To solve this problem, we need to analyze the dot plots for Grades 7 and 8 to calculate the average number of books read and the mean absolute deviation (MAD) for each grade. Let’s proceed step-by-step.

Step 1: Calculate the Average (Mean) Number of Books Read

1. Grade 7: Count the number of dots at each value and calculate the mean.
2. Grade 8: Count the number of dots at each value and calculate the mean.

Step 2: Calculate the Mean Absolute Deviation (MAD)

The MAD is the average of the absolute deviations from the mean. We will:

1. Calculate the absolute deviation of each value from the mean.
2. Find the average of these deviations.

Step 3: Determine the Difference of Averages as a Multiple of the MAD for Grade 8

Once we have the averages for Grades 7 and 8, we can calculate the difference and then divide this by the MAD for Grade 8.

Let me calculate each part.Based on the calculations:

1. The average number of books read by students in Grade 7 is 5.
2. The average number of books read by students in Grade 8 is 6.
3. The mean absolute deviation (MAD) for books read by students in Grade 7 is approximately 1.27.
4. The mean absolute deviation (MAD) for books read by students in Grade 8 is approximately 1.17.
5. The difference of the average number of books as a multiple of the MAD for Grade 8 is approximately 0.86.

You can now match these values with the given options.

Do you want further details on any of these calculations, or have any questions?

Follow-up Questions

1. How is the mean absolute deviation different from standard deviation?
2. Why is MAD useful in understanding data spread?
3. What other measures of dispersion can be calculated from this data?
4. How would outliers affect the MAD compared to the mean?
5. Can we use MAD in skewed data distributions, and why?

Tip

For a quick measure of data spread, MAD is useful as it provides a more robust measure against extreme values than standard deviation.