Box Plots: example 2.25 · Physics Playground

Example 2.25 from Statistics, 2.4 Box Plots

Box Plots: example 2.25

Find the smallest and largest values, the median, and the first and third quartile for Mr. Ramirez's class.
Find the smallest and largest values, the median, and the first and third quartile for Ms. Park's class.
For each data set, what percentage of the data is between the smallest value and the first quartile? the first quartile and the median? the median and the third quartile? the third quartile and the largest value? What percentage of the data is between the first quartile and the largest value?
Create a box plot for each set of data. Use one number line for both box plots.
Which box plot has the widest spread for the middle 50 percent of the data,the data between the first and third quartiles? What does this mean for that set of data in comparison to the other set of data?

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

1
Solution
1. - Min = 32
  - Q₁ = 56
  - M = 74.5
  - Q₃ = 82.5
  - Max = 99
2. - Min = 25.5
  - Q₁ = 78
  - M = 81
  - Q₃ = 89
  - Max = 98
3. Mr. Ramirez's class: There are six data values ranging from 32 to 56: 30 percent. There are six data values ranging from 56 to 74.5: 30 percent. There are five data values ranging from 74.5 to 82.5: 25 percent. There are five data values ranging from 82.5 to 99: 25 percent. There are 16 data values between the first quartile, 56, and the largest value, 99: 80 percent. Ms. Park’s class: There are seven data values ranging from 25.5 to 78: 32 percent. There are seven data values ranging from 78 through 32 percent. There are seven data values ranging 81 to 89: 32 percent. There are six data values ranging from 89 to 98: 27 percent. There are 17 values between the first quartile, 78, and the largest value, 98: 77 percent.
4. Figure 2.16
5. The first data set has the wider spread for the middle 50 percent of the data. The IQR for the first data set is greater than the IQR for the second set. This means that there is more variability in the middle 50 percent of the first data set.

How did it go?