The variance for the given data set $\{2, 3, 7, 7, 1, 1\}$ is $6.6$, rounded to the nearest tenth.

Do you need more details or have any questions?

Here are five related questions you could explore:

1. What is the standard deviation of this data set?
2. How does variance change if all values in the data set are increased by 1?
3. What is the relationship between variance and standard deviation?
4. How is variance affected by extreme values (outliers) in the data set?
5. How do you calculate variance for a population versus a sample?

Tip: Variance measures how spread out the data is from the mean. The larger the variance, the more spread out the values.