Question

describe the shape of the histogram. skewed left skewed right roughly symmetric find the mean. $mu = 4.23$ find the variance. $sigma^{2}=2.03612$ find the standard deviation. round to four decimal places, if necessary. $sigma = 1.4269$

Explanation:

Step1: Recall shape - skewness rules

If tail is on right, skewed right.

Step2: Analyze histogram

The histogram has a tail on the right side.

Step3: Recall mean formula

For a discrete - probability distribution, $\mu=\sum_{x}x\cdot P(x)$. But since we are not given probabilities explicitly, we assume we are working with frequency - based data and use $\mu=\frac{\sum_{i = 1}^{n}x_{i}f_{i}}{\sum_{i = 1}^{n}f_{i}}$.

Step4: Recall variance formula

$\sigma^{2}=\sum_{x}(x - \mu)^{2}\cdot P(x)$ (for probability distribution) or $\sigma^{2}=\frac{\sum_{i = 1}^{n}(x_{i}-\mu)^{2}f_{i}}{\sum_{i = 1}^{n}f_{i}}$ (for frequency - based data).

Step5: Recall standard deviation formula

$\sigma=\sqrt{\sigma^{2}}$.

Answer:

Describe the shape of the histogram:

• Skewed right

Find the mean: (No data to recalculate, assume correct value needs to be calculated from original data source)
Find the variance: (No data to recalculate, assume correct value needs to be calculated from original data source)
Find the standard deviation: (No data to recalculate, assume correct value needs to be calculated from original data source)