Question

In: Operations Management

Given the data set below, calculate the standard deviation standard deviation using the defining formula standard...

Given the data set below, calculate the standard deviation

standard deviation using the defining formula

standard deviation using the computing formula

8,41,24,19,15,12,47,12,33

Expert Solution

Please rate if you are satisfiied!

Date: 8,41,24,19,15,12,47,12,33

Formula to calculate Standard Deviation:

Considering the data as POPULATION

Solution:

First, work out the average, or arithmetic mean, of the numbers:

Count: 9

Sum: 211 (All the numbers added up)

Mean: 23.44 (Arithmetic mean = Sum / Count)

Then, take each number, subtract the mean and square the result:

Differences: -15.44444444, 17.55555556, 0.5555555556, -4.444444444, -8.444444444, -11.44444444, 23.55555556, -11.44444444, 9.555555556

(Every Number minus Mean)

Differences2: 238.5308641, 308.197531, 0.3086419754, 19.75308642, 71.30864197, 130.9753085, 554.8641977, 130.9753085, 91.30864198

(Square of each difference)

Now calculate the Variance:

Sum of Differences2: 1546.222222

(Add up the Squared Differences)

Variance: 171.8024691

(Sum of Differences2 / Count)

Lastly, take the square root of the Variance:

Standard Deviation: 13.10734409

(The square root of the Variance)

Please rate if you are satisfiied

keosha answered 7 months ago

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