviation and its coefficient? Which one is the best? Write with reason.

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.

In a continuous series, ∑fm = 1000, N = 50 and ∑f|𝑚 - X̅| = 308 then find the mean deviation from mean and its coefficient.

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

In a continuous series,∑f|𝑚 - X̅| = 680, mean deviation (MD) = 17 find ∑f.

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.

In a continuous series, median (Md) = 40, ∑f = 50 and ∑f|m - Md| = 530 then find the mean deviation from median and its coefficient.

Here,
∑f|m - Md| = 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

In a continuous series, coefficient of mean deviation is 0.5 and median = 40 then find the mean deviation (MD).

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