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)

Question

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.