Question

the graph shows a distribution of data.
what is the variance of the data?
0.0625
0.25
0.5
1.5

Explanation:

Identify the distribution type

The graph shows a symmetric, bell-shaped curve, which represents a Normal Distribution Parameters model.

Determine the mean and standard deviation

The peak of the curve is at the mean:

$$\mu = 4$$

The dashed vertical lines show the standard deviation intervals. The first dashed lines on either side of the mean are at \(3.75\) and \(4.25\), and the next are at \(3.5\) and \(4.5\). This indicates:

$$\sigma = 0.25$$

Calculate the variance

Using the standard deviation \(\sigma = 0.25\):

$$\sigma^2 = (0.25)^2 = 0.0625$$

Answer:

• (A) 0.0625 (Correct answer)
• (B) 0.25
• (C) 0.5
• (D) 1.5