Variance for 65,77,81,98,100,80,129
350
333
380
280
Answers
Step-by-step explanation:
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Step-by-step explanation:
65,77,80,81,98,100,129
Total number of observation are:
N = 7
So mean of observation are:
\mathbf{\bar{X}=\dfrac{\sum X_{i}}{N}}
X
ˉ
=
N
∑X
i
\mathbf{\bar{X}=\dfrac{65+77+80+81+98+100+129}{7}}
X
ˉ
=
7
65+77+80+81+98+100+129
\mathbf{\bar{X}=90}
X
ˉ
=90
Means mean of observation are 90.
\mathbf{Calculate \ \sum (X_{i}-\bar{X})^{2}}Calculate ∑(X
i
−
X
ˉ
)
2
:
\mathbf{\sum (X_{i}-\bar{X})^{2}}∑(X
i
−
X
ˉ
)
2
=(65-90)²+(77-90)²+(80-90)²+(81-90)²+(98-90)²+(100-90)²+(129-90)²= 2660
Standard deviation can be find by formula:
\mathbf{Standard\ Deviation\ (\sigma )=\sqrt{\dfrac{(\sum X_{i}-\bar{X})^{2}}{N}}}Standard Deviation (σ)=
N
(∑X
i
−
X
ˉ
)
2
\mathbf{Standard\ Deviation\ (\sigma )=\sqrt{\dfrac{2660}{7}}}Standard Deviation (σ)=
7
2660
\mathbf{Standard\ Deviation\ (\sigma )=\sqrt{380}}Standard Deviation (σ)=
380
\mathbf{Standard\ Deviation\ (\sigma )=19.49}Standard Deviation (σ)=19.49
So standard deviation of following observation are 19.49