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Bar Chart

Competitive Mathematics · Data Interpretation

7 Part2 worked examples12 practice questions

A bar chart has one bar for each category (year, city, company), and its height is proportional to the value. A taller bar means a bigger value, so you can see at a glance which is bigger; exact values are read from the top of the bar or from the axis scale. There are four main kinds: simple (one variable), clustered (several bars side by side for each category), sub-divided/stacked (one bar split into parts) and the histogram (frequencies of classes).

The three key formulas for bar charts
1

Reading a bar chart

Simple and clustered

Reading a bar’s value, totals, averages and differences.

One bar, one value

Check the scale and unit first

The basic rules for a simple bar chart.

Below is a simple bar chart of a shop’s sales (₹ lakh) over four years.

020406080201940202050202145202260Sales
Annual sales of a shop (₹ lakh)
  • Axes first: check the vertical scale (does it start at 0?) and the unit. If values are not written on the bars, read them off the scale.
  • Total = sum of all bars; average = total ÷ number of bars; difference = taller bar − shorter bar.
  • Clustered chart: each category has several bars — choose the bar of the right series (shade); do not forget the legend (the key below).
Example 1 · Basic
From the chart above, the total sales over the four years and the average annual sales.
Solution, step by step
  1. 1Total lakh.
  2. 2Average lakh
Answer ₹ 195 lakh; ₹ 48.75 lakh
Example 2 · Standard
From the chart above, the percent increase from 2019 to 2022, and the year with the highest percent increase over its previous year.
Solution, step by step
  1. 12019 to 2022: .
  2. 2Year over year: in 2020; in 2021; in 2022 ⟹ 2022 is highest
Answer 50%; 2022

Bar chart: Sugar output of a factory (in thousand tonnes). Study the chart and answer the questions.

05010015020020161102017115201812520191302020145Output
Sugar output of a factory (in thousand tonnes)
BasicTry it yourself first
What is the value of “Output” in 2018 (in thousand tonnes)?
BasicTry it yourself first
What is the total of “Output” over all the categories (in thousand tonnes)?
BasicTry it yourself first
Find the average value of “Output” (in thousand tonnes, to one decimal).
BasicTry it yourself first
Find the difference between the values of “Output” in 2019 and 2018 (in thousand tonnes).
BasicTry it yourself first
Find the ratio of “Output” in 2020 to “Output” in 2019.
StandardTry it yourself first
Find the percent increase in “Output” from 2017 to 2020. (to one decimal)

Bar chart: Exports and imports of a country (₹ crore). Study the chart and answer the questions.

0100200300400500600201633036020173303902018410410201948046020204004102021410540ExportsImports
Exports and imports of a country (₹ crore)
BasicTry it yourself first
What is the value of “Exports” in 2020 (in ₹ crore)?
BasicTry it yourself first
What is the total of “Exports” over all the categories (in ₹ crore)?
BasicTry it yourself first
Find the total of all the series in 2019 (in ₹ crore).
BasicTry it yourself first
Find the difference between the values of “Exports” in 2018 and 2017 (in ₹ crore).
BasicTry it yourself first
Find the average value of “Imports” (in ₹ crore, to one decimal).
BasicTry it yourself first
Find the ratio of “Exports” in 2016 to “Exports” in 2020.
2

Growth and comparison

Percent growth, ratio, average

Percent change from bars, the year of highest growth and comparing two series.

Comparing two series

Look at the pair of bars in every year

Charts like demand vs production or exports vs imports.

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3

Sub-divided (stacked) bar chart

One bar, several parts

Where one bar is split into parts — each part’s value, the bar’s total and a part’s percent.

Parts and total

A segment’s height is its value

The rules for a stacked chart.

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4

Histogram

Marks classes and frequency

Data grouped into classes: counts, percents, the modal class and the average.

Class and frequency

Bars touch; class widths are equal

The rules for a histogram.

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5

Traps and fast tricks

Slips · tricks

Where marks go in bar-chart questions.

The commonest mistakes

Seven traps

The slips that cost marks.

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Fast tricks

Estimating from the bars

Habits for speed.

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6

The practice ladder

Basic → standard → advanced

New bar charts and questions of every type, in three levels.

Level 1 — Basic

Reading bars, totals, averages, differences

One-step questions.

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Level 2 — Standard

Growth, comparison, share

Exam-level questions.

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Level 3 — Advanced

Many steps and mixed charts

Questions at the hard end of competitive exams.

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7

Revision — formula cards

Flip each card and test yourself

Read the front, think, then flip.

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