Topic 1.5: Representing a Quantitative Variable with Graphs

Learning Objectives:

Classify quantitative variables as discrete or continuous.
Distinguish between counted quantities and measured quantities.
Represent quantitative data with dotplots, stem-and-leaf plots, and histograms.
Describe the advantages and disadvantages of common graphs for quantitative data.
Explain how changing histogram interval widths can change the display.

Essential Knowledge:

A discrete variable can take on a countable number of values and has gaps between possible values.
A continuous variable can take on infinitely many values with no gaps between possible values.
Discrete variables usually come from counting, while continuous variables usually come from measuring.
A dotplot shows each observation as a dot and makes the shape of a distribution easy to see.
A stem-and-leaf plot splits each value into a stem and a leaf and also shows individual values.
A histogram groups data into intervals, and the height of each bar shows how many observations fall in that interval.
Changing histogram interval widths can change the appearance of the graph.
Dotplots and stem-and-leaf plots are harder to make for very large data sets.
Histograms are useful for large data sets but do not show each individual value.

Key Vocabulary

Quantitative Variable	A variable that takes numerical values for a measured or counted quantity.
Discrete Variable	A quantitative variable with countable values and gaps between possible values.
Continuous Variable	A quantitative variable with infinitely many possible values and no gaps.
Dotplot	A graph that represents each observation with a dot above its value.
Stem	The leading digit or digits in a stem-and-leaf plot.
Leaf	The final digit, usually written to the right of the stem.
Split Stem	A stem that is divided into two rows when one stem has many values.
Histogram	A graph that groups quantitative data into intervals and shows counts or proportions.
Interval / Bin	A range of values used for one bar in a histogram.
Shape	The overall pattern of a distribution shown by a graph.

Video 1: Representing a Quantitative Variable with Graphs

[0:00 – 8:37]

1. [0:15] In this video, we are talking about representing a variable with graphs.

2. [0:27] One question is what are the two types of quantitative variables and how do we them.

3. [0:36] Another question asks about the graphs used for quantitative data and the and disadvantages of each.

Quick Review [0:45 – 1:10] The video reviews the difference between categorical variables, which use labels, and quantitative variables, which use numerical values for a measured or counted quantity.

4. [0:53] A quantitative variable takes numerical values for a measured or quantity.

5. [1:21] The first type of quantitative variable is .

6. [1:30] A discrete variable can take a countable number of values with .

7. [1:42] The number of siblings is a variable because values like 2.5 siblings are not possible.

8. [2:01] A continuous variable can take on values with no .

9. [2:17] A person's height is an example of a variable.

10. [2:38] Typically, a discrete variable comes from , while a continuous variable comes from .

Flint Water Crisis Data [2:51 – 3:53] The lesson returns to the Flint water crisis data set with lead levels measured in 71 water samples from Flint residents between January and June 2015.

11. [3:21] The Flint water sample variable is quantitative and .

12. [3:38] Even though the values were rounded to whole numbers, the original measurements included .

Classifying Quantitative Variables [1:21 – 3:40]

Discrete variables are countable and have gaps.
Continuous variables have infinitely many possible values and no gaps.
Counting usually leads to discrete data.
Measuring usually leads to continuous data.

13. [3:58] The teacher's personal favorite display is the .

14. [4:06] In a dotplot, each observation is represented by a .

15. [4:16] A dotplot makes it easy to see the of the distribution.

16. [4:27] A disadvantage of dotplots is that they can be difficult to make for very data sets.

17. [4:52] In a stem-and-leaf plot, each value is split into a stem and a .

18. [5:15] When one stem has lots of values, it can be into two stems.

Stem-and-Leaf Example [5:02 – 5:33] The value 104 is shown with a stem of 10 and a leaf of 4. Split stems can separate 0–4 from 5–9 when many values land on the same stem.

19. [5:43] Like a dotplot, a stem-and-leaf plot lets you see every individual .

20. [6:05] For larger data sets, another option is a .

21. [6:07] A histogram uses of values and counts how many observations fall in each.

22. [6:28] The value 10 belongs in the bar for the endpoint.

23. [6:44] Changing the interval can change the appearance of the histogram.

24. [7:11] A histogram is easier for large data sets, but it does not show each individual .

Graph Comparison Takeaways [7:59 – 8:20]

Display	Best Feature	Main Limitation
Dotplot	Shows each value and the shape	Hard to make for very large data sets
Stem-and-leaf plot	Shows each value and the shape	Hard to make for very large data sets
Histogram	Works well for large data sets and shows shape	Does not show each exact value

25. Reflection: Explain the difference between a discrete quantitative variable and a continuous quantitative variable. Use one example from the lesson.

26. Reflection: Compare a dotplot or stem-and-leaf plot with a histogram. When is a histogram more useful, and what information do you lose?

Exit Ticket

A teacher recorded the number of siblings for 12 students. The quantitative variable is number of siblings.

Student	1	2	3	4	5	6	7	8	9	10	11	12
Siblings	0	1	1	2	2	2	3	3	4	4	5	6

(a) Classify the variable as discrete or continuous.

(b) Explain why that classification fits the possible values.

(c) Decide whether a dotplot, stem-and-leaf plot, or histogram would be the best display for this data set.

(d) Justify your choice in context by giving one advantage of your chosen display and explaining why a histogram would hide useful information here.

Topic 1.5: Representing a Quantitative Variable with Graphs

Key Vocabulary

Video 1: Representing a Quantitative Variable with Graphs

Exit Ticket

Class Responses (Esc to close)