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A dog trainer compared the mean numbers of lessons for two groups of dogs to learn a new trick.

\begin{tabular}{|l|l|l|}
\hline
& Mean number of lessons & Mean absolute deviation (MAD) \\
\hline
Group A & 4 & 1 \\
\hline
Group B & 8 & 1 \\
\hline
\end{tabular}

Which statement about the data is true?

A. The mean number of lessons for group A is less than the mean for group B by 1 MAD.
B. On average, the dogs in group A required more lessons than the dogs in group B.
C. The mean number of lessons for group A is less than the mean for group B by 4 MADs.
D. The MAD for group A is less than the MAD for group B.

Sagot :

GinnyAnswer
Let's analyze the data given in the problem and evaluate each statement to determine which one is true.

Given Data:
- Mean number of lessons for Group A = 4
- Mean number of lessons for Group B = 8
- Mean Absolute Deviation (MAD) for both groups = 1

Now let's break down each statement:

Statement A: The mean number of lessons for group A is less than the mean for group B by 1 MAD.
- Difference in means between Group B and Group A: [tex]\( 8 - 4 = 4 \)[/tex]
- The given MAD is 1.

Since the difference between the means is 4, and not 1 MAD (which would be 1), this statement is false.

Statement B: On average, the dogs in group A required more lessons than the dogs in group B.
- Mean number of lessons for Group A is 4, and for Group B is 8.
- 4 is less than 8, meaning Group B needed more lessons on average.

Therefore, this statement is false.

Statement C: The mean number of lessons for group A is less than the mean for group B by 4 MADs.
- Difference in means between Group B and Group A: [tex]\( 8 - 4 = 4 \)[/tex]
- Given the MAD is 1, then [tex]\( 4 \)[/tex] MADs would be [tex]\( 4 \times 1 = 4 \)[/tex].

This statement correctly equates the difference in means (4) to 4 times the MAD. Therefore, it is true.

Statement D: The MAD for group A is less than the MAD for group B.
- We are given that the MAD for both groups is the same, which is 1.

Since there is no difference in MAD between groups, this statement is false.

Given the evaluation of the statements above, the true statement is:
- Statement C: The mean number of lessons for group A is less than the mean for group B by 4 MADs.
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