Question

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

Explanation:

Step1: Recall the relationship between variance and standard deviation in a normal distribution

In a normal distribution, the variance is the square of the standard deviation. From the graph (assuming it's a normal distribution), if we assume the standard deviation \( \sigma = 0.5\) (by visual inspection of the spread of the normal curve around the mean).

Step2: Calculate the variance

The formula for variance \( \sigma^{2}\). Substitute \( \sigma = 0.5\) into the formula \( \sigma^{2}=(0.5)^{2}\).

$$ \sigma^{2}=0.25 $$

Answer:

0.25