Answer to Question #126979 in Statistics and Probability for mengesha

Question

For the following data compute variance and standard deviation.


2



9 1 81 9 81
8 2 64 16 128
7 3 49 21 147
6 3 36 18 108
5 5 25 25 125
4 3 16 12 48
3 2 9 6 18
2 1 4 2 4
1 2 1 2 2
0 1 0 0 0

24. For a given set of data m3 = 10.8 and m2 = 9.2; determine and explain the skewness of the distribution.
25. A given distribution has m4 = 108.8 and m2 = 8.0; determine and explain kurtosis of the distribution.

Answer 1

Given data: 2,9,1,81,9,81,8,2,64,16,128,125,4,3,16,12,48,3,2,9,6,18,2,1,4,2,4,1,2,1,2,2,0,1,0,0,0

Using ti84 , enter all data in L1, press 1 vars stat L1 and press enter to see standard deviation and variance . or in excel, use =STDEV(input data) and press enter ,

sd= 33.69

and Variance = sd²= 33.69² =1135.021

24).skewness=$\frac{m_3^2}{m_2^3}$ = $\frac{10.8^2}{9.2^3}$ =0.1498

If skewness is between -0.5 and 0.5, the distribution is approximately symmetric.Hence here it is approximately symmetric.

25)kurtosis= $\frac{m_4}{m_2^2}$ =$\frac{108.8}{8^2}$ =1.7

since the kurtosis is greater than zero, then the distribution has heavier tails and is called a leptokurtic distribution