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Maths > Data Handling > Histograms and Pie Charts
Data Handling

Histograms and Pie Charts

If you look around you, you will notice many visual interpretations of data around. Be it graphs, tables, charts, lines etc. They communicate the information clearly and at one glance. Here we will be learning about two such widely used visual representations, namely Histograms and Pie Charts.

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Histogram

A histogram is what we call an area diagram. It indicates the frequency of a class interval. The class interval or the range of values is known as bins or classes with reference to histograms. A bar indicates the number of data points within a specific class. That means the higher the frequency of a particular class, higher the bar.

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Let us see an example of a Histogram. From the below-given table of the various heights of trees in a region, we will draw a histogram to illustrate how it is done. Let us look at the frequency table now.

Height of Trees (ft) No. of trees
60-65 3
65-70 3
70-75 8
75-80 10
80-85 5
85-90 2

Now here the heights of the tree are continuous data. These class intervals are the bins. And the number of trees are obviously the frequency. And now let us draw a histogram (given below) that represents the above data.

Histograms and Pie Charts

Histograms vs Bar Charts

  • In bar graphs, each bar represents one value or category. On the other hand in a histogram, each bar will represent a continuous data
  • In a bar graph, the x-axis need not always be a numerical value. It can also be a category. However, in a histogram, the X-axis is always quantitative data and it is continuous data.
  • Due to the above factor, a histogram can be observed for its skewness i.e. a pattern or tendency of data to fall in more on the low end or high end etc. Same cannot be done for a bar chart

Pie Charts

A pie chart or a pie graph is a circular representation of data. A pie chart not only represents frequency but also numerical proportion. Each section of a pie chart is the proportionate quantity of the whole data. And the total value of a pie chart is always 100 (just as a percentage)

How to draw a Pie Chart

Let us now take a step-by-step look at how to represent data via pie charts

  • Data: Gather your values and arrange them in a descending order.
  • Find denominator: Add all the values to arrive at a whole value or number. This will be your denominator
  • Percentage: Now we calculate the percentage of each value in relation to the total values. We simply divide each value with the denominator we got from step 2. Also, it will be easier to leave the value in decimal form
  • Calculate the angles: So we multiply each percentage (in decimal form) by 360 (degrees in a circle)
  • Circle: And now we draw a circle to begin drawing a pie chart
  • Draw individual sections: Now with the help of a protractor we draw each section of the pie chart. We use the angles we obtained from step 4
  • Colour: Each section must be a different colour so it can be easily identified.
  • Review: And the final step is to review the information.

Solved Example

Question 1: The below pie chart shows the monthly budget of A. If the total budget is RS.2000. How much he spends on utility bill?

  1. 440
  2. 230
  3. 220
  4. 180

Pie Charts

Answer : A spends 12% on Utility bills. If total budget is 2000 then

Utility Bills = 12% x 2000 = Rs 240

Question 2: What is a pie chart and why we call it a pie chart?

Answer: A pie chart is a circular chart that represents data in a circular statistical graphic. Moreover, this data is divided into slices to illustrate numerical proportions. Besides, it is called a pie chart because of its resemblance to a pie, which has been sliced, and there are variations on the way it can be presented.

Question 3: What is the use of a pie chart?

Answer:Commonly, pie charts help us to express proportional or percentage data and frequently the percentage represented by each category is provided next to the corresponding slice of pie. Furthermore, they are good for displaying data for around 6 categories or fewer.

Question 4: Why we should avoid the pie chart?

Answer: The main problem with the pie chart is that they force us to compare areas or angles that are pretty difficult. However, a bar chart is a better option for visualizing the part-to-whole relations of a data set. Because with the help of pie charts we can compare different objects by their length, which are one-dimensional.

Question 5: Is a pie chart quantitative or qualitative?

Answer: Pie charts are qualitative because in it each category is represented by a slice of the pie. Also, the area of the slice is proportional to the percentage of responses in the category.

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