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

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What is the frequency of times the limit was exceeded by more than 1 item?

ans =

Solution

To determine the frequency of times the limit was exceeded by more than 1 item, we can look at the histogram data. The categories of the histogram represent the following ranges:

  1. 0.5 to 1.5: 7
  2. 1.5 to 2.5: 8
  3. 2.5 to 3.5: 14
  4. 3.5 to 4.5: 10
  5. 4.5 to 5.5: 12
  6. 5.5 to 6.5: 8
  7. 6.5 to 7.5: 5
  8. 7.5 and above: (this category is "7 or more items," but we don't have a specific count for it)

To find the frequency for violations exceeding 1 item, we need to consider the categories starting from 1.5 and above:

  • 1.5 to 2.5: 8
  • 2.5 to 3.5: 14
  • 3.5 to 4.5: 10
  • 4.5 to 5.5: 12
  • 5.5 to 6.5: 8
  • 6.5 to 7.5: 5
  • 7.5 and above: (unknown, let's denote it as xx)

Calculating the total frequency:

8+14+10+12+8+5+x=57+x8 + 14 + 10 + 12 + 8 + 5 + x = 57 + x

Since we do not know the exact frequency for the last category ("7 or more items"), the total frequency of times the limit was exceeded by more than 1 item is 57+x57 + x.

Answer: The frequency of times the limit was exceeded by more than 1 item is 57+x57 + x, where xx is the frequency for "7 or more items."

Would you like more details on how to interpret this data or any specific calculations? Here are some related questions to consider:

  1. What is the total frequency of violations recorded?
  2. How can we calculate the mean number of items over the limit?
  3. What are the implications of this data for store policy?
  4. How can we visualize this data in a different way?
  5. What trends might we infer if this data were collected over multiple shifts?

Tip: Always ensure to clearly define your categories when analyzing histogram data to avoid ambiguity.

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Math Problem Analysis

Mathematical Concepts

Data Analysis
Histograms
Frequency Distribution

Formulas

Sum of frequencies

Theorems

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Suitable Grade Level

Grades 6-8