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 standard deviation of the data?

Answer 1

To calculate the standard deviation of the heights of the starting 5 players, we will follow these steps:

1. Calculate the mean (average) of the heights.
2. Compute the squared differences from the mean.
3. Find the average of these squared differences (variance).
4. Take the square root of the variance to find the standard deviation.

### Step 1: Calculate the Mean

The heights are: \( 66, 70, 63, 75, 66 \).

\[
\text{Mean} = \frac{66 + 70 + 63 + 75 + 66}{5} = \frac{340}{5} = 68
\]

### Step 2: Calculate the Squared Differences from the Mean

Next, we'll calculate the differences from the mean and then square those values.

\[
(66 - 68)^2 = (-2)^2 = 4
\]

\[
(70 - 68)^2 = (2)^2 = 4
\]

\[
(63 - 68)^2 = (-5)^2 = 25
\]

\[
(75 - 68)^2 = (7)^2 = 49
\]

\[
(66 - 68)^2 = (-2)^2 = 4
\]

Now we can summarize the squared differences:

\[
4, 4, 25, 49, 4
\]

### Step 3: Calculate the Variance

Now compute the variance by averaging the squared differences:

\[
\text{Variance} = \frac{4 + 4 + 25 + 49 + 4}{5} = \frac{86}{5} = 17.2
\]

### Step 4: Calculate the Standard Deviation

The standard deviation is the square root of the variance:

\[
\text{Standard Deviation} = \sqrt{17.2} \approx 4.14
\]

### Conclusion

The standard deviation of the data is approximately **4.14 inches**.