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. 118.6 127.4 138.4 130.0 113.7 122.0 108.3 131.5 133.2a. What is the median of the reported blood pressure values?b. Suppose the blood pressure of the second individual is 127.6 rather than 127.4 (a small change in a single value). Howdoes this affect the median of the reported values? What does this say about the sensitivity of the median to rounding orgrouping in the data

Answer 1

a) And the value on the fifth position is
`Median=127.4`

b) Since we have the same sample size the position for the median would be the 5th on the dataset ordered, and for this case the
`Median=127.6`

The median on this case was affected by the change of one value.

The median is not affected by outliers for this case this measure is a rubusteness estimator compared to the sample mean that is very affected by outliers.

When we have rounding or grouping, the median can be hoghly sensitive to small changes.

Explanation:

The median by dfinition is "the middle number in a sorted, ascending or descending, list of numbers and can be more descriptive of that data set than the average".

For this case we have the following datsaset:

118.6 127.4 138.4 130.0 113.7 122.0 108.3 131.5 133.2

The first step on this case is sort the data on increasing order, and after do this we got:

108.3, 113.7, 118.6,122, 127.4,130,131.5,133.2,138.4

Part a

For this case since we have a sample size of n =9 and is and odd number we the median would be on the following position from the data ordered:

`(n+1)/(2) =(9+1)/(2)=5`

And the value on the fifth position is
`Median=127.4`

Part b

For this case we have the following dataset with the change:

118.6 127.6 138.4 130.0 113.7 122.0 108.3 131.5 133.2

And after order the data we got:

108.3, 113.7, 118.6,122, 127.6,130,131.5,133.2,138.4

And again since we have the same sample size the position for the median would be the 5th on the dataset ordered, and for this case the
`Median=127.6`

The median on this case was affected by the change of one value.

The median is not affected by outliers for this case this measure is a rubusteness estimator compared to the sample mean that is very affected by outliers.

When we have rounding or grouping, the median can be hoghly sensitive to small changes.