Questions
If each observation of a raw data whose variance is is multiplied by h, then the variance of the new set is
a
σ2
b
h2σ2
c
hσ2
d
h+σ2
detailed solution
Correct option is B
Let x1,x2,…,xn be the raw data. Then, σ2=1n∑i=1n xi−X¯2If each value is multiplied by h, then the values become hx1,hx2,…,hxn Then AM of the values is hx1+hx2+⋯+hxnn=hX¯Therefore, the variance of the new set of values is1n∑i=1n hx1−hX¯2=h21n∑i=1n xi−X¯2=h2σ2Talk to our academic expert!
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The standard deviation of some temperature data in oC is 5. If the data were converted into oF, the new variance would be
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