Question

what effect will the outlier have on the median of the data if the outlier is excluded? 2, 4, 1, 2, 8, 4, 22
decreases
does not change
insufficient information to conclude
increases

Explanation:

Step1: Identify outlier, sort full data

Original data: $2, 4, 1, 2, 8, 4, 22$. Sorted: $1, 2, 2, 4, 4, 8, 22$. Outlier is $22$.

Step2: Calculate median of full data

For $n=7$ (odd), median = 4th value: $4$

Step3: Sort data without outlier

Data without outlier: $1, 2, 2, 4, 4, 8$. Sorted: $1, 2, 2, 4, 4, 8$

Step4: Calculate median of trimmed data

For $n=6$ (even), median = $\frac{3\text{rd value} + 4\text{th value}}{2} = \frac{2+4}{2}=3$

Step5: Compare the two medians

Original median $4$, new median $3$: median decreases.

Answer:

A. decreases