State the type of data most suitable for a Pareto chart.
A Pareto chart has two vertical axes.
Which graph is for the left vertical axis?
Which graph is for the right vertical axis?
State whether a Pareto chart would be useful in the following circumstances:
Displaying the same data using both a column graph and a line graph.
Determining the distribution in a set of numerical data.
Analysing the mean, median and mode of a set of data.
Determining the sources of the most defects in a product.
Consider the following Pareto chart:
Is the gradient increasing or decreasing from left to right?
In which part of the graph is the gradient steepest?
The Pareto chart shows the total medal tally of each country at the Winter Olympics:
What does the height of each column represent?
What does the line graph represent?
The major reasons flights were delayed at an international airport over a one month period are shown in the following Pareto chart:
Find the number of flights delayed due to the plane needing to be refueled.
Estimate the percentage of flights that arrived late because of extreme weather.
The following graph shows the sales of various products in a furniture store:
State the three products that together make up nearly 90\% of sales at the store.
Estimate, to the nearest ten thousand, the combined value of sales for the store.
The store is deciding on a promotion to boost their sales. For the same amount of money, which of the following promotions should they choose?
A promotion that would double the sales of rugs only.
A mattress promotion that would increase only mattress sales by 50\%.
General promotion that would increase sales for all products by 25\%.
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:
Find the total number of people on the carriage (excluding Bill).
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.
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.
Find the total number of overheated cars that were brought into the centre.
Find the percentage of cars that had a worn seal.
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?
Susana attached an energy metre 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:
Find the total of her quarterly electricity bill.
How much more did the air conditioner cost to run than the oven?
Find the percentage of the total bill that was due to the oven. Round your answer to the nearest whole percent.
Which single source of electricity cost would Susana need to stop using to reduce her bill by approximately 10\%?
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 to marked grid lines.
What percentage of monthly expenses goes towards the three least contributing expenses.
After expenses the family is able to save \$870 each month, determine their net monthly income.
Is the bar graph or the line graph more useful for interpreting how much each expense contributes relative to the total expense?
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.
Find the total number of customers who expressed dissatisfaction last month.
Using the bar section of the Pareto chart, find the percentage of customer complaints made up by the three most frequent complaints. Round your answer to the nearest percentage.
Pareto wants to significantly improve customer satisfaction in the next month. What single change would improve customer satisfaction the most?
What percentage of customer complaints are related to the composition of the burrito and may be resolved by reviewing how their chefs make their burritos? Round your answer to the nearest percentage.
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.
Find the difference between the number of the most and least caught fish species.
Perch are often targeted in commercial fishing. The marine scientist is concerned about whether their numbers have decreased relative to other species. Determine the percentage of fish caught that were Perch.
It is expected that population of mullet and perch will have a cumulative percentage of 50\%. How different is this to the cumulative percentage the marine scientist observed?
A vehicle service centre wants to investigate the main causes of an engine overheating. Data on the cause was collected and organised into the table below:
| Cause | Frequency | Cumulative frequency | Cumulative percentage |
|---|---|---|---|
| \text{Damaged radiator core} | 31 | 31 | |
| \text{Faulty fans} | 20 | 51 | |
| \text{Faulty thermostat} | 8 | 59 | |
| \text{Loose fan belt} | 5 | 64 | |
| \text{Damaged radiator fins} | 4 | 68 | |
| \text{Coolant leakage} | 3 | 71 | |
| \text{Total} | 71 | - | - |
Complete the table by finding the cumulative percentage to the nearest whole percent.
Which column in the table is used to create the vertical bars in the Pareto chart?
Which column in the table is used to create the line graph of the Pareto chart?
Construct a Pareto chart of the data.
How many vehicles had a faulty thermostat?
Which two faulty components contributed the most to overheating?
Find the percentage of overheating cases that were due to a loose fan belt.
A group of 142 students were asked to write down what they thought was the most important environmental issue in Australia. The results were collected and organised into the table below:
| Environmental issue | Frequency | Cumulative frequency | Cumulative percentage |
|---|---|---|---|
| \text{Climate change} | 64 | 64 | |
| \text{Waste generation and processing} | 35 | 99 | |
| \text{Future food supplies} | 18 | 117 | |
| \text{Deforestation} | 14 | 131 | |
| \text{Air pollution} | 8 | 139 | |
| \text{Flooding} | 2 | 141 | |
| \text{Poor drinking water} | 1 | 142 | |
| \text{Total} | 142 | - | - |
Complete the table by finding the cumulative percentage to the nearest whole percent.
Construct a Pareto chart of the data.
What part of a Pareto chart is generated by the frequency column?
Which axis of a Pareto chart displays the frequency of responses for each issue?
Find the percentage of students surveyed thought the top two issues in the table were the most important. Give your answer as a percentage to the nearest whole number.
Find the change in percentage support between the first and second top issue. Give your answer as a percentage to the nearest whole number.
A group of 165 adults were asked about the issues they thought were most important in Australia. The results were collected and organised into the table below:
| Issue | Frequency | Cumulative frequency | Cumulative percentage |
|---|---|---|---|
| \text{Cost of living} | 61 | 37 | |
| \text{Health care} | 54 | ||
| \text{Environment} | 17 | 132 | |
| \text{Public transport} | 9 | ||
| \text{Personal debt} | 9 | 150 | 91 |
| \text{Defence} | 8 | 158 | |
| \text{Taxation} | 7 | 100 | |
| \text{Total} | 165 | - | - |
Complete the table by finding the missing values. Round the cumulative percentage to the nearest whole percent.
Construct a Pareto chart of the data.
How many issues made up the top 80\% of responses on the survey?
How many issues made up the remaining 20\% of responses on the survey?
Find the percentage of people surveyed chose "Environment" as the top issue.
The following table was used to record incoming complaints about the public transport system:
| Complaint type | Number of complaints | Cumulative frequency | Cumulative percentage |
|---|---|---|---|
| \text{Information about delays} | 19 | 33 | |
| \text{Frequency of service} | 15 | 59 | |
| \text{Delays in service} | 12 | 46 | |
| \text{Journey time} | 6 | 52 | |
| \text{Bus shelter comfort} | 4 | ||
| \text{Seat availability} | 2 | ||
| \text{Total} | 58 | - | - |
Complete the table by finding the missing values. Round the cumulative percentage to the nearest whole percent.
Construct a Pareto chart of the data.
The public transport system has an employee who reads the complaints. How many complaint types will they have to read if they aim to see 75\% of all complaints?
Which three factors contribute to over 75\% of complaints?
Between which two percentage values is the gradient of the line graph the steepest?