To calculate the variance for the given data set:

Data set: 26, 28, 16, 23, 20

Steps to calculate variance:

1. Find the mean (average): $\text{Mean} = \frac{26 + 28 + 16 + 23 + 20}{5} = \frac{113}{5} = 22.6$

2. Find the squared differences from the mean: $(26 - 22.6)^2 = 3.4^2 = 11.56$ $(28 - 22.6)^2 = 5.4^2 = 29.16$ $(16 - 22.6)^2 = (-6.6)^2 = 43.56$ $(23 - 22.6)^2 = 0.4^2 = 0.16$ $(20 - 22.6)^2 = (-2.6)^2 = 6.76$

3. Find the average of these squared differences: $\text{Variance} = \frac{11.56 + 29.16 + 43.56 + 0.16 + 6.76}{5} = \frac{91.2}{5} = 18.24$

The closest option is 18.2.

So, the variance for this data set is 18.2.

---

Would you like more details on the process or have any other questions? Here are some related questions to explore:

1. What is the standard deviation, and how is it related to variance?
2. How do you calculate the sample variance instead of the population variance?
3. What are the differences between variance and mean absolute deviation (MAD)?
4. How does the variance change if one of the data points is significantly larger or smaller than the others?
5. Can the variance be negative, and if so, what would that mean?

Tip: Remember that variance measures how spread out the data is from the mean. Larger variance indicates more spread.