To determine the effect of removing the outlier on the mean points scored, we first need to calculate the mean of the original data set and then the mean after removing the outlier.
Points Scored:
- 85
- 78
- 90
- 52
- 81
- 79
Step 1: Calculate the original mean
- Sum of points: \( 85 + 78 + 90 + 52 + 81 + 79 = 465 \)
- Number of games: 6
- Mean: \( \frac{465}{6} = 77.5 \)
Step 2: Identify the outlier
Looking at the data, 52 seems to be an outlier compared to the other scores.
Step 3: Calculate the mean without the outlier
Removing the outlier (52), we are left with:
- 85
- 78
- 90
- 81
- 79
- Sum of remaining points: \( 85 + 78 + 90 + 81 + 79 = 413 \)
- Number of games: 5
- Mean without outlier: \( \frac{413}{5} = 82.6 \)
Step 4: Compare the means
- Original mean: 77.5
- New mean without the outlier: 82.6
Difference in means
\( 82.6 - 77.5 = 5.1 \)
Thus, the mean points scored increases by 5.1 when the outlier is removed.
Final Response:
The mean points scored increases by 5.1.