Data Representation • Topic 2 of 3

Bar Graphs and Histograms

What is a Bar Graph?

A bar graph (or bar chart) is a visual representation of data using rectangular bars of different heights. The height of each bar represents the frequency of that category.

Features of a Bar Graph:

  • X-axis (horizontal): Categories (e.g., colors, subjects, months)
  • Y-axis (vertical): Frequency or values
  • Bars: Separate rectangles with gaps between them
  • Title: Describes what the graph shows
  • Labels: Name the axes and categories

What is a Histogram?

A histogram is similar to a bar graph but is used for continuous data grouped into class intervals. In a histogram, bars touch each other (no gaps) because the data is continuous.

Bar Graph vs Histogram:

FeatureBar GraphHistogram
Data typeCategorical/discreteContinuous
Bar spacingGaps between barsBars touch each other
X-axisCategories (no order)Number line (ordered)
ExampleFavorite colorsHeights of students

Types of Bar Graphs:

TypeDescription
Vertical Bar GraphBars go upward from horizontal axis
Horizontal Bar GraphBars go sideways from vertical axis
Double/Grouped Bar GraphMultiple bars per category for comparison
Stacked Bar GraphBars divided into parts showing components

Real-life Applications:

  • Comparing sales of different products
  • Showing population of different cities
  • Displaying test scores distribution
  • Analyzing weather patterns
Histogram — Heights of Students (cm) 02468 3140-1445145-1497150-1547155-1593160-164 Frequency Note: Bars touch each other (continuous data)
1
Worked Example

The following data shows the number of students in different clubs: Music: 25, Sports: 40, Art: 30, Drama: 20, Science: 35. Draw a bar graph to represent this data.

Solution
  • Step 1: Draw X-axis and Y-axis
  • Step 2: Label X-axis as "Clubs", Y-axis as "Number of Students"
  • Step 3: Choose scale: 1 unit = 5 students (up to 45)
  • Step 4: Mark clubs: Music, Sports, Art, Drama, Science
  • Step 5: Draw bars of heights: Music=25 (5 units), Sports=40 (8 units), Art=30 (6 units), Drama=20 (4 units), Science=35 (7 units)
  • Step 6: Add title: "Student Participation in Clubs"

Answer: Bar graph drawn with appropriately scaled bars.

2
Worked Example

The heights (in cm) of 40 students are grouped as: 150-155: 5 students, 156-161: 12 students, 162-167: 15 students, 168-173: 8 students. Draw a histogram.

Solution
  • Step 1: Draw X-axis: Heights (continuous intervals)
  • Step 2: Draw Y-axis: Frequency (number of students)
  • Step 3: Scale Y-axis: 0 to 16 (1 unit = 2 students)
  • Step 4: Draw bar for 150-155: height 5
  • Step 5: Draw bar for 156-161: height 12 (touching previous bar)
  • Step 6: Draw bar for 162-167: height 15 (touching)
  • Step 7: Draw bar for 168-173: height 8 (touching)
  • Step 8: Title: "Distribution of Student Heights"

Answer: Histogram drawn with touching bars representing continuous data.

3
Worked Example

A double bar graph shows the number of boys and girls in three classes: Class A: Boys 15, Girls 12; Class B: Boys 18, Girls 14; Class C: Boys 12, Girls 16. What is the total number of boys and girls? Which class has the most students?

Solution
  • Step 1: Calculate total boys = 15 + 18 + 12 = 45
  • Step 2: Calculate total girls = 12 + 14 + 16 = 42
  • Step 3: Total students = 45 + 42 = 87
  • Step 4: Class A total = 15 + 12 = 27
  • Step 5: Class B total = 18 + 14 = 32
  • Step 6: Class C total = 12 + 16 = 28
  • Step 7: Class B has the most students (32)

Answer: Total boys = 45, Total girls = 42, Total students = 87. Class B has the most students (32).

Key Points

  • Bar graph displays categorical data with separate bars (gaps between bars)
  • Histogram displays continuous grouped data with touching bars
  • X-axis shows categories (bar graph) or number line (histogram)
  • Y-axis shows frequency or quantity
  • Always label axes and give the graph a title
  • Choose appropriate scale for clear visualization
  • Double bar graphs compare two related data sets side by side
Tap an option to check your answer0 / 4
Q1.A bar graph is used for ___ data.
Explanation: Discrete.
Q2.A histogram is used for ___ data.
Explanation: Grouped/continuous.
Q3.The height of a bar shows the:
Explanation: Frequency.
Q4.In a histogram, between the bars there are:
Explanation: No gaps.