Question

describe the shape of the histogram.
skewed left
skewed right
roughly symmetric
find the mean.
μ =
find the variance.
σ² =
find the standard deviation. round to four decimal places, if necessary.
σ =

Explanation:

Step1: Assume frequency values

Let's assume the frequencies for \(x = 0,1,\cdots,7\) are \(f_0,f_1,\cdots,f_7\) based on the height of the bars in the histogram. Since the exact values are not given numerically, for the formula of the mean \(\mu=\frac{\sum_{i = 0}^{7}x_if_i}{\sum_{i=0}^{7}f_i}\), variance \(\sigma^{2}=\frac{\sum_{i = 0}^{7}(x_i-\mu)^2f_i}{\sum_{i=0}^{7}f_i}\) and standard - deviation \(\sigma=\sqrt{\sigma^{2}}\).

Step2: Analyze shape

The tail of the histogram extends to the right side (the values of \(x\) from 5 - 7 have lower frequencies compared to the peak around \(x = 4\)), so it is skewed right.

Answer:

Describe the shape of the histogram:

• Skewed right

Find the mean: (No numerical data for frequencies, cannot calculate exactly)
Find the variance: (No numerical data for frequencies, cannot calculate exactly)
Find the standard deviation: (No numerical data for frequencies, cannot calculate exactly)