Math Problem Statement

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

Solution

The question asks for the frequency of times the limit was exceeded by more than 1 item.

Looking at the histogram:

  • The x-axis represents the number of items over the limit (in intervals), and the y-axis shows the frequency for each interval.
  • The first bar (centered at 0.5) corresponds to violations where customers exceeded the limit by less than or equal to 1 item.
  • Therefore, we are interested in all bars where the number of items exceeded the limit by more than 1 item, which corresponds to the bars centered at 1.5, 2.5, 3.5, 4.5, 5.5, and 6.5.

To find the total frequency:

  1. For the bar at 1.5, the frequency is 7.
  2. For the bar at 2.5, the frequency is 10.
  3. For the bar at 3.5, the frequency is 9.
  4. For the bar at 4.5, the frequency is 12.
  5. For the bar at 5.5, the frequency is 7.
  6. For the bar at 6.5, the frequency is 5.

Summing these values gives:
7 + 10 + 9 + 12 + 7 + 5 = 50.

Thus, the frequency of times the limit was exceeded by more than 1 item is 50.

Would you like further clarification or details? Here are 5 follow-up questions you could consider:

  1. How is frequency related to histograms in general?
  2. Can you explain why the first bar is excluded from the count?
  3. What if the question asked for violations exceeding 3 items?
  4. How would the graph change if fewer violations occurred?
  5. What other types of data can be represented in histograms?

Tip: When reading histograms, always check both the x-axis intervals and y-axis frequency to ensure accurate interpretation!

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Math Problem Analysis

Mathematical Concepts

Data Analysis
Histograms
Frequency Distribution

Formulas

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Theorems

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Suitable Grade Level

Grades 6-9