Question

Blood pressure values are often reported to the nearest 5 mmHg (100, 105, 110, etc.). The actual blood pressure values for nine randomly selected individuals are given below. 118.6 127.4 138.4 130.0 113.7 122.0 108.3 131.5 133.2 (a) What is the median of the reported blood pressure values? mmHg (b) Suppose the blood pressure of the second individual is 127.8 rather than 127.4 (a small change in a single value). What is the new median of the reported values? mmHg What does this say about the sensitivity of the median to rounding or grouping in the data? When there is rounding or grouping, the median can be highly sensitive to small change. When there is rounding or grouping, the median is not sensitive to small changes. When there is rounding or grouping, the median is only sensitive to large changes.

Answer 1

Given that Blood pressure values are often reported to the nearest 5 mm Hg

(a) First we will arrange the values in ascending order and by taking nearest whole number

Blood pressure level	Nearest number
108.3	105
113.7	115
118.6	120
122	120
127.4	125
130	130
131.5	130
133.2	135
138.4	140

Here, Median is the (N+1)/2 th number = 5th number which is 125 mm Hg

(b) If the second value changes from 127.4 to 127.8 then the nearest number by 5 to 127.4 is 130 mm Hg so the median will be changed to 130 mm Hg.

(c) In rounding in grouping median will be changed with high sensitivity.