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)

Answer 1

Let's analyze the dataset before and after adding the outlier:

Original Dataset:

The original dataset is: 12, 15, 13, 14, 15

1. Mean:
   Mean = (12 + 15 + 13 + 14 + 15) / 5 = (69) / 5 = 13.8

2. Median:
   To find the median, we first sort the data: 12, 13, 14, 15, 15. The median is the middle number.
   Median = 14

3. Mode:
   The mode is the number that appears most frequently. Here, 15 appears twice, while all other numbers appear once.
   Mode = 15

Dataset with Outlier:

Now, adding the outlier of 50, the new dataset is: 12, 15, 13, 14, 15, 50

1. Mean:
   Mean = (12 + 15 + 13 + 14 + 15 + 50) / 6 = (119) / 6 ≈ 19.83

2. Median:
   The sorted data is: 12, 13, 14, 15, 15, 50. The median is the average of the two middle numbers (14 and 15).
   Median = (14 + 15) / 2 = 14.5

3. Mode:
   The mode remains unchanged because 15 is still the number that appears most frequently.
   Mode = 15

Summary of Effects:

• Mean: Increased from 13.8 to approximately 19.83 due to the outlier.
• Median: Decreased from 14 to 14.5 as the outlier shifted the balance but is still more representative than the mean.
• Mode: Remains the same at 15, as it depends on frequency rather than the values themselves.

In conclusion, the outlier significantly affects the mean, increases the median slightly, and does not change the mode.