Question

1) The standard deviation of the data set above is 9.74. How many of the 56 values lie within one-and-a-quarter standard deviations of the mean?

2) In the data set below, what is the percentile rank of 14?

Weekly Exercise Hours 0 3.5 5 10 0 3.5 5 10 0.5 4 6 12 1 4712.5 1.5 4 713.5 2 4713.5 2 4713.5 2 4814 2 4.5 8.5 14 3 5 917.5 3 5 920 3 5 930 3 5 9.5 50 3 5 10 50 0 5 5 6 67777 8 10 12 13 13 14 15 15 16 18 20 25 25 25 29 31 31 33 33 35 49

Answer 1

1) From the data given above

Calculation for the mean and standard deviation:

Mean = Sum of observation / Total Observations

Standard deviation = SQRT(Variance)

Variance = Sum Of Squares (SS) / n - 1, where SS = SUM(X - Mean)².

n	56
Sum	474
Average	8.46
SS(Sum of squares)	5214.9296
Variance = SS/n-1	94.817
Std Dev=Sqrt(Variance)	9.74

The mean = 8.46. We want to find how many of the values lie within 1 and a quarter standard deviations of the mean

1.25 * 9.74 = 12.175

So we need to find the values from (9.75 - 12.175 to (9.74 + 12.175) = -2.435 to 21.915

Excepting the last 3 values . Therefore 53 values come within this specification.

2) There are 30 data in which 14 is the 15th data. Therefore the percentile rank is (15/30) * 100 = 50%