To determine how the removal of the outlier affects the mean points scored, we'll first calculate the mean of the original data set and then calculate the mean after removing the outlier.
The points scored are:
- 85
- 78
- 90
- 52 (potential outlier)
- 81
- 79
Step 1: Calculate the mean of the original data set.
-
Calculate the total points: \[ 85 + 78 + 90 + 52 + 81 + 79 = 465 \]
-
Count the total number of games: \[ 6 \]
-
Calculate the mean: \[ \text{Mean} = \frac{\text{Total Points}}{\text{Number of Games}} = \frac{465}{6} = 77.5 \]
Step 2: Identify and remove the outlier.
In this case, 52 appears to be significantly lower than the other scores and is likely the outlier.
Step 3: Calculate the mean without the outlier (52).
-
New total points: \[ 85 + 78 + 90 + 81 + 79 = 413 \]
-
New number of games: \[ 5 \]
-
Calculate the new mean: \[ \text{Mean} = \frac{413}{5} = 82.6 \]
Step 4: Compare the means.
- Original mean: 77.5
- New mean after removing outlier: 82.6
Step 5: Calculate the change in mean. \[ 82.6 - 77.5 = 5.1 \]
Since the mean increased by 5.1 when the outlier was removed, the correct response is:
The mean points scored increases by 5.1.