Question

Find the standard deviation for the following dataset: 5, 7, 9, 10, 11, 13, 15
*
2 points
2.75
3.42
4.12
5.0

Answer 1

To calculate the standard deviation of the dataset \( 5, 7, 9, 10, 11, 13, 15 \), follow these steps:

1. **Calculate the mean (average)**:
\[
\text{Mean} = \frac{5 + 7 + 9 + 10 + 11 + 13 + 15}{7} = \frac{70}{7} = 10
\]

2. **Calculate the squared deviations from the mean**:
- For 5: \( (5 - 10)^2 = (-5)^2 = 25 \)
- For 7: \( (7 - 10)^2 = (-3)^2 = 9 \)
- For 9: \( (9 - 10)^2 = (-1)^2 = 1 \)
- For 10: \( (10 - 10)^2 = 0^2 = 0 \)
- For 11: \( (11 - 10)^2 = 1^2 = 1 \)
- For 13: \( (13 - 10)^2 = 3^2 = 9 \)
- For 15: \( (15 - 10)^2 = 5^2 = 25 \)

3. **Sum the squared deviations**:
\[
25 + 9 + 1 + 0 + 1 + 9 + 25 = 70
\]

4. **Calculate the variance**:
Since we have a sample, we will divide by \( n - 1 \) (where \( n \) is the number of observations, which is 7):
\[
\text{Variance} = \frac{70}{7 - 1} = \frac{70}{6} \approx 11.67
\]

5. **Calculate the standard deviation**:
\[
\text{Standard Deviation} = \sqrt{11.67} \approx 3.42
\]

The standard deviation for the dataset \( 5, 7, 9, 10, 11, 13, 15 \) is approximately \( 3.42 \).

Therefore, the answer is **3.42**.