# In the data set, what is the variance? 6 8 1 9 4

The variance is the average of the squared differences from the mean.

## Answer: The variance of this data set is 10.3

**Explanation:**

To figure out the variance, we first calculate the difference between each point and the mean.

Then we square and average the results.

Mean = (6 + 8 + 1 + 9 + 4) ÷ 5 = 5.6

Variance (σ) = [(6 - 5.6)^{2} + (8 - 5.6)^{2} + (1 - 5.6)^{2} + (9 - 5.6)^{2} + (4 - 5.6)^{2}] ÷ (5 - 1)

⇒ σ = [(0.4)^{2} + (2.4)^{2} + (-4.6)^{2} + (3.4)^{2} + (1.4)^{2}] ÷ 4

⇒ σ = [.16 + 5.76 + 21.16 + 11.56 + 2.56] ÷ 4

⇒ σ = 41.2 ÷ 4

⇒ σ = 10.3