Question

For the following data, 25, 27, 29, 36, 20, 26. Determine.

a) Average deviation b) Asymmetry coefficient c) Coefficient of kurtosis

Answer 1

Given data: 25, 27, 29, 36, 20, 26

n= number of data values = 6

a)

First, we find the mean

  

X
25	2.1667
27	0.1667
29	1.8333
36	8.8333
20	7.1667
26	1.1667
Total

Hence,

Therefore, average deviation = 3.5556.

b)

We need to find the second and third central moment.

X
25	4.6946	-10.1718
27	0.0278	-0.0046
29	3.3610	6.1617
36	78.0272	689.2376
20	51.3616	-368.0931
26	1.3612	-1.5881
Total

Therefore, asymmetry coefficient = 0.4725.

Since the asymmetry coefficient = 0.4725 > 0, therefore the distribution of the given data is positively skewed.

c)

Now here we need to find the fourth central moment

X
25	22.0392
27	0.0008
29	11.2962
36	6088.2422
20	2638.0128
26	1.8528
Total

We have,

Therefore the coefficient of kurtosis is 2.7273.

Since the coefficient of kurtosis = 2.7273 < 3, therefore the distribution of the given data is platykurtic.