Question

describe the skewness and kurtosis with the distribution graph.
X (income)	No. of persons	Cumulative frequency (cf)
180	16	16
200	24	40
250	26	66
280	30	96

Answer 1

X	No. Of person	Cf	Xf	(X-xbar)^2 f	(X-xbar)^3 f	(X-xbar)^4 f
180	16	16	2880	48770.3056	-2692608.6	148658919
200	24	40	4800	29753.8584	-1047633.4	36887170.4
250	26	66	6500	5687.3466	84115.8562	1244073.51
280	30	96	8400	60184.323	2695655.83	120738424
Total	96		22580	144395.834	-960470.24	307528588
$\small \bar{x}, m_{2},m_{3},m_{4}$	na	na	235.21	1504.12	-10004.898	3203422.79

Skewness,

$\small g_{1}=\frac{m_{3}}{m_{2}^{3/2}}=\frac{-10004.898}{1504.12^{3/2}}= -0.172$

Kurtosis,

$\small g_{2}=\frac{m_{4}}{m_{2}^{2}}=\frac{3203422.79}{1504.12^{2}}= 1.416$

Normal 30- Mean 235.2 StDev 38.99 N 96 25 20- Fequency 15 10 - 5 - 0 150 180 210 270 300 240 х

The data is negatively skewed and platykurtic.

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