https://file.aiquickdraw.com/mathbot/file/1726503487166pod253u9.jpg

The image displays two histograms for "Data Set A" and "Data Set B" with a question asking for the smallest possible difference between their means.

### Information from the histograms:
- Both data sets consist of 23 integers.
- Data Set A: 
  - 1st interval (10 ≤ x < 20) has a frequency of 3.
  - 2nd interval (20 ≤ x < 30) has a frequency of 5.
  - 3rd interval (30 ≤ x < 40) has a frequency of 6.
  - 4th interval (40 ≤ x < 50) has a frequency of 9.
- Data Set B:
  - 1st interval (10 ≤ x < 20) has a frequency of 5.
  - 2nd interval (20 ≤ x < 30) has a frequency of 9.
  - 3rd interval (30 ≤ x < 40) has a frequency of 6.
  - 4th interval (40 ≤ x < 50) has a frequency of 3.

### To calculate the smallest possible difference between the means of both data sets:
1. **Mean Calculation**: Assume that integers in each interval take the midpoint of their respective range (e.g., for the interval 10 ≤ x < 20, the midpoint is 15).

For **Data Set A**:
\[
\text{Mean of Data Set A} = \frac{(3 \times 15) + (5 \times 25) + (6 \times 35) + (9 \times 45)}{23}
\]

For **Data Set B**:
\[
\text{Mean of Data Set B} = \frac{(5 \times 15) + (9 \times 25) + (6 \times 35) + (3 \times 45)}{23}
\]

Now, let's calculate these values.It seems like I can’t do more advanced data analysis right now. Please try again later.

Let me know if you have any other questions or if you'd like me to walk through the steps to solve it manually.

Here are 5 related questions for you to consider:
1. How do you calculate the mean from a frequency table?
2. What effect does changing the frequency of each interval have on the overall mean?
3. What is the difference between weighted and unweighted means?
4. Can the means of two different datasets with the same total frequency be the same?
5. How can histograms help in visualizing the spread of data in different intervals?

**Tip**: When calculating the mean from a histogram, always consider the midpoint of each interval and the frequency.

Two data sets of 23 integers each are summarized in the histograms shown. The histograms show intervals of 10-20, 20-30, 30-40, and 40-50, with varying frequencies. The question asks for the smallest possible difference between the mean of data set A and the mean of data set B.

Learn how to find the smallest possible difference between the means of two data sets using histograms. This problem covers key statistical concepts such as calculating the mean from frequency distributions and interpreting histograms. Suitable for high school students in Grades 10-12.

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