1. Representing Quantitative Data
Histograms
Dot Plots
Stem Plots
Box Plots
Dr. De León
Probability and Statistics with Applications Honors

2. Number of Pages Read per Student Last Weekend
Remember Frequency Tables?
Number of Pages Read per Student Last Weekend
Number
1–10
11–20
21–30
31–40
Frequency
This table shows that 2 students read between 1 and 10 pages, 4 students read between 11 and 20 pages, 1 student read between 21 and 30 pages, and 3 students read between 31 and 40 pages.

3. A histogram is a bar graph that shows the number of data items that occur within each interval.

4. Constructing a Histogram
Step 1: If you did a frequency table, then copy the classes from that table. If not, choose an appropriate scale and interval.
Step 2: Draw a bar for the number of students in each interval. The bars should touch but not overlap.
Step 3: Title the graph and label the axes.

6. DOT PLOTS
A data display in which each data item is shown as a dot above a number line
In a dot plot a cluster shows where a group of data points fall.
A gap is an interval where there are no data items.

7. STEPS TO CREATE A DOT PLOT
Order numbers from least to greatest.
Draw a number line.
Label the number line with the minimum and the maximum then all the numbers that fall between them.
Put a dot above each number on the number line for each data entry in your set.
Don’t forget a title and labels!

8. Display the data in a dot plot.
CREATING A DOT PLOT
In an airline training program, the students are given a test in which they are given a set of tasks and the time it takes them to complete the tasks is measured. The following is a list of the time (in seconds) for a group of new trainees.
61, 61, 64, 67, 70, 71, 71, 71, 72, 73, 74, 74, 75, 77,
79, 80, 81, 81, 83
Display the data in a dot plot.

9. Airline Training Program Test
CREATING A DOT PLOT
Airline Training Program Test
New Trainees
= 1 person
Time in Seconds 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83

10. Stem-and-Leaf Plot Uses place value to organize data
Shows data in an organized way so it can be analyzed easily
Organizes data so it is easier to find the median, mode, and range

11. Here are the scores for a freshman basketball team
Here is the same data organized into a stem-and-leaf plot.

12. stem-and-leaf plot was made?
Can you tell how the
stem-and-leaf plot was made?
The first number in the data is 27.
Here is the 2 in the tens place.
Here is the 7 in the ones place.

13. The key shows us which place value the digits represent.

14. The stems all represent tens place in this stem-and-leaf plot.
The leaves all represent ones.

15. Let’s try one together…

16. Here are one student’s math test scores.
Make a stem-and-leaf plot for this data.
First, draw the dividing lines.

17. Here are one student’s math test scores.
Make a stem-and-leaf plot for this data.
Stems Leaves
Next, label the stem side and the leaf side.

18. Here are one student’s math test scores.
Make a stem-and-leaf plot for this data.
Stems Leaves
7 5
Find the smallest piece of data and plot it on the grid.

19. Here are one student’s math test scores.
Make a stem-and-leaf plot for this data.
Stems Leaves
7 5 9
The 7 for the tens place is already there. We just add the 9.
Find the next smallest piece of data and plot it on the grid.

20. Now, keep going….
Stems Leaves
7 5 9

21. Test Scores
Stems Leaves
7 5 9
8 3
Key: means 75

22. Box and Whisker Plots
A box plot summarizes data using the median, upper and lower quartiles, and the extreme (least and greatest) values. It allows you to see important characteristics of the data at a glance.

23. The 5 Number Summary
The five number summary is another name for the visual representation of the box and whisker plot.
The five number summary consist of :
The median ( 2nd quartile)
The 1st quartile
The 3rd quartile
The maximum value in a data set
The minimum value in a data set

24. Box and Whisker Diagrams. Anatomy of a Box and Whisker Diagram.
Lower Quartile
Upper Quartile
Lowest Value
Median
Highest Value
Box
Whisker 4 5 6 7 8 9 10 11 12
Box Plots

25. Constructing a box and whisker plot
Step 1 - take the set of numbers given…
34, 18, 100, 27, 54, 52, 93, 59, 61, 87, 68, 85, 78, 82, 91
Place the numbers in order from least to greatest:
18, 27, 34, 52, 54, 59, 61, 68, 78, 82, 85, 87, 91, 93, 100

26. Constructing a box and whisker plot
Step 2 - Find the median.
Remember, the median is the middle value in a data set.
18, 27, 34, 52, 54, 59, 61, 68, 78, 82, 85, 87, 91, 93, 100
68 is the median of this data set.

27. NOTE: Even Numbered Data Sets
If the data set has an even number of pieces of data, we find the mean of the two middle numbers to find the median of the set 2, 4, 5, 6, 7, 8, 9, 11, 19, = divided by 2 = 7.5 The median is 7.5

28. BACK TO OUR DATA: Constructing a box and whisker plot
Step 3 – Find the lower quartile.
The lower quartile is the median of the data set to the left of 68.
(18, 27, 34, 52, 54, 59, 61,) 68, 78, 82, 85, 87, 91, 93, 100
52 is the lower quartile

29. Constructing a box and whisker plot
Step 4 – Find the upper quartile.
The upper quartile is the median of the data set to the right of 68.
18, 27, 34, 52, 54, 59, 61, 68, (78, 82, 85, 87, 91, 93, 100)
87 is the upper quartile

30. AGAIN! Lower and Upper Quartiles for Even Numbered Data
The lower quartile is the median of the bottom half of the data (to the left of the median).
[ 2, 4, 5, 6, 7] 7.5 [8, 9, 11, 19, 20]
Lower Quartile for this data = 5
The upper quartile is the median of the top half of the data (to the right of the median).
[ 2, 4, 5, 6, 7] 7.5 [8, 9, 11, 19, 20]
The upper quartile for this data set = 11

31. BACK TO OUR DATA: Constructing a box and whisker plot
Step 5 – Find the maximum and minimum values in the set.
The maximum is the greatest value in the data set.
The minimum is the least value in the data set.
18, 27, 34, 52, 54, 59, 61, 68, 78, 82, 85, 87, 91, 93, 100
18 is the minimum and 100 is the maximum.

32. Constructing a box and whisker plot
Step 5 – Find the inter-quartile range (IQR).
The inter-quartile (IQR) range is the difference between the upper and lower quartiles.
Upper Quartile = 87
Lower Quartile = 52
87 – 52 = 35
35 = IQR

33. The 5 Number Summary Organize the 5 number summary Median – 68
Lower Quartile – 52
Upper Quartile – 87
Max – 100
Min – 18

34. Graphing The Data
Notice, the Box includes the lower quartile, median, and upper quartile.
The Whiskers extend from the Box to the max and min.
The data values found inside the box represent the middle half ( 50%) of the data.
The line segment inside the box represents the media

35. Interpreting the Box Plot:
Study your Box and Whisker Plot to determine what it is telling you. Make a statement about what it is saying, then support the statement with facts from your graph.

36. You should include the following in your interpretation:
Range or spread of the data and what it means to your graph
Quartiles—compare them. What are they telling you about the data?
Median- this is an important part of the graph, and should be an important part of the interpretation.
Percentages should be used to interpret the data, where relevant.