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)

Answer 1

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

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

2. **Calculate the variance**:
The variance is calculated as the average of the squared differences from the mean.
\[
\text{Variance} = \frac{\sum (x_i - \text{mean})^2}{N}
\]
Where \(x_i\) are the individual responses and \(N\) is the number of responses.

Calculating each squared difference:
- For \(1\): \((1 - 2)^2 = (-1)^2 = 1\)
- For \(1\): \((1 - 2)^2 = (-1)^2 = 1\)
- For \(2\): \((2 - 2)^2 = (0)^2 = 0\)
- For \(3\): \((3 - 2)^2 = (1)^2 = 1\)
- For \(3\): \((3 - 2)^2 = (1)^2 = 1\)

Now summing these squared differences:
\[
1 + 1 + 0 + 1 + 1 = 4
\]

Now divide by the number of responses to get the variance:
\[
\text{Variance} = \frac{4}{5} = 0.8
\]

3. **Calculate the standard deviation**:
The standard deviation is the square root of the variance.
\[
\text{Standard Deviation} = \sqrt{\text{Variance}} = \sqrt{0.8} \approx 0.8944
\]

Thus, the standard deviation of the data is approximately **0.894**.