Statistics • Topic 2 of 3

Graphical Representation of Data

What are Graphical Representations?

Graphical representations are visual ways to display data, making it easier to understand patterns, trends, and comparisons at a glance.

Types of Graphs:

Graph TypeBest Used ForKey Feature
**Histogram**Showing distribution of continuous dataBars touch each other (no gaps)
**Frequency Polygon**Comparing multiple distributionsLine connecting midpoints

Bar Graph:

  • Used for discrete data (separate categories)
  • Bars have equal width with gaps between them
  • Height of bar represents frequency
  • Can be vertical or horizontal

Histogram:

  • Used for continuous data grouped into class intervals
  • Bars touch each other (no gaps)
  • Width of bar represents class interval size
  • Area of bar represents frequency

Frequency Polygon:

  • Created by joining the midpoints of histogram bars
  • Starts and ends on the x-axis (at frequency 0)
  • Useful for comparing two or more data sets on same graph
Measures of Central TendencyMeanSum of all values / Total count(32+45+67)/3 = 48MMedianMiddle value when sorted32,45,67 → Median=45MoModeMost frequently occurring value32,45,45,67 → Mode=45Median Rules:Odd n: Median = ((n+1)/2)th valueEven n: Median = average of (n/2)th and (n/2+1)th valuesA dataset can have no mode, one mode, or multiple modes (bimodal/multimodal)Empirical relationship: Mode ≈ 3×Median − 2×Mean
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Worked Example

Solve a standard problem on Graphical Representation of Data.

Solution

Apply the formula/method shown in the concept section above.

Key Points

  • Understand the definition and properties of Graphical Representation of Data.
  • Study the worked examples and practice similar problems.
  • Always verify your answer using the original conditions.
Tap an option to check your answer0 / 4
Q1.A bar graph is used for:
Explanation: Discrete data.
Q2.A histogram is used for:
Explanation: Grouped/continuous.
Q3.In a histogram, between the bars there are:
Explanation: No gaps.
Q4.A frequency polygon is drawn by joining the:
Explanation: Class marks (tops).