Question

Given the dataset 68, 85, 88, 97, 85, 89, 98, 93, 95, and 99 how does the median change when the new data point of 97 is added?(1 point)
Responses

The median is higher
The median is higher

The median is lower
The median is lower

The median does not change

Answer 1

To determine how the median changes when the new data point of 97 is added, we need to calculate the median of both the original dataset and the new dataset after adding the point.

**Original dataset:**
68, 85, 85, 88, 89, 93, 95, 97, 98, 99

First, sort the data (it's already sorted):
1. 68
2. 85
3. 85
4. 88
5. 89
6. 93
7. 95
8. 97
9. 98
10. 99

Since there are 10 numbers (even dataset), the median is the average of the 5th and 6th values:
Median = (89 + 93) / 2 = 91

**New dataset after adding the new data point of 97:**
68, 85, 85, 88, 89, 93, 95, 97, 97, 98, 99

Sort the new data:
1. 68
2. 85
3. 85
4. 88
5. 89
6. 93
7. 95
8. 97
9. 97
10. 98
11. 99

Now there are 11 numbers (odd dataset), so the median is the 6th value:
Median = 93

**Comparison of medians:**
- Original median = 91
- New median = 93

Since 93 is higher than 91, we conclude that:

**The median is higher.**