Question

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: Find the five - number summary from the stem - and - leaf plot

First, list out the data values from the stem - and - leaf plot: 74, 78, 85, 86, 87, 92, 99, 100, 100, 101, 105, 105, 108, 110, 110, 114, 116, 117, 120, 120. The minimum value is 74. To find the median (Q2), since there are n = 20 data points, the median is the average of the 10th and 11th ordered values. The 10th value is 101 and the 11th value is 105, so Q2=$\frac{101 + 105}{2}=103$. The lower half of the data is 74, 78, 85, 86, 87, 92, 99, 100, 100, 101. The median of the lower half (Q1) is the average of the 5th and 6th ordered values in the lower half, so Q1=$\frac{87+92}{2}=89.5$. The upper half of the data is 105, 105, 108, 110, 110, 114, 116, 117, 120, 120. The median of the upper half (Q3) is the average of the 5th and 6th ordered values in the upper half, so Q3=$\frac{110 + 114}{2}=112$. The maximum value is 120.

Step2: Match with box - and - whisker plots

A box - and - whisker plot has a box from Q1 to Q3 with a line at Q2, and whiskers from the minimum to Q1 and from Q3 to the maximum. We look for a box - and - whisker plot with a minimum around 74, Q1 around 89.5, Q2 around 103, Q3 around 112, and a maximum around 120.

Answer:

You need to visually inspect the box - and - whisker plots given in the original problem (not shown here in full) and choose the one with the minimum value at 74, Q1 at 89.5, median (Q2) at 103, Q3 at 112, and maximum at 120.