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7.05 Stacked area graphs, Radar graphs and Pareto charts

Worksheet
Radar graphs
1

The annual sales of two products are shown in the following radar chart:

a

What were the average monthly sales of product A to the nearest cent?

b

What were the average monthly sales of product B to the nearest cent?

c

What was the range of the monthly sales of product A?

d

What was the range of the monthly sales of product B?

2

The annual sales of two products are shown in the following radar chart:

a

How many units of Product B were sold in March?

b

How many units of Product A were sold in November?

c

How many units of Product A were sold throughout the entire year?

3

The following table shows the monthly sales of two products:

MonthProduct A (number sold)Product B (number sold)
\text{January}\quad \qquad \quad \enspace 10\quad \qquad \quad \enspace 7
\text{February}\quad \qquad \quad \enspace 4\quad \qquad \quad \enspace 6
\text{March}\quad \qquad \quad \enspace 6\quad \qquad \quad \enspace 5
\text{April}\quad \qquad \quad \enspace 1\quad \qquad \quad \enspace 8
\text{May}\quad \qquad \quad \enspace 3\quad \qquad \quad \enspace 8
\text{June}\quad \qquad \quad \enspace 7\quad \qquad \quad \enspace 4
\text{July}\quad \qquad \quad \enspace 10\quad \qquad \quad \enspace 3
\text{August}\quad \qquad \quad \enspace 2\quad \qquad \quad \enspace 5
\text{September}\quad \qquad \quad \enspace 4\quad \qquad \quad \enspace 4
\text{October}\quad \qquad \quad \enspace 9\quad \qquad \quad \enspace 7
\text{November}\quad \qquad \quad \enspace 3\quad \qquad \quad \enspace 7
\text{December}\quad \qquad \quad \enspace 8\quad \qquad \quad \enspace 9

Construct a radar chart that represents the two sets of data.

Stacked area graphs
4

The revenue generated from a company's three major products is shown in the following stacked area chart:

a

Find the revenue generated by Product C in the first month.

b

Find the maximum revenue generated by Product A.

c

Determine the difference between the revenue generated in month 4 and the revenue generated in month 5 by Product B.

d

Calculate the total revenue generated by Product C during the 7 months.

e

By how much did the revenue generated by Product C exceed that of Product A in the 7th month?

5

The revenue generated from a company's three major products are shown in the following table. Construct a stacked area graph that represents the data.

\text{Month}\text{Product A }(\$000)\text{Product B }(\$000)\text{Product C }(\$000)
\text{January} \qquad \quad \enspace12 \qquad \quad \enspace25 \qquad \quad \enspace12
\text{February} \qquad \quad \enspace20 \qquad \quad \enspace30 \qquad \quad \enspace18
\text{March} \qquad \quad \enspace18 \qquad \quad \enspace28 \qquad \quad \enspace29
\text{April} \qquad \quad \enspace16 \qquad \quad \enspace34 \qquad \quad \enspace10
\text{May} \qquad \quad \enspace22 \qquad \quad \enspace37 \qquad \quad \enspace15
\text{June} \qquad \quad \enspace11 \qquad \quad \enspace35 \qquad \quad \enspace26
\text{July} \qquad \quad \enspace13 \qquad \quad \enspace31 \qquad \quad \enspace17
\text{August} \qquad \quad \enspace17 \qquad \quad \enspace29 \qquad \quad \enspace13
\text{September} \qquad \quad \enspace20 \qquad \quad \enspace27 \qquad \quad \enspace19
\text{October} \qquad \quad \enspace19 \qquad \quad \enspace30 \qquad \quad \enspace24
\text{November} \qquad \quad \enspace16 \qquad \quad \enspace26 \qquad \quad \enspace20
\text{December} \qquad \quad \enspace16 \qquad \quad \enspace34 \qquad \quad \enspace28
6

The following graph shows the recorded music revenue per capita in the United States from 1973-2009:

a

Has US recorded music revenue increased or decreased since 2004?

b

Have CD sales increased or decreased since 2004?

c

Have digital music sales increased or decreased since 2004?

d

Has the booming growth in digital music sales been high enough to make up for the drop in CD sales?

7

Answer the following questions based on the graph:

a

According to the graph, the resting (before exercise) heart rate of a fit person lies between which two values?

b

What is the peak heart rate of an unfit person?

c

Before exercising, John measures his pulse and counts 26 beats in a 20 second time period. According the graph, is John considered to be a fit or unfit person?

Pareto charts
8

The Pareto chart shows the total medal tally of each country at the Winter Olympics:

a

What does the height of each column represent?

b

What does the line graph represent?

9

A marine scientist spent the day fishing to collect data on the range of species in an enclosed dam. She recorded the number of each fish species that were caught, and constructed the following Pareto chart. Assume that the bars are in line with the gridlines, or exactly halfway between gridlines.

a

Find the number of Bream caught.

b

Find the number of Bass caught.

c

Find the difference between the number of Bream and Bass caught.

d

Determine the percentage of fish caught that were Bass.

e

Determine the percentage of fish caught that were Mullet.

f

Determine the total percentage of fish caught that were either Mullet or Bass.

g

It is expected that the population of Mullet and Bass will make up 50\% of the fish population. Determine the difference between this percentage and the total percentage the marine scientist observed in part (f).

10

At Pareto's Burritos, the owners regularly ask their customers if and why they are not happy with their burritos. They created the chart below for last month's feedback. Assume that the bars are in line with the labels on the left vertical axis, or exactly halfway between two labels.

a

Find the number of complaints for each of the following reasons of customer dissatisfaction:

i

Wait time

ii

Guac amount

iii

Not fresh

iv

Too spicy

v

Filling amount

vi

Expensive

b

Find the total number of customers who expressed dissatisfaction last month.

c

Identify the following:

i

Most frequent complaint

ii

Second most frequent complaint

iii

Third most frequent complaint

d

Find the percentage of customer complaints made up by the following. Round your answer to the nearest percentage.

i

Most frequent complaint

ii

Second most frequent complaint

iii

Third most frequent complaint

e

Hence, find the percentage of customer complaints made up by the three most frequent complaints.

11

A mechanic recorded the major reasons overheated cars were brought into the centre. The Pareto chart shows the results. Assume that each bar and point either lines up with a given value or is midway between.

a

Find the number of cars brought to the centre due to the following faulty parts:

i

Radiator

ii

Fan

iii

Thermostat

iv

Fan belt

v

Coolant

vi

Seal

b

Find the total number of overheated cars that were brought into the centre.

c

Find the percentage of cars brought to the centre due to the following faulty parts:

i

Radiator

ii

Fan

iii

Thermostat

iv

Fan belt

v

Coolant

vi

Seal

d

The mechanic put in an order for parts to fix the cars with a faulty fan, a broken fan belt or a crack in the radiator. What percentage of all cars brought in did he place an order for?

12

Bill caught the train and noted what activity each person in his carriage (excluding himself) was doing between the next two stops. The following Pareto chart shows the results:

a

Find the total number of people on the carriage (excluding Bill).

b

Using the bar section of the Pareto chart, find the percentage of people on the carriage (excluding Bill) that make up the three most common activities. Round your answer to the nearest whole percent.

13

The major reasons flights were delayed at an international airport over a one month period are shown in the following Pareto chart:

a

Find the number of flights delayed due to the plane needing to be refuelled.

b

Estimate the percentage of flights that arrived late because of extreme weather.

14

A family analysed how much of their monthly income goes towards various expenses. The following Pareto chart shows the results. Assume that the height of each bar is either on a marked grid line, or exactly halfway between two marked grid lines.

a

What percentage of monthly expenses goes towards the three least contributing expenses.

b

After expenses the family is able to save \$870 each month, determine their net monthly income.

c

Is the bar graph or the line graph more useful for interpreting how much each expense contributes relative to the total expense?

15

Susana attached an energy meter to the household items that use electricity to determine how much each contributes to her quarterly electricity bill. The results are shown in the following Pareto chart:

a

Find the total of her quarterly electricity bill.

b

How much more did the air conditioner cost to run than the oven?

c

Find the percentage of the total bill that was due to the oven. Round your answer to the nearest whole percent.

d

Which single source of electricity cost would Susana need to stop using to reduce her bill by approximately 10\%?

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Outcomes

1.4.1

interpret information presented in graphs, such as: conversion graphs, line graphs, step graphs, column graphs and picture graphs

1.4.3

discuss and interpret graphs found in the media and in factual texts

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