Grade 8
  1. Number Systems  1.1. Rational Numbers  1.2. Irrational Numbers  1.3. Real Numbers  1.4. Properties of Real Numbers  1.4.1. Commutative Property  1.4.2. Associative Property  1.4.3. Distributive Property  1.5. Representation on the Number Line  1.6. Operations on Real Numbers  1.6.1. Addition and Subtraction  1.6.2. Multiplication and Division  1.7. Rationalization  1.8. Exponents and Powers  1.9. Square Roots and Cube Roots
  2. Algebra  2.1. Algebraic Expressions  2.2. Identities and Simplification  2.2.1. Multiplying Binomials  2.2.2. Using Algebraic Identities  2.3. Factorization  2.3.1. Common Factors  2.3.2. Factorization by Grouping  2.3.3. Factorization of Trinomials  2.3.4. Special Products  2.4. Linear Equations in One Variable  2.4.1. Solving Linear Equations  2.4.2. Word Problems on Linear Equations
  3. Geometry  3.1. Understanding Quadrilaterals  3.1.1. Properties of Quadrilaterals  3.1.2. Types of Quadrilaterals  3.1.2.1. Parallelogram  3.1.2.2. Rectangle  3.1.2.3. Square  3.1.2.4. Rhombus  3.1.2.5. Trapezium  3.2. Constructions  3.2.1. Constructing Quadrilaterals  3.2.2. Constructing Bisectors  3.2.3. Constructing Angles  3.2.4. Constructing Triangles  3.3. Symmetry and Transformations  3.3.1. Reflection  3.3.2. Rotation  3.3.3. Translation  3.3.4. Symmetry in Patterns
  4. Mensuration  4.1. Area and Perimeter  4.1.1. Perimeter of Polygons  4.1.2. Area of Triangles  4.1.3. Area of Quadrilaterals  4.1.4. Area of Circles  4.2. Surface Area and Volume  4.2.1. Cubes  4.2.2. Cuboids  4.2.3. Cylinders  4.2.4. Cones  4.2.5. Spheres
  5. Data Handling  5.1. Organizing Data  5.2. Frequency Distribution Tables  5.3. Graphical Representation of Data  5.3.1. Bar Graphs  5.3.2. Histograms  5.3.3. Pie Charts  5.3.4. Line Graphs (added)  5.4. Probability  5.4.1. Introduction to Probability  5.4.2. Experimental Probability
  6. Coordinate Geometry  6.1. Cartesian Plane  6.2. Plotting Points  6.3. Coordinate System  6.4. Distance Between Points  6.5. Applications of Coordinate Geometry
  7. Introduction to Graphs  7.1. Linear Graphs  7.2. Applications of Graphs  7.3. Distance-Time Graphs  7.4. Speed-Time Graphs
  8. Comparing Quantities  8.1. Ratio and Proportion  8.2. Percentage  8.2.1. Increase and Decrease Percent  8.2.2. Discount in Percentage  8.2.3. Profit and Loss in Percentage  8.2.4. Simple Interest  8.2.5. Compound Interest
  9. Exponents and Powers  9.1. Laws of Exponents  9.2. Negative Exponents  9.3. Standard Form  9.4. Applications of Exponents
  10. Introduction to Squares and Square Roots  10.1. Properties of Square Numbers  10.2. Finding Square Roots  10.2.1. Prime Factorization Method  10.2.2. Division Method  10.3. Estimating Square Roots
  11. Introduction to Cubes and Cube Roots  11.1. Properties of Cube Numbers  11.2. Finding Cube Roots  11.2.1. Prime Factorization Method in Finding Cube Roots

Grade 8 → Data Handling → Graphical Representation of Data ↓


Histograms


In the field of statistics, graphs are a powerful tool that provide us with visual insights into data. One such type of graph is the histogram. A histogram is a type of bar graph that is particularly useful when you have a large set of data and you want to understand the frequency distribution of the data points. In this guide, we will explore histograms, how they are created, their components, and how they are used to interpret data.

What is a histogram?

A histogram is a graphical representation that arranges a group of data points into user-specified ranges, called bins. It visually displays the number of data points that fall into each of those bins.

Unlike regular bar charts, histograms depict continuous data. This means that the data can take any value within a given range, and the bars in a histogram touch each other to show that the intervals are continuous.

Parts of a histogram

Before we discuss the examples, let us look at the various components of a histogram:

  • Bins: These are the intervals that group your data. Each bin represents a range of values.
  • Frequency: It indicates the number of data points that fall in each bin.
  • X-axis: Displays the bins and shows the range of the data.
  • Y-axis: Displays the frequency and shows the number of data points in each bin.

Creating a histogram

There are several steps involved in building a histogram. Let's look at them using an example:

Example

Suppose we have a data set showing the ages of a group of students:

12, 13, 14, 15, 13, 14, 12, 16, 15, 14, 13, 17, 14, 15, 14

The steps to create a histogram from this data are as follows:

  1. Collect the data: The raw data we are using is already available.
  2. Decide on the number of compartments: Let's say we decide to create compartments for ages 12 to 17 using the categories 12-13, 14-15, and 16-17 compartments.
  3. Count the number of data points inside each bin: Count how many data points fall into each bin range.
  4. Create a histogram: For each bin, create a bar that scales to the frequency associated with that bin.

Visual example

Here's a visual SVG example of a histogram by age:


        
        
        

        
        

        12-13
        14-15
        16-17

        2
        4
        3

Each blue rectangle in the SVG example represents a bar in the histogram, with the base at the bin label on the x-axis, and the height representing the frequency.

Analyzing the histogram

Once you have a histogram, it is important that you analyze it to take advantage of the information it provides. Here are some aspects you can look at:

  • Shape: The shape of the histogram (e.g., symmetrical, skewed to the left, skewed to the right) gives a visual summary of the distribution of the data.
  • Central tendency: See if the data tend to cluster around a particular point that represents the mean, median, or mode of the distribution.
  • Dispersion: Check the width of the histogram, which indicates whether the data is spread wide or narrow.

Text example

Consider the histogram made from the data of students' height in centimeters:

120-130: 2, 131-140: 5, 141-150: 9, 151-160: 6, 161-170: 3

The highest bar in the histogram corresponds to the 141-150 cm range, which is the most common height range in this data set. It represents the mode.

Advantages of using a histogram

Histograms have several benefits that make them essential in data management:

  • Ease of use: Simple to create and easy to read, histograms simplify data analysis because they provide visible data trends.
  • Comprehensive view: By using bins, histograms present at a glance both the frequency of different values and the shape of the data distribution.
  • Identify outliers: With peaks and gaps, histograms make it easy to identify potential outliers in a dataset, which can be useful in refining the data.

Common mistakes made while plotting a histogram

Although histograms are generally straightforward, some mistakes can make them misleading:

  • Incorrect bin size: Choosing bins that are too small or too large can misrepresent the data. Large bins can hide important details, while small bins can create noise.
  • Non-continuous data: Histograms should only be used for variables that are continuous, not for individual discrete data points.
  • Inconsistent bin widths: Using bins of different sizes can distort the interpretation of the data distribution.

Further exploration

As a practice, take any set of numerical data and try to create a histogram by following the steps mentioned. Analyze its shape, central tendency and variance. This will strengthen your understanding and you will become familiar with the general patterns in the data distribution.

Data examples for practice

Try using the following data set that shows daily temperatures (in degrees Celsius) recorded over two weeks:

20, 22, 23, 21, 21, 23, 24, 22, 25, 22, 23, 21, 24, 23

Decide the appropriate bins, plot the histogram and analyse its pattern.

Histograms are foundational in statistical data visualization, helping to summarize vast arrays of data, making it easier to make informed decisions and draw evidence-based conclusions. The skill of reading and creating histograms translates into a better understanding of data in many disciplines including economics, biology, engineering, and the social sciences where continuous data is prevalent.


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Histograms

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