Question

Find the variance of the scores in the data set: 30, 50,
20, 30,
20
(3)
SELECT THE CORRECT ANSWER
200
110
150
None of the given answers

Answer 1

To find the variance of the scores in the data set: \(30, 50, 20, 30, 20\), we will follow these steps:

1. **Calculate the mean (average)** of the data set.
2. **Calculate the squared differences** between each score and the mean.
3. **Find the variance** by averaging those squared differences.

### Step 1: Calculate the mean

\[
\text{Mean} = \frac{\text{Sum of all scores}}{\text{Number of scores}} = \frac{30 + 50 + 20 + 30 + 20}{5} = \frac{150}{5} = 30
\]

### Step 2: Calculate the squared differences

Now, calculate the squared differences from the mean:

- For \(30\): \((30 - 30)^2 = 0\)
- For \(50\): \((50 - 30)^2 = 20^2 = 400\)
- For \(20\): \((20 - 30)^2 = (-10)^2 = 100\)
- For \(30\): \((30 - 30)^2 = 0\)
- For \(20\): \((20 - 30)^2 = (-10)^2 = 100\)

Now, list the squared differences:

\[
0, 400, 100, 0, 100
\]

### Step 3: Find the variance

Now, calculate the variance by finding the average of these squared differences:

\[
\text{Variance} = \frac{\text{Sum of squared differences}}{\text{Number of scores}} = \frac{0 + 400 + 100 + 0 + 100}{5} = \frac{600}{5} = 120
\]

Since this answer is not among the provided options, we select:

**None of the given answers**