From the image provided, the problem is about analyzing a histogram of customer violations at an express lane in a store. The histogram shows the number of items over the 10-item limit that customers placed on the conveyor belt.

Here are some observations and answers based on the histogram and the questions:

Observations from the Histogram:

• The x-axis represents the number of items over the limit.
• The y-axis represents the frequency (how many customers exceeded the limit by a certain number of items).
• The last bar on the right represents customers who exceeded the limit by 7 or more items.

Answers to Questions:

1. What was the sample size collected by the clerk?

   • The sample size refers to the total number of violations recorded by the clerk, which is the sum of the frequencies shown on the histogram. However, the number 7 is already filled in as the answer, likely representing a specific category's frequency. If this is asking for the total frequency, the sum of all frequencies should be calculated.

2. What is the frequency of times the limit was exceeded by more than four items?

   • From the histogram, we can see that the bars corresponding to more than four items include:
     • 4.5 items (around 11 customers).
     • 5.5 items (14 customers).
     • 6.5 items (around 4 customers).
     • 7+ items (around 6 customers).
   • Total frequency = 11 + 14 + 4 + 6 = 35 times.
   • However, the number 4 is filled in, which may represent something else, perhaps in another range.

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

   • This is asking for all violations where more than 1 item was placed over the limit. The bars representing more than 1 item start from 1.5 items onward:
     • 1.5 items (around 6 customers).
     • 2.5 items (around 9 customers).
     • 3.5 items (around 13 customers).
     • 4.5 items (around 11 customers).
     • 5.5 items (14 customers).
     • 6.5 items (around 4 customers).
     • 7+ items (around 6 customers).
   • Total frequency = 6 + 9 + 13 + 11 + 14 + 4 + 6 = 63 times.
   • Again, the number 7 is filled in, so clarification may be needed here.

Would you like a more detailed breakdown of the histogram analysis or additional clarifications?

Related Questions:

1. How do we calculate the total sample size using a histogram?
2. What is the significance of grouping data into bins in histograms?
3. How can we determine the exact frequency for specific ranges in a histogram?
4. What are the common uses of histograms in statistics?
5. How could the express lane clerk improve the study for better data collection?

Tip: When analyzing histograms, always pay attention to the labels and axes, as they represent the key values needed to answer most questions.