Class 20-22 22-24 24-26 26-28 28-30 30-32 33-35 40-42 18-20 Frequency 3 2 1 3 2 4 3 2 3 a. Calculate Skewness from the following grouped data b. Calculate the Kurtosis
Class 20-22 22-24 24-26 26-28 28-30 30-32 33-35 40-42 18-20 Frequency 3 2 1 3 2 4 3 2 3 a. Calculate Skewness from the following grouped data b. Calculate the Kurtosis
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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2nd pic sample photo:
Transcribed Image Text:Class
20-22
22-24
24-26
26-28
28-30
30-32
33-35
40-42
18-20
Frequency
3
2
1
3
2
4
3
2
3
a. Calculate Skewness from the following grouped data
b. Calculate the Kurtosis
Transcribed Image Text:Examples
1. Calculate Sample Skewness,
Sample Kurtosis from the
following grouped data
Class
Frequency
2-4
4-6
6-8
8-10
Class
(1)
2-4
4-6
6-8
8-10
3
4
2
1
Mid value (x)
(2)
3 =2+4/2
5 =4+6/2
7=6+8/2
9=8+10/2
S
(3)
3
4
2
1
…….
Mean x-x
=52
10
<-5.2
n-10
9=3×3
(4)-(2)x(3)
20=4x5
(4)-(2)×(3)
14=2x7
(4)-(2)x(3)
(frequency x mid value)
f-x
(4)=(2)x(3)
9=1x9
(4)-(2)×(3)
---
Sample Standard deviation
S=√(x-x) 2
fx-52
=√35.6
9
=√3.9556
=1.9889
(mid value-mean)
(5)
-2.2= 3-5.2
x-5.2
-0.2= 15-5.2
x-5.2
1.8= 7-5.2
xx-5.2
3.8=19-5.2
x-5.21
Skewness=(x-x) ³
(n-1)-S3
34.56
9-(1.9889)
34.56
9-7.867
=0.4881
f-(x-x)2
(6)=(3)×(5)
14.52-3x-2.2-2.2
(6)-(2)×(5)
0.16 4×-0.2x-0.2
(6)-(2)×(5)
6.48 2x1.8x1.8
(6)-(2)×(5)
14.44 1×3.8×3.8
(6)-(2)×(5)
-35.6
Kurtosis =(x-x)*
(n-1).
299.792
9-(
299.792
9-15.6464
=2.1289
f(x-x)3
(7)=(5)×(6)
X= tem in data sel
= Sample mean
Σ - Sum
n=Sample size
-31.944 14.52*-2.2
(7)-(2)x(6)
-0.032 0,16×-0.2
(7)=(2)×(6)
11.664-6.48×1.8
(7)-(2)x(6)
54.872 14.44×3.8
-34.56
(7)-(2)×(6)
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