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Compute the range, sample variance, and sample standard deviation for the following scores: 25, 36, 41, 28, 29, 32, 39, 37, 34, 34, 37, 35, 30, 36, 31, 31

User Barryred
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Answers:

range = 16

sample variance = 18.395833 approximately

sample standard deviation = 4.289036 approximately

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Step-by-step explanation

The range is found by subtracting the largest and smallest values.

Range = max - min

Range = 41 - 25

Range = 16

The larger the range, the more spread out the values will be.

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To get the sample variance, it will take a bit of steps. First we'll need the sample mean xbar.

xbar = (add up the values)/(number of values)

xbar = (25+36+41+28+29+32+39+37+34+34+37+35+30+36+31+31)/16

xbar = 535/16

xbar = 33.4375

This value is exact and hasn't been rounded.

Once we know the sample mean, subtract it from each data value. Then square that result. These computations are shown in the spreadsheet image attachment (see below).

The highlighted portion in yellow represents the sum of the squared error (SSE). It's the result of adding up everything in the (x-xbar)^2 column.

Divide the SSE over (n-1) to get the sample variance.

sample variance = SSE/(n-1)

sample variance = 275.937496/(16-1)

sample variance = 18.395833 approximately

We take the square root of this to get the sample standard deviation.

sqrt(18.395833) = 4.289036 is the approximate sample standard deviation.

Round the approximate decimal values however your teacher instructs.

Many calculators can quickly compute the sample variance and sample standard deviation in one step. If you don't have a calculator, search out "sample variance calculator".

Compute the range, sample variance, and sample standard deviation for the following-example-1
User BobbyTables
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