A researcher tests three different brands of $2 \%$ milk to see how many grams of fat are in each 8 ounce glass. The results are shown below.
$\begin{array}{|c|c|c|}
\hline \text { Brand A } & \text { Brand B } & \text { Brand C } \
\hline 4.68 & 4.64 & 4.70 \
\hline 4.70 & 4.67 & 4.68 \
\hline 4.64 & 4.68 & 4.71 \
\hline 4.71 & 4.66 & 4.69 \
\hline 4.67 & 4.69 & 4.68 \
\hline
\end{array}$
What is the sum of the ranks of Brand A?
A) 38.5
B) 39.5
C) 40.0
D) 40.5

Question

A researcher tests three different brands of $2 \%$ milk to see how many grams of fat are in each 8 ounce glass. The results are shown below.
$\begin{array}{|c|c|c|}
\hline \text { Brand A } & \text { Brand B } & \text { Brand C } \
\hline 4.68 & 4.64 & 4.70 \
\hline 4.70 & 4.67 & 4.68 \
\hline 4.64 & 4.68 & 4.71 \
\hline 4.71 & 4.66 & 4.69 \
\hline 4.67 & 4.69 & 4.68 \
\hline
\end{array}$ 
What is the sum of the ranks of Brand A?
A) 38.5
B) 39.5
C) 40.0
D) 40.5

Quizplus · Accepted Answer

To find the sum of ranks for Brand A, we need to rank all the values and add them up. We start by combining all the values into a single list and ranking them from smallest to largest:

$\begin{array}{|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|}
\hline 4.64 & 4.64 & 4.67 & 4.66 & 4.68 & 4.68 & 4.69 & 4.68 & 4.70 & 4.71 & 4.67 & 4.69 & 4.68 & 4.70 & 4.71 &  \
\hline 1 & 1 & 3 & 4 & 6.5 & 6.5 & 8.5 & 6.5 & 10.5 & 12 & 3 & 8.5 & 6.5 & 10.5 & 12 &  \
\hline
\end{array}$

Note that the two values of 4.64 each have a rank of 1, so the next rank is 3 (not 2). Also note that the three values of 4.68 are assigned "average" ranks of $\frac{6+6.5+8.5}{3}=7.0$, which is why they all have a decimal rank of 6.5.

Now we can see that the sum of ranks for Brand A is $1+1+3+4+6.5+6.5+6.5+10.5+12=40.5$. Therefore, the answer is (D).

A Researcher Tests Three Different Brands Of 2%2 \%2% Milk to See How Many Grams of Fat Are in to See

A Researcher Tests Three Different Brands Of $2 \%$ Milk to See How Many Grams of Fat Are in to See