Question

calulate karl Pearson coefficients of skewner for a frequency distribution having mean 50,mode 56 and standard deviation = 15​

Answer 1

$\begin{gathered}\begin{gathered}\bf Given -  \begin{cases} &\rm{mean \: = \: 50} \\ &\rm{mode \: = \: 56}\\ &\rm{standard \: deviation \: = \: 15} \end{cases}\end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}\bf  To \:  Find :-  \begin{cases} &\rm{Karl \: Person \: Coefficient \: of \: Skewness}  \end{cases}\end{gathered}\end{gathered}$

$\large\underline\purple{\bold{Solution :- }}$

We know,

The Karl Person Coefficient of Skewness is given by

$\rm : \implies \: \boxed{ \pink{ \rm \: S_k = \dfrac{mean - mode}{standard \: deviation} }}$

$\rm : \implies \: S_k \: = \: \dfrac{50 - 56}{15}$

$\rm: \implies \: S_k \: = - \dfrac{6}{15}$

$\rm: \implies \: S_k \: = - \: 0.4$

Explore more :-

• The direction of skewness is given by the sign.
• The coefficient compares the sample distribution with a normal distribution.
• The larger the value, the larger the distribution differs from a normal distribution.
• A value of zero means no skewness at all.
• A large negative value means the distribution is negatively skewed.
• A large positive value means the distribution is positively skewed.

Answer 2

Answer:

Given−

⎩

⎪

⎪

⎨

⎪

⎪

⎧

mean=50

mode=56

standarddeviation=15

\begin{gathered}\begin{gathered}\bf To \: Find :- \begin{cases} &\rm{Karl \: Person \: Coefficient \: of \: Skewness} \end{cases}\end{gathered}\end{gathered}

To Find:− {

KarlPersonCoefficientofSkewness

\large\underline\purple{\bold{Solution :- }}

Solution:−

We know,

The Karl Person Coefficient of Skewness is given by

\rm : \implies \: \boxed{ \pink{ \rm \: S_k = \dfrac{mean - mode}{standard \: deviation} }}:⟹

S

k

=

standarddeviation

mean−mode

\rm : \implies \: S_k \: = \: \dfrac{50 - 56}{15}:⟹S

k

=

15

50−56

\rm: \implies \: S_k \: = - \dfrac{6}{15}:⟹S

k

=−

15

6

\rm: \implies \: S_k \: = - \: 0.4:⟹S

k

=−0.4

Explore more :-

The direction of skewness is given by the sign.

The coefficient compares the sample distribution with a normal distribution.

The larger the value, the larger the distribution differs from a normal distribution.

A value of zero means no skewness at all.

A large negative value means the distribution is negatively skewed.

A large positive value means the distribution is positively skewed