Question

A study is run to estimate the mean Systolic Blood Pressure level in adults 60 to 80 years of age. A sample of 10 participants is selected and their Systolic Blood Pressure levels are measured as follows.
125      135      160      146      135      140      154      170      110      140
Compute Quartiles 1 and 3

		Q1=135 and Q2= 152
		Q1=152 and Q2=135
		Q1=125 and Q2=160
		a and b

Answer 1

First arrange the data in increasing order.

110, 125, 135, 135, 140, 140, 146, 154, 160, 170

n = number of observations = 10 which is even.

Median = average of (n/2)th and (n/2)+1 th observation

            = average of 5th and 6th observation

           = (140+140)/2

          = 140

Median = 140

Lower half of data is {110, 125, 135, 135, 140}

Upper half of data is {140, 146, 154, 160, 170}

Q1 is nothing but the median of lower half of data.

Q1 = median of {110, 125, 135, 135, 140}

     = 135

Q1 = 135

Q3 is nothing but the median of upper half of data

Q3 = median of {140, 146, 154, 160, 170}

     = 154

Q3 = 154

.