CEMC's Open Courseware - Lesson 9: Scatter Plots

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  - What Is a Scatter Plot?
  - Variables in a Scatter Plot
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- - Question 1
  - Question 2
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Exercises

Create a scatter plot from the given data. Plot the variable in the first column on the horizontal axis.

Temperature	Drink Sales ($$$)
$12^{\circ}$C	$200$
$14^{\circ}$C	$220$
$18^{\circ}$C	$300$
$20^{\circ}$C	$350$
$26^{\circ}$C	$450$

Create two scatter plots from the given data relating two variables. First, place Variable 1 on the horizontal axis and Variable 2 on the vertical axis. Then, interchange the roles of the variables for the second plot.

Variable 1 Variable 2

$1$ $1$

$3.5$ $4.5$

$3$ $6$

$5$ $1$

$2$ $4$

How does the shape of the graph change when you interchange the roles of the variables?
Determine the two variable quantities present in each situation. Do you think that one of the two variables should be dependent on the other? Explain.
1. How does the condition of a vehicle change over time?
2. Does the brand name of a car affect the car's resale value?
3. Does the popularity of a vehicle depend on its colour?

Variable 1	Variable 2
\(1\)	\(1\)
\(3.5\)	\(4.5\)
\(3\)	\(6\)
\(5\)	\(1\)
\(2\)	\(4\)

The table shows recent test scores for a science class. The first test score is for a practice test, and the second score is for the final test.

Practice Test	$93$	$20$	$50$	$72$	$97$	$15$	$87$	$46$	$75$	$22$	$28$	$49$	$65$	$50$	$25$	$20$	$44$	$48$
Final Test	$84$	$57$	$50$	$89$	$100$	$60$	$92$	$76$	$57$	$85$	$57$	$72$	$68$	$56$	$52$	$60$	$73$	$53$

Was the mean score higher on the practice test or on the final test? What is the difference between the two mean scores?
What percentage of the students improved from the practice test to the final test? Which student showed the largest improvement?
Create a scatter plot of the data with the practice test score on the horizontal axis and the final test score on the vertical axis. Can you answer any of the questions from part a) or part b) more easily using the graph instead of the data table? Explain.
Can you describe the shape of the data points as a whole? What information can you read off of this graph?

The ages and heights of people randomly selected from a shopping mall are displayed in the following table.

Age (years)	$21$	$9$	$27$	$19$	$16$	$13$	$20$	$11$	$17$	$34$	$23$	$13$	$15$	$47$
Height (cm)	$166$	$126$	$153$	$173$	$139$	$138$	$166$	$130$	$159$	$160$	$146$	$163$	$144$	$156$

Display the ages in a histogram.
Display the heights in a histogram.
Explain why a line graph is not an appropriate way to graph the age and height data together.
Graph the data using a scatter plot. Explain your choice of which variable to put on the horizontal axis.

Is it possible that all of the points in a particular scatter plot lie on a single straight line? If so, what would that indicate?
In each part below, you are given an empty table that relates three variable quantities that can be recorded for one individual. What kind of data will be collected for each variable? Can you use your knowledge of scatter plots to graph all three variables on one scatter plot to compare the quantities? Explain.
1. Age Vision Score Reaction Time
2. Age Arm Length Leg Length

Here is data collected from $10$ Canadian residents.

Individual	Age	Height	Salary	City of Residence	City of Birth	Number of Pets	Car Owner
$1$	$33$	$165$ cm	$$62~900$	Waterloo, CA	Waterloo, CA	$0$	Yes
$2$	$60$	$168$ cm	$$68~800$	Toronto, CA	Halifax, CA	$1$	Yes
$3$	$45$	$179$ cm	$$92~400$	Vancouver, CA	Seattle, USA	$1$	Yes
$4$	$38$	$164$ cm	$$65~500$	Toronto, CA	Montréal, CA	$2$	No
$5$	$30$	$162$ cm	$$56~200$	Winnipeg, CA	Regina, CA	$0$	Yes
$6$	$25$	$171$ cm	$$35~500$	Vancouver, CA	Calgary, CA	$3$	No
$7$	$42$	$159$ cm	$$45~600$	Hamilton, CA	Toronto, CA	$0$	Yes
$8$	$16$	$163$ cm	$$0$	Toronto, CA	Detroit, USA	$0$	Yes
$9$	$57$	$166$ cm	$$89~450$	Toronto, CA	Ottawa, CA	$2$	Yes
$10$	$29$	$175$ cm	$$96~100$	Ottawa, CA	Kingston, CA	$1$	No

Study the table and make as many graphs as you can to appropriately display sections of this data. Can you display some of this data in a circle graph, a line graph, a bar graph, or a histogram? Can you compare two of the quantities using a scatter plot? Explain why you chose each particular graph.

Temperature	Drink Sales (\($\))
\(12^{\circ}\)C	\(200\)
\(14^{\circ}\)C	\(220\)
\(18^{\circ}\)C	\(300\)
\(20^{\circ}\)C	\(350\)
\(26^{\circ}\)C	\(450\)

Practice Test	\(93\)	\(20\)	\(50\)	\(72\)	\(97\)	\(15\)	\(87\)	\(46\)	\(75\)	\(22\)	\(28\)	\(49\)	\(65\)	\(50\)	\(25\)	\(20\)	\(44\)	\(48\)
Final Test	\(84\)	\(57\)	\(50\)	\(89\)	\(100\)	\(60\)	\(92\)	\(76\)	\(57\)	\(85\)	\(57\)	\(72\)	\(68\)	\(56\)	\(52\)	\(60\)	\(73\)	\(53\)

Age (years)	\(21\)	\(9\)	\(27\)	\(19\)	\(16\)	\(13\)	\(20\)	\(11\)	\(17\)	\(34\)	\(23\)	\(13\)	\(15\)	\(47\)
Height (cm)	\(166\)	\(126\)	\(153\)	\(173\)	\(139\)	\(138\)	\(166\)	\(130\)	\(159\)	\(160\)	\(146\)	\(163\)	\(144\)	\(156\)

Individual	Age	Height	Salary	City of Residence	City of Birth	Number of Pets	Car Owner
\(1\)	\(33\)	\(165\) cm	\($62~900\)	Waterloo, CA	Waterloo, CA	\(0\)	Yes
\(2\)	\(60\)	\(168\) cm	\($68~800\)	Toronto, CA	Halifax, CA	\(1\)	Yes
\(3\)	\(45\)	\(179\) cm	\($92~400\)	Vancouver, CA	Seattle, USA	\(1\)	Yes
\(4\)	\(38\)	\(164\) cm	\($65~500\)	Toronto, CA	Montréal, CA	\(2\)	No
\(5\)	\(30\)	\(162\) cm	\($56~200\)	Winnipeg, CA	Regina, CA	\(0\)	Yes
\(6\)	\(25\)	\(171\) cm	\($35~500\)	Vancouver, CA	Calgary, CA	\(3\)	No
\(7\)	\(42\)	\(159\) cm	\($45~600\)	Hamilton, CA	Toronto, CA	\(0\)	Yes
\(8\)	\(16\)	\(163\) cm	\($0\)	Toronto, CA	Detroit, USA	\(0\)	Yes
\(9\)	\(57\)	\(166\) cm	\($89~450\)	Toronto, CA	Ottawa, CA	\(2\)	Yes
\(10\)	\(29\)	\(175\) cm	\($96~100\)	Ottawa, CA	Kingston, CA	\(1\)	No

Age	Vision Score	Reaction Time

Age	Arm Length	Leg Length