Question

Over the first 20 games of the season, the distribution of a basketball teams scores is bell shaped with a mean of 94 points per game and a high of 109. Over the next 10 games the team scored 94,110,93,98,99,121,96,94 and 108 points. Which statement best describes the change in the teams average number of point per game?
A.the new mean is less than the previous mean
B. The new mean is less than the previous median
C. The new median is the same as the the previous median
D. The new mean is greater than the previous mean

Answer 1

To determine which statement best describes the change in the basketball team's average number of points per game after the additional 10 games, we can calculate the new mean.

1. **Calculate the old mean:**
The old mean for the first 20 games is given as 94 points.

2. **Calculate the total points scored in the first 20 games:**
Total points for the first 20 games = Old mean × Number of games
Total points = 94 × 20 = 1880 points

3. **Scores for the next 10 games:**
The scores are: 94, 110, 93, 98, 99, 121, 96, 94, 108
Total points for these 10 games = 94 + 110 + 93 + 98 + 99 + 121 + 96 + 94 + 108
Total = 1013 points

4. **Calculate the new total points:**
New total points = Total points from first 20 games + Total points from next 10 games
New total = 1880 + 1013 = 2893 points

5. **Calculate the new mean:**
New mean = New total points / Total number of games
New mean = 2893 / 30 = 96.4333 points

6. **Comparison of means:**
- Old Mean = 94 points
- New Mean ≈ 96.43 points

Since the new mean (approx. 96.43) is greater than the previous mean (94), we can conclude:

**The correct statement is:**
D. The new mean is greater than the previous mean.