Question

The height (in inches) of the starting 5 players on the intramural basketball team is shown.
66, 70, 63, 75, 66

What is the five number summary of the data?

Answer 1

To find the five-number summary of the given data set (the heights of the players), we need to determine the following:

1. **Minimum**: The smallest number in the data set.
2. **First Quartile (Q1)**: The median of the first half of the data.
3. **Median (Q2)**: The middle number in the data set.
4. **Third Quartile (Q3)**: The median of the second half of the data.
5. **Maximum**: The largest number in the data set.

First, let's sort the data in ascending order:

63, 66, 66, 70, 75

Now we can calculate the five-number summary:

1. **Minimum**: 63
2. **Maximum**: 75
3. **Median (Q2)**: Since there are 5 numbers, the median is the middle number, which is the third number in this sorted list: **66**.
4. **First Quartile (Q1)**: This is the median of the first half of the data (63, 66). The average of these two numbers is (63 + 66) / 2 = **64.5**.
5. **Third Quartile (Q3)**: This is the median of the second half of the data (66, 70, 75). The median is 70: **70**.

Putting it all together, the five-number summary is:

- Minimum: **63**
- Q1: **64.5**
- Median (Q2): **66**
- Q3: **70**
- Maximum: **75**

Thus, the five-number summary is:

**63, 64.5, 66, 70, 75**