Question

during one shift, the express lane clerk recorded how many times customers violated the \10 items or less\ rule for his lane. in particular, he recorded how many items over the limit each violator placed on the conveyor belt. this data is summarized in the histogram below. note: the last class actually represents 7 or more items,\ not just 7 items.
what is the most frequent number of over - the - limit items for this data set?
ans =
what is the frequency of the most frequent number of over - the - limit items?
ans =

Explanation:

First Sub - Question:

Step1: Analyze the histogram's x - axis classes

The x - axis classes are \(0.5 - 1.5\), \(1.5 - 2.5\), \(2.5 - 3.5\), \(3.5 - 4.5\), \(4.5 - 5.5\), \(5.5 - 6.5\), \(6.5 - 7.5\). The mid - point of a class interval \((a,b)\) is calculated as \(\frac{a + b}{2}\).
For the class \(2.5-3.5\), the mid - point is \(\frac{2.5 + 3.5}{2}=\frac{6}{2}=3\).

Step2: Identify the tallest bar

The tallest bar in the histogram corresponds to the class \(2.5 - 3.5\). The mid - point of this class (which represents the typical value in the class) is 3. So the most frequent number of over - the - limit items is around the mid - point of the class with the highest frequency.

Step1: Observe the frequency of the tallest bar

Looking at the y - axis (frequency) of the histogram, the tallest bar (corresponding to the class \(2.5 - 3.5\)) has a frequency of 15 (from the graph, the height of the bar is at 15, between 14 and 16).

Answer:

3

Second Sub - Question: