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}](https://tex.z-dn.net/?f=Median%3A%5C%5C%5Ctext%7BIf%20n%20is%20odd%2C%20then%7D%5C%5C%5C%5CMedian%20%3D%20%5Cdisplaystyle%5Cfrac%7Bn%2B1%7D%7B2%7Dth%20~term%20%5C%5C%5C%5C%5Ctext%7BIf%20n%20is%20even%2C%20then%7D%5C%5C%5C%5CMedian%20%3D%20%5Cdisplaystyle%5Cfrac%7B%5Cfrac%7Bn%7D%7B2%7Dth~term%20%2B%20%28%5Cfrac%7Bn%7D%7B2%7D%2B1%29th~term%7D%7B2%7D)
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](https://tex.z-dn.net/?f=%5Cdfrac%7B9%20%2B%201%7D%7B2%7D%5E%7Bth%7D%5Ctext%7B%20term%7D%20%3D%205%5E%7Bth%7D%5Ctext%7B%20term%7D%20%3D%20117.4)
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](https://tex.z-dn.net/?f=%5Cdfrac%7B9%20%2B%201%7D%7B2%7D%5E%7Bth%7D%5Ctext%7B%20term%7D%20%3D%205%5E%7Bth%7D%5Ctext%7B%20term%7D%20%3D%20117.9)
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