Question

The accompanying data represent the pulse rates (beats per minute) of nine students enrolled in a statistics course. Treat the nine students as a population. Complete parts (a) through (e).

            Student                                              Pulse

            Perpectual_Bempah                        69

            Megan_Brooks                                 87

            Jeff_Honeycutt                                 79

            Clarice_Jefferson                             61

            Crystal_Kurtenbach                         66

            Janette_Lantka                                 81

            Kevin_McCarthy                               84

            Tammy_Ohm                        81

            Kathy_Wojdya                                  87

a)        Compute the population mean.

b)        Compute the population variance.

c)         Compute the population standard deviation.

d)        What value is the 70^th percentile for the data set?

e)        Find the percentile rank for the value of 79 in the data set.

f)         Find the five-number summary for the data set.

g)         Draw a box and whiskers plot using the five-number summary you found in part f.

h)        Determine the sample standard deviation of the following simple random samples of       size 3.

            i           Sample 1: {Clarice, Janette, Kevin}

            ii          Sample 2: {Tammy, Jeff, Megan}

            Which samples underestimate the population standard deviation? Which overestimate    the population standard deviation?

Answer 1

Solve using Excel functions:

a) Population mean = AVERAGE( ) = 77.22

b) Population variance = VAR.P( ) = 80.62

c) Population standard deviation = STDEV.P( ) = 8.98

d) Arrange ascending order: 61,66,69,79,81,81,84,87,87

70th percentile = (70/100*n)th = (0.7*9)th = 6.3th value = 6th value = 81

e) Percentile rank for the value of 79 = PERCENTRANK.INC(array,79) = 0.38 = 38th percentile

f) Five-number summary:

1. Minimum = MIN( ) = 61

2. Q1 = QUARTILE.EXC(array,1) = 67.5

3. Q2 = MEDIAN( ) = 81

4. Q3 = QUARTILE.EXC(array,3) = 85.5

5. Maximum = MAX( ) = 87

g) Box plot

h) Sample 1 Standard deviation = STEDV.S(61, 81, 84) = 12.5

Sample 2 Standard deviation = STEDV.S(81,79,87) = 4.16

Sample 1 and sample 2 underestimate the population standard deviation.