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:
108.6 117.4 128.4 120.0 103.7 112.0 98.3 121.5 123.2
(a) What is the median of the reported blood pressure values?(b) Suppose the blood pressure of the second individual is 117.9 rather than 117.4 (a small change in a single value). What is the new median of the reported values?(c) What does this say about the sensitivity of the median to rounding or grouping in the data?A. When there is rounding or grouping, the median can be highly sensitive to small change.B. When there is rounding or grouping, the median is only sensitive to large changes.C. When there is rounding or grouping, the median is not sensitive to small changes.

Answer 1

Answer:

a) 117.4

b) 117.9

c) Option A)  When there is rounding or grouping, the median can be highly sensitive to small change

Step-by-step explanation:

We are given the following data set in the question:

108.6, 117.4, 128.4, 120.0, 103.7, 112.0, 98.3, 121.5, 123.2

$Median:\\\text{If n is odd, then}\\\\Median = \displaystyle\frac{n+1}{2}th ~term \\\\\text{If n is even, then}\\\\Median = \displaystyle\frac{\frac{n}{2}th~term + (\frac{n}{2}+1)th~term}{2}$

n = 9

a) Median of the reported blood pressure values

Sorted Values: 98.3, 103.7, 108.6, 112.0, 117.4, 120.0, 121.5, 123.2, 128.4

Median =

$\dfrac{9 + 1}{2}^{th}\text{ term} = 5^{th}\text{ term} = 117.4$

b) New median of the reported values

Data: 108.6, 117.9, 128.4, 120.0, 103.7, 112.0, 98.3, 121.5, 123.2

Sorted Values: 98.3, 103.7, 108.6, 112.0, 117.9, 120.0, 121.5, 123.2, 128.4

New Median =

$\dfrac{9 + 1}{2}^{th}\text{ term} = 5^{th}\text{ term} = 117.9$

c) Since median is a position based descriptive statistics, a small change in values can bring a change in the median value as the order of the data may change.

Option A)  When there is rounding or grouping, the median can be highly sensitive to small change