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
.
The standard deviation is
.
Answers
GPT-4o mini
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**.
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**.