Question

1. Systolic blood pressures recorded on a random sample of six males are as follows:
156 85 103 92 108 128
a. Compute the sample mean
b. Compute the sample standard deviation
c. Compute the sample median
d. Compute the sample quartiles
e. Generate a box-whisker plot

Answer 1

Let X be the Systolic blood pressures recorded on a random sample of size n=6

a) The sample mean is calcaulted as

b) The sample standard deviation is

c) The sample median

When the sample size n is even the sample median is the average of (n/2 )th and (n/2+1)th observation in the ordered sample.

First we order the data in ascending order as below

85

92

103

108

128

156

n=6 is even. the (n/2) = (6/2) = 3rd observetaion is 103. (n/2+1) = (6/2+1) = 4th observation is 108

Sample median =

d) The first quartile Q1 is the observation at 25th percentile. One way of calcaulating (Tukey's method) this is to pick the median of the data which is less than the median. The data which is less than median,

85

92

103

there are 3 elements in this. Since n=3 is odd, the median of this is (n+1)/2 = ((3+1)/2=2nd observation, which is 92

Hence Q1=92

the third Quartile Q3 is the observation at 75th percentile

To get this using Tukey's method, we take the median of the data which is greater than the median.

The data which is greater than the median is

108

128

156

The 2nd observation in this is the median of this data set.

the third Quartile Q3=128

e) The inter quartile range IQR is

The lower limit of inner fence is

The upper limit of the inner fence is

The minimum of the data set is 85, the maximum is 156.

Since the lower limit of 38 is lower than the minimum, which is 85, the lower whisker will go till 85

Since the upper limit of 182 is higher than the maximum, which is 156, the upper whisker will go till 156

The box plot is below