S - Analyzing Graphs Lesson

Analyzing Graphs

So far, you've learned how to display data graphically. Now, we will use the graphs to analyze the data and find measures of center and variability. Graphical displays of data can also be helpful when comparing two or more sets of data.

Example:

The table shows the number of wins of two middle school basketball teams for the past ten years.

Lakeview MS	24	26	24	10	8	11	8	13	16	10
Mountainside MS	14	11	11	16	14	9	18	11	16	15

Which team had a greater range of wins?
- Solution: Lakeview MS $26-8=18$ ; Mountainside MS $18-9=9$
  - Lakeview MS has the greater range of wins.
What is the mean number of wins for each team?
- Solution: Lakeview MS $\frac{\left(24+26+24+10+8+11+8+13+16+10\right)}{10}=15$
  - Mountainside MS $LaTeX: \frac{\left(14+11+11+16+14+9+18+11+16+15\right)}{10}=13.5$ $\frac{\left(14+11+11+16+14+9+18+11+16+15\right)}{10}=13.5$

To be able to compare the data easily, let's arrange the data above into a back-to-back stem-and-leaf plot.

Lakeview MS	Stem	Mountainside MS
8 8 0 0 1 3 6 4 4 6 Key: 4\|2 = 24 games	0 1 2	9 1 1 1 4 4 5 6 6 8 Key: 1\|1 = 11 games

Lakeview MS

Stem

Mountainside MS

8 8

0 0 1 3 6

4 4 6

Key: 4|2 = 24 games

1 1 1 4 4 5 6 6 8

Key: 1|1 = 11 games

Which middle school has a more consistent number of wins?
- Solution: Mountainside MS has a more consistent number of wins because most of the values are in one stem. The wins for Lakeview MS are spread out in three stems.
Find the median number of wins for each team.

- Solution: There are 10 data values for each team and they are already listed in order. Find the average of the 5th and 6th values for each team.
  - Lakeview MS $LaTeX: \frac{\left(11+13\right)}{2}=\frac{24}{2}=12$ $\frac{\left(11+13\right)}{2}=\frac{24}{2}=12$
  - Mountainside MS $LaTeX: \frac{\left(14+14\right)}{2}=\frac{28}{2}=14$ $\frac{\left(14+14\right)}{2}=\frac{28}{2}=14$

Watch the video below to learn more about analyzing graphs.

Analyzing Graphs Assignment

Download the "Analyzing Graphs Assignment" by clicking here. Be sure to work all of the problems on paper. You will use these problems and solutions to complete the "Statistics Homework Quiz 2." Remember you can always go back and review the lessons and videos for more help. Links to an external site.

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