Question

Suppose you have the data set 12, 15, 13, 14, 15 and you add in the outlier of 50. How does the outlier affect the mean, median, and mode?(3 points)
increases decreases no change
Mean



Median



Mode

Answer 1

Let's analyze the impact of the outlier (50) on the mean, median, and mode of the data set.

**Original Data Set:** 12, 15, 13, 14, 15

1. **Mean:**
- Original mean = (12 + 15 + 13 + 14 + 15) / 5 = 69 / 5 = 13.8
- New data set with outlier: 12, 15, 13, 14, 15, 50
- New mean = (12 + 15 + 13 + 14 + 15 + 50) / 6 = 119 / 6 ≈ 19.83
- Effect on mean: **increases**

2. **Median:**
- To find the median, we must first sort the original data set: 12, 13, 14, 15, 15
- The median value of the original data (5 values): 14 (middle value)
- For the new data set (with the outlier): 12, 13, 14, 15, 15, 50 (6 values)
- The median of the new data is the average of the 3rd and 4th values: (14 + 15) / 2 = 14.5
- Effect on median: **increases**

3. **Mode:**
- The mode of the original data set is 15 (it appears most frequently).
- The mode of the new data set is still 15 (the most frequently occurring value).
- Effect on mode: **no change**

In summary:
- Mean: **increases**
- Median: **increases**
- Mode: **no change**