# Standard Deviation and Coefficient of Variation

Define standard deviation.

What is coefficient of standard deviation? Also, write its formula.

Its formula is:

Coefficient of standard deviation = $\frac{σ}{\overline{X}}$

Define coefficient of variation. Also, write its formula.

Its formula is:

CV = $\frac{\text{standard deviation}}{\text{mean}}$ × 100%

What is the meaning a low coefficient of variation?

Write the difference between standard deviation and mean deviation.

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

Write the difference between coefficient of standard deviation and the coefficient of variation.

Coefficient of standard deviation = $\frac{σ}{\overline{X}}$

Coefficient of variation = $\frac{σ}{\overline{X}}$ × 100%

In a continuous series, ∑𝑓(𝑚 - X̅)^{2} = 484, N = 24 and X̅ = 25 find the standard deviation and its coefficient.

∑𝑓(𝑚 - X̅)

^{2}= 484

N = 24

X̅ = 25

Standard deviation (σ) = ?

Coefficient of σ = ?

Now, we have,

σ = $\sqrt{\frac{∑𝑓(𝑚 - \overline{X})^2}{N}}$ = $\sqrt{\frac{484}{24}}$ = 4.49

Coefficient of σ = $\frac{σ}{\overline{X}}$ = $\frac{4.49}{25}$ = 0.179

In a continuous series ∑fd = 0, ∑fd^{2} = 848, N = 100, assumed mean (A) = 12 then find the standard deviation and its coefficient.

∑fd = 0

∑fd

^{2}= 848

N = 100

Assumed mean (A) = X̅ = 12

Standard deviation (σ) = ?

Coefficient of σ = ?

Now, we have,

σ = $\sqrt{\frac{\sum fd^2}{N} - (\frac{\sum fd}{N})^2}$ = $\sqrt{\frac{848}{100} - 0}$ = 2.91

Coefficient of σ = $\frac{σ}{\overline{X}}$ = $\frac{2.91}{12}$ = 0.24

If ∑fd'^{2} = 125, ∑fd' = -4, N = 20, C = 10, find SD (σ).

∑fd'

^{2}= 125

∑fd' = -4

N = 20

C = 10

Standard deviation (σ) = ?

Now, we have,
σ = $\sqrt{\frac{\sum fd'^2}{N} - (\frac{\sum fd'}{N})^2}$ × C
or, σ = $\sqrt{\frac{125}{20} - \frac{16}{400}}$ × 10

∴ σ = 24.92