Now we will discuss about the construction of pie chart or pie graph. In brief let us recall about, what is a pie chart?
The pie chart is a pictorial representation of data relative to a whole. Each portion in the circle represent an element of the collected data. The pie chart represents the composition of various elements in a whole. The total value of the pie chart is always 100%. Each portion in the circle shows a fraction or percentage of the total.
Pie chart is a circular graph which is used to represent data. In this :
● Various observations of the data are represented by the sectors of the circle.
● The total angle formed at the centre is 360°.
● The whole circle represents the sum of the values of all the components.
● The angle at the centre corresponding to the particular observation component is given by
● If the values of observation/components are expressed in percentage, then the centre angle corresponding to particular observation/component is given by
How to construct a pie chart?
Steps of construction of pie chart for a given data:
● Find the central angle for each component using the formula given on the previous page.
● Draw a circle of any radius.
● Draw a horizontal radius
● Starting with the horizontal radius, draw radii, making central angles corresponding to the values of respective components.
● Repeat the process for all the components of the given data.
● These radii divide the whole circle into various sectors.
● Now, shade the sectors with different colors to denote various components.
● Thus, we obtain the required pie chart.
Here the pie chart shows the type of books preferred by the students of a class.
Given below is a pie chart showing the type of books preferred by the students of a class. Observe the chart and answer the questions given below.
(i) What fraction of students like Comic books?
Answer: The sector in the pie chart shows = \(\frac{1}{4}\)
(ii) What fraction of students like Story books?
Answer: The sector in the pie chart shows = \(\frac{1}{2}\)
(iii) Which 2 books have equal fraction of preference?
Answer: Poem and Puzzle books.
(iv) What fraction of students does not like story books?
Answer: \(\frac{1}{2}\)
(iv) Which type of book do you like to read?
Answer: Comic books
Solved Example on Construction of Pie Chart/Pie Graph:
1. The following table shows the numbers of hours spent by a child on different events on a working day.
Represent the adjoining information on a pie chart
Activity | No. of Hours |
School | 6 |
Sleep | 8 |
Playing | 2 |
Study | 4 |
T. V. | 1 |
Others | 3 |
The central angles for various observations can be calculated as:
Activity | No. of Hours | Measure of central angle |
School | 6 | (^{6}/_{24} × 360)° = 90° |
Sleep | 8 | (^{8}/_{24} × 360)° = 120° |
Playing | 2 | (^{2}/_{24} × 360)° = 30° |
Study | 4 | (^{4}/_{24} × 360)° = 60° |
T. V. | 1 | (^{1}/_{24} × 360)° = 15° |
Others | 3 | (^{3}/_{24} × 360)° = 45° |
Now, we shall represent these angles within the circle as different sectors. Then we now make the pie chart:
2. The favourite flavours of ice-cream for the children in a locality are given in percentage as follow. Draw the pie chart to represent the given information
Flavours | % of Students Prefer the Flavours |
Vanilla | 25 % |
Strawberry | 15 % |
Chocolate | 10 % |
Kesar-Pista | 30 % |
Mango Zap | 20 % |
The central angles for various observations can be calculated as:
Flavours | % of Students Prefer the Flavours | Measure of Central Angles |
Vanilla | 25 % | (^{25}/_{100} × 360)° = 90° |
Strawberry | 15 % | (^{15}/_{100} × 360)° = 54° |
Chocolate | 10 % | (^{10}/_{100} × 360)° = 36° |
Kesar-Pista | 30 % | (^{30}/_{100} × 360)° = 108° |
Mango Zap | 20 % | (^{20}/_{100} × 360)° = 72° |
Now, we shall represent these angles within a circle to obtain the required pie graph.
Questions and Answers on Construction of Pie Chart:
1. 80 girls were asked about their favourite sport? The collected information is given in the table. Read the information and label the graph.
Sports |
Number of Girls |
Badminton |
41 |
Tennis |
9 |
Swimming |
23 |
Volleyball |
7 |
Answer:
2. 100 students of a school were surveyed for their favourite activity. The information is represented in a pie chart as given below. Observe the chart and answer the questions given below.
(i) Which is the most favourite pastime activity of students?
(ii) How many students like music?
(iii) What percentage of students like to dance?
(iv) What percentage of students like to read books?
Answers:
(i) Playing Outdoor games
(ii) 25
(iii) 12.5%
(iv) 12.5%
● Statistics
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