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.

24681012140.51.52.53.54.55.56.57.5# items over 10Frequency[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],[1.5,6]);rect([1.5,0],[2.5,8]);rect([2.5,0],[3.5,14]);rect([3.5,0],[4.5,11]);rect([4.5,0],[5.5,12]);rect([5.5,0],[6.5,8]);rect([6.5,0],[7.5,6]);]

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

Answer:  times

Solution

From the histogram description, the number of items over the 10-item limit is represented in bins (0-1, 1-2, 2-3, etc.), and the heights of the bars indicate the frequency. We are asked to find the frequency of times the limit was exceeded by more than 3 items.

This corresponds to the bins starting from 3-4, 4-5, 5-6, and "7 or more items." Let's analyze the frequencies for these bins:

  • 3-4 items over the limit: Frequency = 11
  • 4-5 items over the limit: Frequency = 12
  • 5-6 items over the limit: Frequency = 8
  • 7 or more items over the limit: Frequency = 6

Now, sum these frequencies: 11+12+8+6=3711 + 12 + 8 + 6 = 37

So, the frequency of times the limit was exceeded by more than 3 items is 37 times.

Would you like further details or clarifications?

Here are 5 related questions:

  1. What is the total number of violators recorded in the histogram?
  2. What percentage of the violators exceeded the limit by 5 or more items?
  3. What is the mode for the number of items over the limit?
  4. How many times did customers exceed the limit by exactly 1 item?
  5. What is the median number of items over the limit?

Tip: Histograms help to visualize the frequency distribution of data, showing how often each range of values occurs.

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Math Problem Analysis

Mathematical Concepts

Histograms
Frequency Distribution
Summation

Formulas

Sum of frequencies for bins representing more than 3 items

Theorems

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Suitable Grade Level

Grades 7-9