Question

describe the skewness and kurtosis with the distribution graph.
X (income)	No. of persons (F)
200	24
250	26
180	16
300	20
350	6
280	30

Answer 1

X (income)	No. of persons (F)	x*F	$(x-\bar{x})^2F$	$(x-\bar{x})^3F$	$(x-\bar{x})^4F$
200	24	4800	63593	-3273487.5	168504108.3
250	26	6500	56.598	-83.504787	123.2037837
180	16	2880	81740	-5842381.9	417586643.9
300	20	6000	47093	2285154.8	110886199.8
350	6	2100	58243	5738325.3	565366144.5
280	30	8400	24410	696272.9	19860899.23
Total	122	30680	275134.4	-396199.9463	1282204119
Average=	$\bar{x}=$	251.48	8.9679	-1.4400232	-3236.255

$m_2=\frac{1}{N}\sum (x-\bar{x})^2F=8.9679\\\\ m_3=\frac{1}{N}\sum (x-\bar{x})^3F=-1.4400232\\\\ m_4=\frac{1}{N}\sum (x-\bar{x})^4F=-3236.255\\\\ Measure~of~skewness=\gamma_1=\frac{m_3}{m_2^{3/2}}=-0.0536\approx 0.\\\\ Hence~the~distribution~is~almost~symmetric.\\\\ Measure~of~kurtosis=\gamma_2=\frac{m_4}{m_2^2}-3=-43.2403<0\\\\ Hence~it~is~platykurtic.$

35 30 25 20 Frequency 15 10 5 0 200 250 180 300 350 280 Income