Ivan was given two data sets, one without an outlier and one with an outlier.

Data without an outlier: 108, 113, 105, 118, 124, 121, 109
Data with an outlier: 108, 113, 105, 118, 124, 121, 109, 61

How is the median affected by the outlier?
The outlier slightly affected the median.
The outlier made the median higher than all the other values.
The outlier made the median lower than all the other values.
The median is the exact same number in both data sets.

1 answer

To analyze how the outlier affects the median, we first need to calculate the median for both data sets.

Data without an outlier: 108, 113, 105, 118, 124, 121, 109
First, we arrange the data in ascending order:
105, 108, 109, 113, 118, 121, 124

Since there are 7 values (an odd number), the median is the middle value, which is the 4th number:
Median without an outlier: 113

Data with an outlier: 108, 113, 105, 118, 124, 121, 109, 61
Again, we arrange the data in ascending order:
61, 105, 108, 109, 113, 118, 121, 124

Now there are 8 values (an even number), so the median will be the average of the 4th and 5th values:
(109 + 113) / 2 = 111

Median with an outlier: 111

Now let's compare the two medians:

Median without an outlier: 113
Median with an outlier: 111

The outlier (61) caused the median to decrease from 113 to 111.

Thus, the correct answer is: The outlier made the median lower than all the other values.