Calculate the requested statistics for the following sample data: 10, 9, 12, 11,

Question

Calculate the requested statistics for the following sample data:

     10,     9,     12,     11,     10

Give the answer to the proper number of decimal places outlined below •.

(a) sample mean =

(b) sample standard deviation =

...............................................
Rounding Rules:

• Mean, Standard Deviation, and Variance: Your answer should be rounded to one more decimal place than the raw data.

• Median: If you have to take the mean of two numbers then round that result to one more decimal place than the raw data. If one of the elements of the data set is the median, then use that number as is.

• Intermediate Steps: When performing intermediate steps to do something like calculate the standard deviation, it is best to round to at least one extra decimal place than will be used in the final answer.

Explanation / Answer

The given data is

10,     9,     12,     11,     10

There are 5 values.

The sample mean is : (10 + 9 + 12 + 11 + 10) / 5 = 52/5 = 10.40.

Sum of squares of differences = (10 - 10.4)2 + (9 - 10.4)2 + (12 - 10.4)2 + (11 - 10.4)2 + (10 - 10.4)2

= (-0.4)2 + (-1.4)2 + (1.6)2 + (0.6)2 + (-0.4)2

= 0.16 + 1.96 + 2.56 + 0.36 + 0.16

= 5.2.

The sample variance is 5.2 / (5 - 1) = 5.2 / 4 = 1.30.

The sample standard deviation is 1.30 = 1.1402.

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