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
a
.

Answer 1

To calculate the standard deviation of the data set provided (1, 1, 2, 3, and 3), we can follow these steps:

1. **Calculate the mean (average)**:
\[
\text{Mean} = \frac{\sum \text{values}}{n} = \frac{1 + 1 + 2 + 3 + 3}{5} = \frac{10}{5} = 2
\]

2. **Calculate the squared deviations from the mean**:
\[
(1 - 2)^2 = 1
\]
\[
(1 - 2)^2 = 1
\]
\[
(2 - 2)^2 = 0
\]
\[
(3 - 2)^2 = 1
\]
\[
(3 - 2)^2 = 1
\]

3. **Sum the squared deviations**:
\[
1 + 1 + 0 + 1 + 1 = 4
\]

4. **Calculate the variance** (since this is a sample, we will divide by \( n - 1 \)):
\[
\text{Variance} = \frac{\text{Sum of squared deviations}}{n - 1} = \frac{4}{5 - 1} = \frac{4}{4} = 1
\]

5. **Calculate the standard deviation** by taking the square root of the variance:
\[
\text{Standard Deviation} = \sqrt{\text{Variance}} = \sqrt{1} = 1
\]

Therefore, the standard deviation of the data is **1**.