Scatter Plots

Show your work for each problem.

1.
A gardener studies how the hours of sunshine per day affect the growth of tomato plants. Which variable goes on the $x$ -axis of the scatter plot?
1. a)Number of plants
2. b)Growth of the plants
3. c)Date of the measurement
4. d)Hours of sunshine
Answer: Hours of sunshine
Sunshine may affect how much the plants grow, not the other way round. So hours of sunshine is the explanatory variable and goes on the $x$ -axis; growth is the response variable on the $y$ -axis.
2.
In a scatter plot, the points go down from left to right. What is the direction of the association?
1. a)Negative
2. b)Non-linear
3. c)Positive
4. d)No direction
Answer: Negative
Going down from left to right means that larger $x$ -values go with smaller $y$ -values: a negative association. Non-linear describes the form, not the direction.
3.
A scatter plot shows the points $(1, 50)$ , $(2, 58)$ , $(3, 65)$ , $(4, 70)$ and $(5, 78)$ , with hours studied on the $x$ -axis and test score on the $y$ -axis. What score did the student who studied 3 hours get?
Answer: 65
The first number of each point is $x$ (hours), the second is $y$ (score). The point with $x = 3$ is $(3, 65)$ , so the score was $65$ .
4.
A table lists the height and the weight of 24 students, one row per student. How many points will the scatter plot have?
Answer: 24
Each student's height and weight make one point, so 24 students give $24$ points. Two variables do not mean two points per student: both values belong to the same dot.
5.
A class plots hours of sleep ( $x$ ) against test score ( $y$ ). Lena slept 7 hours and scored 82. Plot her point step by step.
Answer: (7, 82)
1. Which axis shows the test score? y-axis
2. How far to the right along the $x$ -axis do you go? 7
3. How far up do you go before drawing the dot? 82
6.
The $y$ -values in a table go from $12$ to $47$ . Your $y$ -axis starts at $0$ and has $10$ grid squares. Choose a step for one square.
Answer: 5
1. What is the largest $y$ -value the axis must reach? 47
2. What is $47 \div 10$ ? 4.7
3. Which nice step (1, 2, 5 or 10) is the smallest one that is at least $4.7$ ? 5
4. With this step, what value is at the top of the axis after 10 squares? 50
7.
The points $(1, 1)$ , $(2, 4)$ , $(3, 9)$ , $(4, 16)$ and $(5, 25)$ are plotted. What is the form of the pattern?
1. a)No pattern
2. b)Negative linear
3. c)Non-linear (curved)
4. d)Linear
Answer: Non-linear (curved)
The increases are $3, 5, 7, 9$ : they keep growing, so the points bend upward. Equal steps in $x$ with unequal changes in $y$ mean a non-linear (curved) form.
8.
The $y$ -values of a data set go from $0$ to $120$ . The $y$ -axis is divided into $6$ equal intervals. What value does each interval represent?
Answer: 20
$120 \div 6 = 20$ . The axis is labeled $0, 20, 40, 60, 80, 100, 120$ : equal steps of $20$ .
9.
The points of a scatter plot lie very close to a straight line that goes down from left to right. How do you describe the association?
1. a)Weak, negative, linear
2. b)Strong, positive, linear
3. c)Strong, negative, linear
4. d)Weak, positive, non-linear
Answer: Strong, negative, linear
Very close to the pattern means strong, going down means negative and a straight line means linear: a strong, negative, linear association.
10.
A scatter plot has the points $(2, 14)$ , $(3, 18)$ , $(5, 21)$ , $(6, 25)$ , $(8, 30)$ and $(9, 33)$ . How many points have a $y$ -value greater than $20$ ?
Answer: 4
The $y$ -values are $14, 18, 21, 25, 30, 33$ . Greater than $20$ : $21, 25, 30, 33$ , so $4$ points lie above the line $y = 20$ .
11.
Describe the scatter plot of $(1, 30)$ , $(2, 26)$ , $(3, 23)$ , $(4, 19)$ , $(5, 15)$ : find its direction and form, then the total change in $y$ from $x = 1$ to $x = 5$ .
Answer: -15
1. As $x$ increases, $y$ goes $30, 26, 23, 19, 15$ . Is the direction positive or negative? negative
2. The changes are $-4, -3, -4, -4$ . Is the form linear or non-linear? linear
3. What is the total change in $y$ from $x = 1$ to $x = 5$ ? -15
12.
Is the pattern of the points $(0, 1)$ , $(1, 2)$ , $(2, 4)$ , $(3, 8)$ , $(4, 16)$ linear or non-linear? Compare the increases.
Answer: non-linear
1. By how much does $y$ increase from $x = 0$ to $x = 1$ ? 1
2. By how much does $y$ increase from $x = 3$ to $x = 4$ ? 8
3. The steps in $x$ are equal, but the increases grow. What is the form? non-linear
13.
A scatter plot shows distance to work (km, $x$ ) and travel time (minutes, $y$ ) for nine people: $(2, 8)$ , $(3, 10)$ , $(3, 12)$ , $(4, 11)$ , $(15, 35)$ , $(16, 37)$ , $(16, 38)$ , $(17, 36)$ , $(18, 40)$ . Describe the clusters and the gap.
Answer: 11
1. How many people live 4 km or less from work? 4
2. How many people are in the cluster with $x$ from 15 to 18? 5
3. How wide is the gap on the $x$ -axis between the two clusters (from 4 km to 15 km)? 11
14.
A scatter plot shows the points $(1, 3)$ , $(2, 5)$ , $(3, 7)$ , $(4, 9)$ , $(5, 2)$ and $(6, 13)$ . Which point is an outlier?
1. a) $(4, 9)$
2. b) $(2, 5)$
3. c) $(5, 2)$
4. d) $(6, 13)$
Answer: $(5, 2)$
The points rise by $2$ each time: $3, 5, 7, 9, \ldots, 13$ . At $x = 5$ the pattern gives $11$ , but the point is $(5, 2)$ , far below. Even $(6, 13)$ fits the pattern, so $(5, 2)$ is the outlier.
15.
The $x$ -values of the points in a scatter plot are $1, 2, 3, 4, 11, 12, 13$ . They form two clusters. How wide is the gap between them (from the largest $x$ of the left cluster to the smallest $x$ of the right cluster)?
Answer: 7
The left cluster is $1$ to $4$ , the right cluster $11$ to $13$ . Between them no points lie on an interval of $11 - 4 = 7$ units.
16.
Check whether $(5, 15)$ is an outlier in the scatter plot of $(1, 10)$ , $(2, 20)$ , $(3, 30)$ , $(4, 40)$ , $(5, 15)$ .
Answer: Yes, $(5, 15)$ is an outlier ( $35$ below the pattern)
1. In the first four points, by how much does $y$ increase each time $x$ goes up by 1? 10
2. If the pattern continued, what would $y$ be at $x = 5$ ? 50
3. How far below the pattern is the real point $(5, 15)$ ? 35
4. Is $(5, 15)$ an outlier? yes
17.
You plot height ( $x$ ) against shoe size ( $y$ ) for a class. Heights go from $150$ to $190$ cm and shoe sizes from $36$ to $46$ . The $x$ -axis starts at $150$ with $8$ squares, the $y$ -axis starts at $36$ with $5$ squares. Find both steps.
Answer: 2
1. What is the range of the heights? 40
2. What step does each of the 8 squares on the $x$ -axis represent? 5
3. What is the range of the shoe sizes? 10
4. What step does each of the 5 squares on the $y$ -axis represent? 2
18.
A scatter plot of hours of practice against test score for 20 students shows 12 points in a cluster near $(2, 60)$ , 7 points in a cluster near $(6, 85)$ and one point at $(6, 30)$ . Analyze the clusters and the outlier.
Answer: 35
1. How many points are in the two clusters together? 19
2. How many points are outliers? 1
3. What percent of the students are in the cluster near $(6, 85)$ ? 35