Question

a movie theater showed a new movie 15 times over a weekend. the stem - and - leaf plot shows the number of tickets that were sold for each showing. movie tickets sold stem leaf 7 4,8 8 5,6,7 9 2,9 10 1,5,5,8 11 0,0,4,6 which box - and - whisker graph represents the same data shown in the stem - and - leaf plot?

Explanation:

Step1: Write out the data from the stem - and - leaf plot

The data values are: 74, 78, 85, 86, 87, 92, 99, 101, 105, 105, 108, 110, 110, 114, 116.

Step2: Find the five - number summary

• Minimum: The smallest value is 74.
• First quartile ($Q_1$): There are $n = 15$ data points. The position of $Q_1$ is $\frac{n + 1}{4}=\frac{15+ 1}{4}=4$. So, $Q_1$ is the 4th ordered value, which is 86.
• Median: The position of the median is $\frac{n + 1}{2}=\frac{15 + 1}{2}=8$. So, the median is 101.
• Third quartile ($Q_3$): The position of $Q_3$ is $\frac{3(n + 1)}{4}=\frac{3\times(15 + 1)}{4}=12$. So, $Q_3$ is 110.
• Maximum: The largest value is 116.

Step3: Match with box - and - whisker plots

Based on the five - number summary, we can identify the correct box - and - whisker plot. The box starts at $Q_1 = 86$, ends at $Q_3=110$, the line inside the box is at the median 101, the left - whisker extends to the minimum 74 and the right - whisker extends to the maximum 116.

Answer:

The box - and - whisker plot that has a minimum value of 74, $Q_1$ value of 86, median value of 101, $Q_3$ value of 110 and maximum value of 116. (Since no options are given in text, this is a general description of the correct plot).