# Mean Deviation

Define mean deviation.

What do you mean by coefficient of mean deviation?

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

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.

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 = $\frac{\text{M.D. from median}}{\text{Median}}$

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

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.

∑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.

∑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 - M_{d}| = 530 then find the mean deviation from median and its coefficient.

∑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

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

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