Question

the ages of the people in attendance at the showing of an award - winning foreign film are shown below. attendees of film
which statement must be true according to the histogram?
the data is symmetrical, showing that the majority of the attendees were between the ages of 30 and 50.
the data is symmetrical, showing that the majority of the attendees were between the ages of 21 and 60.
the data is skewed, showing that the majority of the attendees were between the ages of 30 and 50.
the data is skewed, showing that the majority of the attendees were between the ages of 21 and 60.

Explanation:

Step1: Analyze the histogram

The histogram shows the frequency of attendees in different age - groups. The age - group \(21 - 40\) and \(41 - 60\) have higher frequencies compared to \(0 - 20\) and \(61 - 80\).

Step2: Check for symmetry

A symmetrical histogram would have a mirror - image on either side of the center. This histogram is not symmetrical.

Step3: Check for skewness

Since the higher frequencies are in the middle age - groups (\(21 - 60\)), and the lower frequencies are at the two ends (\(0 - 20\) and \(61 - 80\)), the data is not skewed. Also, the age - group \(21 - 60\) (where \(21 - 40\) and \(41 - 60\)) has a large number of attendees.

Answer:

The data is symmetrical, showing that the majority of the attendees were between the ages of 21 and 60.