Respuesta :
Answer:
a) And the value on the fifth position is [tex] Median=127.4[/tex]
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 [tex]Median=127.6[/tex]
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.
Step-by-step 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:
[tex] \frac{n+1}{2} =\frac{9+1}{2}=5[/tex]
And the value on the fifth position is [tex] Median=127.4[/tex]
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 [tex]Median=127.6[/tex]
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.
