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?

What is the standard deviation of the data?

Show your work.

(2 points)
make it simple and like a kid wrote it

Answer 1

Sure! Let's break it down into simple steps.

### Five Number Summary

The five number summary includes:
1. Minimum
2. First Quartile (Q1)
3. Median
4. Third Quartile (Q3)
5. Maximum

#### Step 1: Organize the Data
First, we sort the heights from smallest to largest:
- 63, 66, 66, 70, 75

#### Step 2: Find the Minimum and Maximum
- **Minimum**: The smallest number is **63**.
- **Maximum**: The largest number is **75**.

#### Step 3: Find the Median
The median is the middle number. Since there are 5 numbers:
- The median is the third number in the sorted list, which is **66**.

#### Step 4: Find Q1 and Q3
- **Q1** (first quartile) is the median of the first half (63, 66). The median of these two numbers is (63 + 66) / 2 = 64.5.
- **Q3** (third quartile) is the median of the second half (66, 70, 75). Q3 is the second number in this set, which is **70**.

### Five Number Summary:
- Minimum: 63
- Q1: 64.5
- Median: 66
- Q3: 70
- Maximum: 75

So, the five number summary is **63, 64.5, 66, 70, 75**.

### Standard Deviation

To find the standard deviation, we follow these steps:

#### Step 1: Find the Mean
Add all the heights and divide by how many there are.
(63 + 66 + 66 + 70 + 75) / 5 = 68.

#### Step 2: Calculate Each Deviation from the Mean
Now we subtract the mean from each height and square the result:
- (63 - 68)² = (-5)² = 25
- (66 - 68)² = (-2)² = 4
- (66 - 68)² = (-2)² = 4
- (70 - 68)² = (2)² = 4
- (75 - 68)² = (7)² = 49

#### Step 3: Calculate the Average of Those Squared Deviations
Add them up:
25 + 4 + 4 + 4 + 49 = 86.
Now, divide by the number of measurements (which is 5) for the variance:
Variance = 86 / 5 = 17.2.

#### Step 4: Take the Square Root of the Variance
Now, we take the square root to find the standard deviation:
Standard Deviation = √17.2 ≈ 4.14.

So, the standard deviation of the heights is about **4.14** inches!

### Summary:
Five Number Summary: **63, 64.5, 66, 70, 75**
Standard Deviation: **4.14** inches