Question

no ages of the people in attendance at the showing of an award - winning foreign film are shown below
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:

• A symmetrical histogram has a mirror - image shape on either side of the center. Here, the histogram for ages \(21 - 40\) and \(41 - 60\) has the same frequency (height of the bars), and the frequencies for \(0 - 20\) and \(61 - 80\) are also the same. So, the data is symmetrical.
• The bars for the age groups \(21 - 40\) and \(41 - 60\) (combined as \(21 - 60\)) have a higher frequency compared to \(0 - 20\) and \(61 - 80\). So, the majority of attendees are in the \(21 - 60\) age range.

Answer:

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