Question
Download Solution PDFIf a variable has three values -k, 0 and 3k with corresponding frequencies as 3k, 2k and k respectively, then the value of coefficient of skewness b1 is :
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFCalculation
Mean = X̅ = ∑fx/N = 0/3 = 0
|
X |
f |
fx |
X – X̅ |
(X – X̅)2 |
f.(X – X̅)2 |
(X – X̅)3 |
F(X – X̅)3 |
|
-k |
3k |
-3k2 |
-k |
K2 |
3k3 |
-k3 |
-3k4 |
|
0 |
2k |
0 |
0 |
0 |
0 |
0 |
0 |
|
3k |
k |
3k2 |
3k |
9k2 |
9k3 |
27k3 |
27k4 |
|
Total |
6k |
0 |
2k |
|
12k3 |
|
24k4 |
⇒ Mode = -k
⇒ μ2 = ∑f(X - X̅)2/N = 12k3/6k
⇒ μ2 = 2k2
⇒ μ3 = ∑f(X - X̅)3/N = 24k46k
⇒ μ3 = 4k3
Coefficient of skewness = β1 = μ32/μ23
⇒ β1 = 16k6/8k6
∴ The coefficient of skewness β1 is 2
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