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 data responses (1, 1, 2, 3, 3), follow these steps:

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

\[
\text{Mean} = \frac{(1 + 1 + 2 + 3 + 3)}{5} = \frac{10}{5} = 2
\]

2. **Calculate each response's deviation from the mean, square it, and sum those squared deviations**:

\[
(1 - 2)^2 = (-1)^2 = 1
\]
\[
(1 - 2)^2 = (-1)^2 = 1
\]
\[
(2 - 2)^2 = (0)^2 = 0
\]
\[
(3 - 2)^2 = (1)^2 = 1
\]
\[
(3 - 2)^2 = (1)^2 = 1
\]

Sum of squared deviations:

\[
1 + 1 + 0 + 1 + 1 = 4
\]

3. **Divide the sum of squared deviations by the number of responses (n = 5) to find the variance**:

\[
\text{Variance} = \frac{4}{5} = 0.8
\]

4. **Calculate the standard deviation**:

\[
\text{Standard Deviation} = \sqrt{0.8} \approx 0.8944
\]

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