A survey was given to 8 security officers on about how many

A survey was given to 8 security officers on about how many hrs they worked each week. The results were as follows: 41, 24, 44, 33, 40, 41, 19, and 30.

I. Compute the sample mean, median, and mode

            Answers: Mean ______________ Median _________________   Mode ___________

II. Compute the sample variance and sample standard deviation.

            Answers: Variance ___________________ Standard Deviation __________________

Solution

Mean = Sum of Observations / Number of Observations = 272 / 8 = 34

Median = Middlemost value when arranged in ascending order = 36.5

Mode = Most frequent observation = 41

Variance = summation (( x - mean)^2 / n - 1)

= ( (41 - 34)² + (24 - 34)² + (44 - 34)² + (33 - 34)² + (40 - 34)² + (41 - 34)² + (19 - 34)² + (30 - 34)² ) / 8 - 1)

= 82.2857

Standard deviation = sqrt(Variance)

= sqrt(82.2857)

= 9.0711