Question

Find the standard deviation of the data set, rounded to the nearest hundredth.

(2 points)
Data Point 15 18 11 17 14
Difference
3
2 −1
Squared 0 9
4 1
The standard deviation of the dataset is
.

Answer 1

To find the standard deviation of the data set \( \{15, 18, 11, 17, 14\} \), follow these steps:

1. **Calculate the Mean**:
\[
\text{Mean} = \frac{15 + 18 + 11 + 17 + 14}{5} = \frac{75}{5} = 15
\]

2. **Calculate the Differences from the Mean**:
\[
15 - 15 = 0 \\
18 - 15 = 3 \\
11 - 15 = -4 \\
17 - 15 = 2 \\
14 - 15 = -1
\]

3. **Square the Differences**:
\[
0^2 = 0 \\
3^2 = 9 \\
(-4)^2 = 16 \\
2^2 = 4 \\
(-1)^2 = 1
\]

Thus, the squared differences are:
\[
0, 9, 16, 4, 1
\]

4. **Calculate the Variance**:
- **Sum of Squared Differences**:
\[
0 + 9 + 16 + 4 + 1 = 30
\]
- **Variance** (for population standard deviation):
\[
\text{Variance} = \frac{\text{Sum of Squared Differences}}{n} = \frac{30}{5} = 6
\]

5. **Calculate the Standard Deviation**:
\[
\text{Standard Deviation} = \sqrt{6} \approx 2.44949
\]

6. **Round to the Nearest Hundredth**:
\[
2.45
\]

The standard deviation of the dataset is \(\mathbf{2.45}\).