A basketball coach recorded how many shots each of the 
\[30\] players at tryouts made in a set of 
\[6\] attempts. Here are the results:
A dot plot has a horizontal axis labeled, Number of shots made, marked from 0 to 6, in increments of 1. Dots are plotted above values as follows: 0, 8; 1, 13; 2, 4; 3, 2; 4, 2; 5, 1. A dashed vertical line through the axis at 1 is labeled, A. A dashed vertical line through the axis at approximately 1.33 is labeled, B. A dashed vertical line through the axis at 3 is labeled, C.
\[0\]
\[1\]
\[2\]
\[3\]
\[4\]
\[5\]
\[6\]
The approximate location of the median is point 

The approximate location of the mean is point

To address the problem, let's first break it down step by step:

### Dot Plot Summary:
- **Number of shots made:**
  - \(0\) shots: \(8\) players
  - \(1\) shot: \(13\) players
  - \(2\) shots: \(4\) players
  - \(3\) shots: \(2\) players
  - \(4\) shots: \(2\) players
  - \(5\) shots: \(1\) player

There are no players who made \(6\) shots. The total number of players is \(30\).

### Median Approximation:
The **median** is the middle value of the dataset when the values are arranged in order. Since there are \(30\) players, the median will be the average of the 15th and 16th values when all the players are arranged in ascending order by the number of shots they made.

- The first 8 players made 0 shots.
- The next 13 players (from position 9 to position 21) made 1 shot.
- So, both the 15th and 16th players made 1 shot.

Thus, the median is \(1\). This corresponds to **point A** on the plot.

### Mean Approximation:
The **mean** (average) is calculated by summing the total number of shots made and dividing by the number of players:

\[
\text{Mean} = \frac{(0 \times 8) + (1 \times 13) + (2 \times 4) + (3 \times 2) + (4 \times 2) + (5 \times 1)}{30}
\]
\[
= \frac{0 + 13 + 8 + 6 + 8 + 5}{30} = \frac{40}{30} \approx 1.33
\]

Thus, the mean is approximately \(1.33\), corresponding to **point B** on the plot.

### Conclusion:
- **Median**: Point A (\(1\))
- **Mean**: Point B (\(1.33\))

Would you like more details on any of these steps?

Here are some related questions:
1. How would the mean change if the number of shots made by each player increased by 1?
2. What happens to the median if a new player who made 6 shots joins the group?
3. Can you explain the difference between the mean and median in this data set?
4. How is the distribution of shots made skewed based on the dot plot?
5. Why is the median sometimes preferred over the mean in describing data sets?

**Tip:** The median is less sensitive to extreme values (outliers) than the mean.

A basketball coach recorded how many shots each of the 30 players at tryouts made in a set of 6 attempts. A dot plot is given with shots made ranging from 0 to 5, and points A, B, and C marking specific locations. The problem asks for the approximate location of the median and the mean based on the dot plot data.

Analyze a basketball tryout where 30 players attempted 6 shots. Learn how to find the mean (1.33) and median (1) using a dot plot. This problem demonstrates key statistical concepts, including measures of central tendency, suitable for Grades 6-8.

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