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Mixed Graph

Competitive Mathematics · Data Interpretation

5 Part3 worked examples18 practice questions

Often the whole story does not fit in one display. For example, the total employees may be shown in a pie chart and the ratio of men to women in a separate table. Such a question is a mixed graph, and the same four combinations appear: pie + table, bar + line, table + bar, pie + line. The key never changes: the first display gives a total (a count), the second gives a part of it (a percent or ratio). Do the arithmetic in that order — first find the total, then apply the rate.

The formula that joins the two displays
1

Pie chart + table

Share × rate

The item total from the pie chart, its part from the percent or ratio in the table.

First the total, then the rate

Two steps for every item

Questions with a pie chart plus a percent or ratio table.

An organisation has 2000 employees in all. The pie chart shows each department’s share and the table the ratio of men to women in each.

HR 10%IT 30%Marketing 25%Production 20%Finance 15%
Distribution of employees by department (total 2000)
DepartmentHRITMarketingProductionFinance
Men : Women2 : 33 : 21 : 13 : 22 : 1
  • Step 1 — the department’s total: the pie percent × total (or angle ÷ 360 × total).
  • Step 2 — the part: for a ratio the first group is and the second of it; for a percent take percent × the department’s total.
  • If the total over several departments is asked, find each department’s part separately and add — adding ratios directly is wrong.
  • For “what percent of the total” use the right denominator: that department’s total or the overall total — read the wording carefully.
Example 1 · Basic
From the displays above, the number of men in the Marketing department.
Solution, step by step
  1. 1Marketing total of .
  2. 2Ratio ⟹ men
Answer 250
Example 2 · Standard
From the displays above, the ratio of women in HR to men in IT.
Solution, step by step
  1. 1HR: total , ratio ⟹ women .
  2. 2IT: total , ratio ⟹ men ; ratio
Answer 1 : 3
Example 3 · Standard
From the displays above, the women of Production are what percent of all employees?
Solution, step by step
  1. 1Production: total , ratio ⟹ women .
  2. 2
Answer 8%

Mixed graph: Employees in the departments of an organisation. The first display gives total employees, the second ratio of men to women. Use both together to answer.

HR 10%IT 5%Marketing 45%Production 25%Finance 15%
Employees in the departments of an organisation — distribution of total employees (total 1,200)
ItemHRITMarketingProductionFinance
ratio of men to women1 : 33 : 14 : 14 : 13 : 7
BasicTry it yourself first
Find the men in “Production”.
BasicTry it yourself first
Find the women in “Production”.
StandardTry it yourself first
Find the ratio of the women in “Production” to the men in “Marketing”.
StandardTry it yourself first
What percent of the total of “IT” are women? (to one decimal)
StandardTry it yourself first
The women of “Production” are what percent of the overall total employees? (to one decimal)
StandardTry it yourself first
Find the total women in all the items together.

Mixed graph: Students in the streams of a college. The first display gives total students, the second pass percentage. Use both together to answer.

Arts 40%Commerce 5%Science 20%Computer 20%Management 15%
Students in the streams of a college — distribution of total students (total 1,600)
ItemArtsCommerceScienceComputerManagement
pass percentage (%)65%70%80%70%60%
BasicTry it yourself first
Find the passed students in “Arts”.
BasicTry it yourself first
Find the failed students in “Arts”.
StandardTry it yourself first
Which item has the greatest passed students?
StandardTry it yourself first
What is the total passed students in “Computer” and “Science” together?
StandardTry it yourself first
Taking all the items together, what percent of the total are passed students? (to one decimal)
StandardTry it yourself first
Find the difference between the passed students in “Arts” and “Commerce”.

Mixed graph: Employees in the departments of an organisation. The first display gives total employees, the second ratio of men to women. Use both together to answer.

HR 35%IT 20%Marketing 20%Production 15%Finance 10%
Employees in the departments of an organisation — distribution of total employees (total 1,600)
ItemHRITMarketingProductionFinance
ratio of men to women3 : 77 : 32 : 37 : 31 : 4
AdvancedTry it yourself first
Find the ratio of the women in “Production” to the men in “HR”.
AdvancedTry it yourself first
The women of “IT” are what percent of the overall total employees? (to one decimal)
AdvancedTry it yourself first
Find the total men in all the items together.
AdvancedTry it yourself first
The total of “HR” is approximately what percent of the total of “IT”? (nearest integer)
AdvancedTry it yourself first
Taking all the items together, what percent of the total are women? (to one decimal)
StandardTry it yourself first
Find the difference between the women in “HR” and “Production”.
2

Bar chart + line graph

Quantity and its percent

The quantity from the bar chart, the percent from the line graph; comparing over time.

Quantity × percent, each year

Two figures for every year

When bars show production and the line shows the percent exported.

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3

Traps and fast tricks

Slips · tricks

Where marks go in mixed-graph questions.

The commonest mistakes

Seven traps

The slips that cost marks.

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Fast tricks

Two steps, write both clearly

Habits for speed.

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4

The practice ladder

Basic → standard → advanced

New mixed graphs and questions of every type, in three levels.

Level 1 — Basic

Total → part

One- or two-step questions.

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Level 2 — Standard

Ratio, percent, total

Exam-level questions.

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Level 3 — Advanced

Many steps and mixed calculations

Questions at the hard end of competitive exams.

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5

Revision — formula cards

Flip each card and test yourself

Read the front, think, then flip.

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