Question

Leah asked five of her friends how many sports they play. She received the following responses: 1, 1, 2, 3, and 3. Calculate the standard deviation of the data.(1 point)
The standard deviation is

Answer 1

To calculate the standard deviation of the given data (1, 1, 2, 3, 3), follow these steps:

1. **Calculate the mean (average)** of the data:
\[
\text{Mean} = \frac{\text{Sum of data}}{\text{Number of data points}} = \frac{1 + 1 + 2 + 3 + 3}{5} = \frac{10}{5} = 2
\]

2. **Calculate the deviations from the mean** for each data point:
\[
1 - 2 = -1 \\
1 - 2 = -1 \\
2 - 2 = 0 \\
3 - 2 = 1 \\
3 - 2 = 1
\]
So, the deviations are: -1, -1, 0, 1, 1.

3. **Square each of the deviations**:
\[
(-1)^2 = 1 \\
(-1)^2 = 1 \\
(0)^2 = 0 \\
(1)^2 = 1 \\
(1)^2 = 1
\]
Thus, the squared deviations are: 1, 1, 0, 1, 1.

4. **Calculate the average of the squared deviations** (this is the variance):
\[
\text{Variance} = \frac{\text{Sum of squared deviations}}{\text{Number of data points}} = \frac{1 + 1 + 0 + 1 + 1}{5} = \frac{4}{5} = 0.8
\]

5. **Calculate the standard deviation** by taking the square root of the variance:
\[
\text{Standard Deviation} = \sqrt{0.8} \approx 0.8944
\]

Therefore, the standard deviation of the data is approximately **0.8944**.