Question

Find the standard deviation for the following data set: 1, 1, 2, 3, and 3.
*

Answer 1

To find the standard deviation of the data set \(1, 1, 2, 3, 3\), follow these steps:

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

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

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

4. **Calculate the variance**:
- Since we have a population data set, we divide by \(N\) (the total number of data points):
\[
\text{Variance} = \frac{\text{Sum of squared deviations}}{N} = \frac{4}{5} = 0.8
\]

5. **Calculate the standard deviation**:
\[
\text{Standard deviation} = \sqrt{\text{Variance}} = \sqrt{0.8} \approx 0.8944
\]

Thus, the standard deviation of the data set \(1, 1, 2, 3, 3\) is approximately \(0.8944\).

Answer 2

not the answer