Elementary Statistics (1+1)

Calculate the Skewness value, coefficient of skewness and kurtosis value

18 22 17 18

22 23 22 19

25 25 23 25

24 28 26 27

19 20 27 22

Sl. No.	X Ascending value
1	17	-5.6	31.36	-175.616	983.4496
2	18	-4.6	21.16	-97.336	447.7456
3	18	-4.6	21.16	-97.336	447.7456
4	19	-3.6	12.96	-46.656	167.9616
5	19	-3.6	12.96	-46.656	167.9616
6	20	-2.6	6.76	-17.576	45.6976
7	22	-0.6	0.36	-0.216	0.1296
8	22	-0.6	0.36	-0.216	0.1296
9	22	-0.6	0.36	-0.216	0.1296
10	22	-0.6	0.36	-0.216	0.1296
11	23	0.4	0.16	0.064	0.0256
12	23	0.4	0.16	0.064	0.0256
13	24	1.4	1.96	2.744	3.8416
14	25	2.4	5.76	13.824	33.1776
15	25	2.4	5.76	13.824	33.1776
16	25	2.4	5.76	13.824	33.1776
17	26	3.4	11.56	39.304	133.6336
18	27	4.4	19.36	85.184	374.8096
19	27	4.4	19.36	85.184	374.8096
20	28	5.4	29.16	157.464	850.3096
Total	452	0	206.80	-70.560	4098.0640

m ₁ = = 0

m ₂ = = 10.34

m ₃ = = - 3.528

m ₄ = = 204.9032

1) Karl-Pearson’s Coefficient of Skewness

=

=

= = 0.093295562

2) Brevley’s coefficient of Skewness =

=

= =

= - 0.130434782

3) Skewness from Moments

m ₃ ²

Skewness( b 1) = -----------

m ₂ ³

(-3.528)² 12.446784

= --------------- = -----------------

(10.34)³ 1105.507304

=-0.011258888

4) Kurtosis

m ₄

Kurtosis ( b 2) = ---------------

m ₂ ²

204.9032 204.9032

= --------------------- = -------------------

(10.34)² 106.9156

= 1.91649488

Answers

1)Karl-pearson’s coefficient of Skewness = 0.093295562

2) Buorley’s cooefficient of Skewness = -0.130434782

3)Skewness for moments = -0.011258888

4)Kurtosis=1.91649488