Question

fill in the blanks

Use the table to answer the 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 calculate the standard deviation of the dataset, we need to complete the blanks in the provided table and then compute the standard deviation with the available data points. Let's work through it step by step.

Given data points: 15, 18, 11, 17, 14

1. **Calculate the mean (average)** of the dataset:

\[
\text{Mean} = \frac{15 + 18 + 11 + 17 + 14}{5} = \frac{75}{5} = 15
\]

2. **Calculate the difference** from the mean for each data point:

- For 15: \( 15 - 15 = 0 \)
- For 18: \( 18 - 15 = 3 \)
- For 11: \( 11 - 15 = -4 \)
- For 17: \( 17 - 15 = 2 \)
- For 14: \( 14 - 15 = -1 \)

3. **Fill in the differences in the table**:
- Difference: 0, 3, -4, 2, -1

4. **Calculate the squared differences**:

- For 15: \( 0^2 = 0 \)
- For 18: \( 3^2 = 9 \)
- For 11: \( (-4)^2 = 16 \)
- For 17: \( 2^2 = 4 \)
- For 14: \( (-1)^2 = 1 \)

5. **Fill in the squared differences in the table**:
- Squared: 0, 9, 16, 4, 1

Now we can summarize the filled-in table:

| Data Point | 15 | 18 | 11 | 17 | 14 |
|------------|----|----|----|----|----|
| Difference | 0 | 3 | -4 | 2 | -1 |
| Squared | 0 | 9 | 16 | 4 | 1 |

6. **Calculate the variance**:
- Calculate the average of the squared differences:

\[
\text{Variance} = \frac{0 + 9 + 16 + 4 + 1}{5} = \frac{30}{5} = 6
\]

7. **Calculate the standard deviation**:
- Standard deviation is the square root of the variance:

\[
\text{Standard Deviation} = \sqrt{6} \approx 2.45
\]

Thus, the standard deviation of the dataset is **2.45** when rounded to the nearest hundredth.