A banker has collected the following sample data of the number of loans he approved per day, in the past week:


3  5  12  3  2


The variance of the data set, rounded off to one decimal place, is

To calculate the variance of the data set, we follow these steps:

### Step 1: Find the Mean (Average) of the data
The data set is:  
\[ 3, 5, 12, 3, 2 \]

The mean (\(\mu\)) is calculated by:
\[
\mu = \frac{\sum{x_i}}{n} = \frac{3 + 5 + 12 + 3 + 2}{5} = \frac{25}{5} = 5
\]

### Step 2: Calculate the Squared Differences from the Mean
Now, for each value in the data set, subtract the mean and square the result:
- \( (3 - 5)^2 = (-2)^2 = 4 \)
- \( (5 - 5)^2 = (0)^2 = 0 \)
- \( (12 - 5)^2 = (7)^2 = 49 \)
- \( (3 - 5)^2 = (-2)^2 = 4 \)
- \( (2 - 5)^2 = (-3)^2 = 9 \)

### Step 3: Calculate the Variance
The variance formula is:
\[
\text{Variance} = \frac{\sum{(x_i - \mu)^2}}{n} = \frac{4 + 0 + 49 + 4 + 9}{5} = \frac{66}{5} = 13.2
\]

Thus, the variance of the data set, rounded to one decimal place, is **13.2**.

Would you like further details or have any other questions?

Here are 5 related questions to consider:
1. How is standard deviation related to variance?
2. How would the variance change if there were more data points?
3. What is the difference between population variance and sample variance?
4. How can the variance be used to assess risk in financial contexts?
5. Can variance be negative?

**Tip:** Variance measures how spread out numbers are in a data set. A higher variance indicates greater spread!

A banker has collected the following sample data of the number of loans he approved per day, in the past week: 3  5  12  3  2. The variance of the data set, rounded off to one decimal place, is

Learn how to calculate the variance of loan approvals from a week's sample data. This example walks through finding the mean, calculating squared differences, and determining the variance using key statistical formulas. Suitable for students in Grades 9-12.

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