A self-serve frozen yogurt store made these graphs to study the data collected about its customers' purchases. Which statement is true?
\begin{tabular}{|r|c|l|}
\hline \multicolumn{3}{|c|}{ Ounces Sold Last Friday } \\
\hline Leal (3 to 4 p.m) & Stam & Leaf (7 to 8 p.m) \\
\hline 6088898 & 0 & 78 \\
\hline 00125 & 1 & 2246068 \\
\hline 3 & 2 & 0005 \\
\hline & 3 & 2 \\
\hline
\end{tabular}
Which of the following statements is true?
A. The median number of ounces sold from 3 to 4 p.m. was more than the median number sold from 7 to 8 p.m.
B. Yogurt sales had a decreasing trend during the last four months of 2011.
C. More customers prefer chocolate than strawberry and vanilla combined.
D. The store sold 4,000 fewer units in November than in August.
Answer (1)
List data points for 3-4 p.m.: 6, 0, 8, 8, 8, 9, 8, 0, 0, 10, 11, 12, 15, 23.
List data points for 7-8 p.m.: 7, 8, 12, 12, 14, 16, 10, 16, 18, 20, 20, 20, 25, 32.
Calculate medians: 3-4 p.m. median is 8, 7-8 p.m. median is 16.
Compare medians: 8 is not more than 16, so the first statement is false. The answer is that the first statement is false.
Explanation
Understand the problem and provided data We are given a stem-and-leaf plot representing the ounces of frozen yogurt sold during two different hours on a Friday: 3-4 p.m. and 7-8 p.m. We need to determine which of the four provided statements is true based on the given stem-and-leaf plot.
List data points for 3-4 p.m. First, let's list the data points for 3-4 p.m. from the stem-and-leaf plot. Remember that the stem represents the tens digit and the leaf represents the ones digit. So, we have: 6, 0, 8, 8, 8, 9, 8, 0, 0, 10, 11, 12, 15, 23.
List data points for 7-8 p.m. Next, let's list the data points for 7-8 p.m. from the stem-and-leaf plot: 7, 8, 12, 12, 14, 16, 10, 16, 18, 20, 20, 20, 25, 32.
Calculate the median for 3-4 p.m. Now, let's calculate the median for the 3-4 p.m. data. There are 14 data points. First, we sort the data: 0, 0, 0, 6, 8, 8, 8, 8, 9, 10, 11, 12, 15, 23. The median is the average of the 7th and 8th values, which are 8 and 8. So, the median is (8+8)/2 = 8.
Calculate the median for 7-8 p.m. Next, let's calculate the median for the 7-8 p.m. data. There are 14 data points. First, we sort the data: 7, 8, 10, 12, 12, 14, 16, 16, 18, 20, 20, 20, 25, 32. The median is the average of the 7th and 8th values, which are 16 and 16. So, the median is (16+16)/2 = 16.
Compare the medians and evaluate the first statement Now, let's compare the medians. The median for 3-4 p.m. is 8, and the median for 7-8 p.m. is 16. The first statement says that the median number of ounces sold from 3 to 4 p.m. was more than the median number sold from 7 to 8 p.m. Since 8 is not more than 16, this statement is false.
Evaluate the remaining statements The other three statements refer to data not provided in the stem-and-leaf plot. Therefore, we cannot determine if they are true or false based on the given information. However, since the question states that only one statement is true, and we have shown the first statement to be false, we can assume that the other statements are also false.
Conclusion Therefore, the first statement is false.
Examples
Understanding data distribution, like the ounces of yogurt sold, helps businesses make informed decisions about staffing, inventory, and promotions. For example, if the median sales are higher during certain hours, the store might schedule more staff during those times to handle the increased customer flow. Similarly, analyzing sales trends over months can help in planning marketing campaigns or adjusting inventory levels to match customer demand.
