Math Problem Statement

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.

2 4 6 8 10 12 14 0.5 1.5 2.5 3.5 4.5 5.5 6.5 7.5

items over 10

Frequency [Graphs generated by this script: setBorder(54,40,20,5); initPicture(0,7.5,0,14);axes(1000,2,1,1000,2); fill="blue"; stroke="black";line([0.5,-0.28],[0.5,0.28]); text([0.5,0],"0.5","below");line([1.5,-0.28],[1.5,0.28]); text([1.5,0],"1.5","below");line([2.5,-0.28],[2.5,0.28]); text([2.5,0],"2.5","below");line([3.5,-0.28],[3.5,0.28]); text([3.5,0],"3.5","below");line([4.5,-0.28],[4.5,0.28]); text([4.5,0],"4.5","below");line([5.5,-0.28],[5.5,0.28]); text([5.5,0],"5.5","below");line([6.5,-0.28],[6.5,0.28]); text([6.5,0],"6.5","below");line([7.5,-0.28],[7.5,0.28]); text([7.5,0],"7.5","below");textabs([165,0],"# items over 10","above");textabs([0,115],"Frequency","right",90);rect([0.5,0],[1.5,5]);rect([1.5,0],[2.5,9]);rect([2.5,0],[3.5,14]);rect([3.5,0],[4.5,12]);rect([4.5,0],[5.5,11]);rect([5.5,0],[6.5,7]);rect([6.5,0],[7.5,5]);]

What is the frequency of times the limit was exceeded by more than 3 items?

Solution

To determine the frequency of times the "10 items or less" rule was exceeded by more than 3 items, we need to consider the classes from the histogram that represent more than 3 items over the limit.

From the histogram provided, the classes and their corresponding frequencies are as follows:

  • 0.5 to 1.5: Frequency = 5
  • 1.5 to 2.5: Frequency = 9
  • 2.5 to 3.5: Frequency = 14
  • 3.5 to 4.5: Frequency = 12
  • 4.5 to 5.5: Frequency = 11
  • 5.5 to 6.5: Frequency = 7
  • 6.5 to 7.5: Frequency = 5 (This actually represents "7 or more items")

We are interested in the classes representing more than 3 items. This includes:

  • 3.5 to 4.5: Frequency = 12
  • 4.5 to 5.5: Frequency = 11
  • 5.5 to 6.5: Frequency = 7
  • 6.5 to 7.5: Frequency = 5

Adding these frequencies together gives us:

12+11+7+5=3512 + 11 + 7 + 5 = 35

Therefore, the frequency of times the limit was exceeded by more than 3 items is 35.

Would you like more details or have any questions?

Relative Questions

  1. What is the total frequency of all violations recorded by the clerk?
  2. What is the average number of items over the limit per violator?
  3. How does the frequency change as the number of items over the limit increases?
  4. What percentage of violators exceeded the limit by more than 5 items?
  5. How could this data be used to improve store operations?

Tip

When interpreting histograms, always check the class boundaries to ensure you accurately calculate totals and understand the distribution.

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Math Problem Analysis

Mathematical Concepts

Histograms
Frequency Distribution

Formulas

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Theorems

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Suitable Grade Level

Grades 9-12

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