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Question 3 of 10

The Ridgeport school district collected data about class size in the district. The table shows the class sizes for five randomly selected kindergarten and seventh-grade classes.

[tex]\[
\begin{tabular}{|l|c|c|c|}
\hline
& \textbf{Number of students in} & \textbf{Mean} & \textbf{Mean absolute deviation} \\
& \textbf{randomly selected class} & & \\
\hline
\textbf{Kindergarten} & 17, 17, 21, 20, 20 & 19 & 1.6 \\
\hline
\textbf{Seventh grade} & 28, 30, 30, 29, 28 & 29 & 0.8 \\
\hline
\end{tabular}
\][/tex]

Based on these data, which statement is true?

A. Every seventh-grade class has 10 more students than a kindergarten class.

B. The class sizes are more consistent in the seventh grade than in kindergarten.

C. The mean class size in kindergarten is higher than in the seventh grade.

D. The mean absolute deviation is the same for both kindergarten and seventh grade.



Answer :

GinnyAnswer
Alright class, let's analyze the provided data and determine which statements are true based on the information given.

Kindergarten Class Sizes:
- 17, 17, 21, 20, 20
- Mean: 19
- Mean Absolute Deviation (MAD): 1.6

Seventh Grade Class Sizes:
- 28, 30, 30, 29, 28
- Mean: 29
- Mean Absolute Deviation (MAD): 0.8

Now let’s evaluate the statements one by one.

Statement A: Every seventh-grade class has 10 more students than a corresponding kindergarten class.

To verify this:
- Kindergarten classes: 17, 17, 21, 20, 20
- Seventh grade classes: 28, 30, 30, 29, 28

If every seventh-grade class had 10 more students than each corresponding kindergarten class, we would expect:
- 17 + 10 = 27
- 17 + 10 = 27
- 21 + 10 = 31
- 20 + 10 = 30
- 20 + 10 = 30

However, comparing these with the actual seventh-grade classes:
- 28 (not 27)
- 30 (not 27)
- 30 (not 31)
- 29 (almost 30)
- 28 (almost 30)

This is not consistently true for the last case and some others. Hence, Statement A is false.

Statement B: The mean number of students in the kindergarten classes is less than the mean number of students in the seventh-grade classes.

Given:
- Kindergarten mean: 19
- Seventh grade mean: 29

Clearly, 19 is less than 29, so Statement B is true.

Statement C: The mean absolute deviation (MAD) of the number of students in the kindergarten classes is greater than the mean absolute deviation (MAD) of the number of students in the seventh-grade classes.

Given:
- Kindergarten MAD: 1.6
- Seventh grade MAD: 0.8

Since 1.6 is greater than 0.8, Statement C is true.

Statement D: Not every seventh-grade class has 10 more students than a corresponding kindergarten class.

Since we've already established that Statement A is false, it implies Statement D is the negation of Statement A and should be true.

Thus, based on our analysis, the true statements are:

- Statement B: The mean number of students in the kindergarten classes is less than the mean number of students in the seventh-grade classes.
- Statement C: The mean absolute deviation (MAD) of the number of students in the kindergarten classes is greater than the mean absolute deviation (MAD) of the number of students in the seventh-grade classes.
- Statement D: Not every seventh-grade class has 10 more students than a corresponding kindergarten class.

In conclusion, the true statements based on the data provided are Statements B, C, and D.

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