Question

Points Scored by the Basketball Team in Different Games
Points Scored
85 78 90
52 81 79
The table shows the points a basketball team scored in different games. When the outlier is removed from the data set, what happens to the mean points scored by the basketball team?

(1 point)
Responses

The mean points scored decreases by 5.1.
The mean points scored decreases by 5.1.

The mean points scored decreases by 8.7.
The mean points scored decreases by 8.7.

The mean points scored increases by 5.1.
The mean points scored increases by 5.1.

The mean points scored increases by 8.7.

Answer 1

To find the mean points scored by the basketball team and determine the effect of removing the outlier, we start with the provided data points:

85, 78, 90, 52, 81, 79.

**Step 1: Calculate the mean of the full dataset.**

1. Sum of the points:
\[
85 + 78 + 90 + 52 + 81 + 79 = 465
\]
2. The number of games:
\[
6
\]
3. Mean:
\[
\text{Mean} = \frac{465}{6} \approx 77.5
\]

**Step 2: Identify and remove the outlier.**

The outlier in this set seems to be **52**, as it is much lower than the rest of the scores.

**Step 3: Calculate the mean after removing the outlier.**

Now we will recalculate the mean without the outlier (52) using the remaining points: 85, 78, 90, 81, 79.

1. Sum of the new data points:
\[
85 + 78 + 90 + 81 + 79 = 413
\]
2. The number of games now:
\[
5
\]
3. New mean:
\[
\text{New Mean} = \frac{413}{5} = 82.6
\]

**Step 4: Compare the means.**

- Original mean: \( 77.5 \)
- New mean: \( 82.6 \)

**Step 5: Determine the change in mean.**

To find the change:
\[
\text{Change} = 82.6 - 77.5 = 5.1
\]

Thus, the mean points scored **increases by 5.1** after the outlier is removed.

The correct response is:
- **The mean points scored increases by 5.1.**