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11.07 Investigating data with scatter plots

Worksheet
Scatter plots
1

The following scatterplot shows the height and weight of six students:

a

How tall is the student who weighs \\45kg?

b

How tall is the tallest student?

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\text{Height (cm)}
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\text{Weight (kg)}
2

The following scatterplot shows the height and weight of six children:

a

What is the difference in height between the tallest and shortest child?

b

Does it look like there is a connection between the height and weight of children?

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\text{Height (cm)}
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\text{Weight (kg)}
3

The following scatterplot shows the height and number of storeys of six buildings:

a

How many storeys does the tallest building have?

b

Determine whether the following statements about the plot are true:

i

The shortest building has the most number of storeys.

ii

The tallest building has the most number of storeys.

iii

The tallest building has the least number of storeys.

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\text{Number of storeys}
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\text{Height (m)}
4

The following scatterplot shows the shoe size and number of pets of six students:

a

One student, Robert, wears size 7 shoes. How many pets does he own?

b

Luigi has 12 pets. Hannah has 11 pets. Who wears bigger shoes?

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\text{Shoe size}
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\text{Number of pets}
5

Six students were asked how many people there are in their family, and the number of trees planted in their garden and their responses were plotted on the following graph:

Each dot represents one student.

a

One student, Jack, has 7 people in his family. How many trees are planted in his garden?

b

Do you think there is a connection between the number of people in a student's family and the number of trees in their garden? Explain your answer.

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\text{Number of people in the family}
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\text{Number of trees in the garden}
6

The price of ten houses are graphed against the house's land area on the following graph:

Describe the relationship between land area and house price in the data.

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\text{Area } (m^2)
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\text{Price}
7

A cafe records the number of soups sold and the daily maximum temperature on the following graph:

Describe the relationship between temperature and soups sold in the data.

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\text{Temperature}
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\text{Price}
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A company records the height and annual salary of ten employees on the following graph:

Describe the relationship between height and salary in the data.

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\text{Height (cm)}
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\text{Price}
9

What can we conclude from the following scatterplot?

10

The scatter plot shows the relationship between sea temperature and the amount of healthy coral.

a

Which variable is the dependent variable?

b

Which variable is the independent variable?

11

Scientists were looking for a relationship between the number of hours of sleep and the effect it has on motor and process skills. Subjects slept for different amounts of time, and then did the same driving challenge in which their reaction time was measured. The table shows the results:

a

Construct a scatter plot for this data.

b

Describe the relationship between amount of sleep and reaction time.

Amount of sleep (hours)Reaction time (seconds)
\qquad \qquad \enspace 4\qquad \qquad 1.65
\qquad \qquad \enspace 5\qquad \qquad 1.5
\qquad \qquad \enspace 6\qquad \qquad 1.35
\qquad \qquad \enspace 7\qquad \qquad 1.25
\qquad \qquad \enspace 8\qquad \qquad 1.25
\qquad \qquad \enspace 9\qquad \qquad 1.05
12

The land size of a sample of properties and their selling price were graphed on the scatter plot below:

a

Which size range that contains the most properties?

A
2500 - 3500 \text{ sq ft}
B
3500 - 5500 \text{ sq ft}
C
1000 - 2500 \text{ sq ft}
b

Another property that is not represented in the scatter plot is sold for \$670\,000 and measured 3400 square feet in size. Is this consistent with the relationship shown in the graph?

13

Four different classes with four different professors had the same final exam. The exam results and number of classes attended by each student is displayed for each class below.

Determine whether the following graphs suggest that attending class improves the final exam mark.

a
b
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d
14

A chemical company is testing the effect of different chemicals on slowing the the melting of snow. They are currently testing four different chemicals with the results showing how much ice is remaining after 3 hours at a certain temperature.

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D

A snow sculpture company wants a chemical that will keep snow from melting.

a

Which chemical should they choose to ensure that at least half of the snow is still there after 3 hours?

b

If the company operates at a temperature of 3 \degree\text{C} to 4\degree\text{C}, Which chemical should they choose?

15

After a maths exam, Uther commented that he left out Question 10 because it was not relevant to the topics that were assessed, but that the other questions were fine. The teacher felt that Question 10 and Question 7 were assessing the same skills, but decided to look at the results of students across all 8 classes. She plotted the percentage who had gotten Question 10 correct against the percentage who had gotten Question 7 correct.

a

Determine whether the following describes the data:

i

There is no relationship between students' performance in Q7 and Q10.

ii

Students performed similarly in Q7 and Q10.

iii

Students who performed poorly in Q7 performed well in Q10.

b

Let's assume that Uther performed exceptionally well in every other question. In which region should the teacher expect Uther's data point to be in?

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Outcomes

VCMSP352

Use scatter plots to investigate and comment on relationships between two numerical variables

VCMSP353

Investigate and describe bivariate numerical data where the independent variable is time.

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