Yuri computes the mean and standard deviation for the sample data set 12 , 14 , 9 , and 21 He finds the mean is 14 Yuri's Work s=sqrt(((12−14)^2+(14−14)^2+(9−14)^2+(21−14)^2)/(4)) is equal to square root of the fraction with numerator negative 2 squared plus 0 squared plus negative 5 squared plus 7 squared and denominator 4 end root is equal to square root of the fraction with numerator 4 plus 0 plus 25 plus 49 and denominator 4 end root is equal to square root of 78 fourths is equal to square root of 19 point 5 What is the first error he made in computing the standard deviation?
Answer
A
Yuri failed to square negative 2 correctly.
B
Yuri did not subtract 9 minus 14 correctly.
C
Yuri failed to find the difference between each data point and the mean.
D
Yuri divided by n instead of n minus 1 .
Explanation
The differences from the mean are −2, 0, −5, and 7, and their squares add to 4 + 0 + 25 + 49 = 78. Those calculations are correct. Because the data are described as a sample, the sample standard deviation divides the sum of squared deviations by n − 1, which is 4 − 1 = 3, not by n = 4. Yuri’s first error was dividing by 4.
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