Question

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

Explanation:

Step1: Determine shape of histogram

The tail of the histogram extends to the right, so it is skewed right.

Step2: Assume frequency values from the histogram

Let's assume the frequencies for \(x = 0,1,2,3,4,5,6,7\) are \(f_0,f_1,f_2,f_3,f_4,f_5,f_6,f_7\) (since the actual frequencies are not given in a numerical - value way, for the sake of showing the formula, we use this general form). The mean \(\mu=\frac{\sum_{i = 0}^{7}x_if_i}{\sum_{i=0}^{7}f_i}\). Without the actual frequency values, we can't calculate a numerical value for the mean.

Step3: Calculate the variance formula

The variance \(\sigma^{2}=\frac{\sum_{i = 0}^{7}(x_i-\mu)^2f_i}{\sum_{i = 0}^{7}f_i}\). Since we don't have the mean \(\mu\) (calculated from step 2) and the frequency values \(f_i\), we can't calculate a numerical value for the variance.

Step4: Calculate the standard - deviation formula

The standard deviation \(\sigma=\sqrt{\sigma^{2}}\). Since we don't have the variance \(\sigma^{2}\) (calculated from step 3), we can't calculate a numerical value for the standard deviation.

Answer:

Shape: Skewed right
Mean: Can't be calculated without frequency values
Variance: Can't be calculated without frequency values and mean
Standard deviation: Can't be calculated without variance