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The heights (in inches) of the five starters on a basketball team are67,72,76,76,and84.

Make a table that shows, for each value, its deviation from the mean and its squared deviation from the mean.

Short Answer

Expert verified

The deviation from the calculated mean is5.59and the square deviation of the mean is 31.24.

Step by step solution

01

Given information

Given data :

The heights five starters are : 67,72,76,76,and84.

02

Calculation

On the basis of provided information, the table is as follows;

x
x-x
x-x2
67
-8
64
72
-3
9
76
1
1
76
1
1
84
9
81
Total= 3750
156

The calculated mean is :

localid="1649845044603" x=62+72+76+76+845=3755=75

Hence the standard deviation from the calculated mean is;

localid="1649845109343" σ=xi-μ2N=67-752+72-752+76-752+76-752+84-7525=31.20=5.59

Hence, the deviation from the calculated mean is 5.59and square of deviation is 31.20

03

Concept

By calculating each data point's divergence from the mean, the standard deviation is determined as the square root of variance: σ=Σ(xi−μ)2N

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