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

Show how to calculate the variance and standard deviation from the values in your table.

Short Answer

Expert verified

The sample variance is 39and standard deviation is6.2449

Step by step solution

01

Given information

Given data :

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

02

Concept

Standard deviation is the spread of a group of numbers from the mean.

SV=Σ(xi−x)2N-1

σ=samplevariance

03

Calculation

For the given data 67,72,76,84 table is,

xx-x
x-x2
67-864
72-39
7611
7611
84981
Total=3750156

The mean is calculated as 75

The sample variance is computed using the formula:

=Σ(xi−x)2n-1=1564=39

Standard deviation is calculated as,

σ = samplevariance

σ = 39

=6.2449

The standard deviation is a metric that indicates how far a set of data deviates from its mean. It's a measurement of distance's absolute variability. The standard deviation increases as the dispersion increases. The standard deviation is 6.2449and the sample variance is 39

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