Graphical Representation of Data | Histogram | Pie-chart

Here, we will learn to represent Data graphically through Histogram and Pie Chart. Histogram represents grouped frequency distribution. Pie chart shows the relative frequencies of the data.

Prerequisite / Revise this :

Histogram

Histogram

Histogram is a type of bar diagram that represents grouped frequency distribution graphically. Class intervals are plotted on the horizontal axis and heights of the bars represent frequencies of the respective class intervals.

histograms

In histogram, the bars are of equal width but there is no gap in between as there is no gap between the class intervals.

ℹ If the first class interval in a histogram does not begin with 0, we use jagged (or broken) line along the horizontal line.

Difference between Bar Graph and Histogram

In bar graph we draw bars for individual observations but in histogram we draw bars for grouped observations.

Try This

Q) Observe the histogram above and answer the following.

(i) Which group contain maximum girls.

(ii) How many girls have a height of 145 cm and more.

Ans

(i) (140−145)

(ii) 4+2+1 = 7

Pie-chart or Circle-graph

A pie chart shows the relative frequencies of  data i.e. ratio of frequency of an observation to the total number of observations.

ℹ Like in fraction, part to the whole.

A circle is divided into sectors. The size of each sector is proportionalto the observation it represents.

Sector

Part(or fraction) of a circle enclosed by two radii and an arc is called a sector of the circle.

Central Angle

Angle subtended by a sector at the centre of a circle is called the central angle of that sector.

Try These (Ex 5.2)

Q1. A survey was made to find the type of music that a certain group of young people liked in a city. Adjoining pie chart shows the findings of this survey.

From this pie chart answer the following:

(i) If 20 people liked classical music, how many young people were surveyed?

(ii) Which type of music is liked by the maximum number of people?

(iii) If a cassette company were to make 1000 CD’s, how many of each type would they make?

Ans

(i) Let, the number of people surveyed be x,

then, 10% of x = 20

\frac{10}{100} ×x= 20

x = 20 × 10 = 200

∴ The number of people surveyed = 200

(ii) Light music is liked by maximum people (40%)

(iii) Number of CD’s for classical music = \frac{10}{100}× 1000 = 100

Number of CD’s for semi classical music = \frac{20}{100} × 1000 = 200

Number of CD’s for light music = \frac{40}{100} × 1000 = 400

Number of CD’s for folk music = \frac{30}{100} × 1000 = 300

Drawing Pie charts

ℹ The total angle at the centre of a circle is 360°, so the central angle of the sectors will be a fraction of 360°.

We first find the central angle of the sectors for every observation then we draw a circle of convenient radius and then draw the required sectors.

We can use proportionality equation to find the central angle as,

\boxed{\frac{Central\, Angle}{360^{\circ}}=\frac{Part\,(Sector)}{Whole\,(Circle)}}

\boxed{Central\,Angle=\frac{Quantity\,in\,Sector}{Quantity\,in\,Circle}\times 360^{\circ}}

Ex 5.2 Q5

The number of students in a hostel, speaking different languages is given below.

Display the data in a pie chart.

LanguageNo. of students
Hindi40
English12
Marathi9
Tamil7
Bengali4
Total72

Ans

Central angle for students speaking Hindi = \frac{40}{72} × 360°

= 200°

Central angle for students speaking English = \frac{12}{72} × 360°

= 60°

Central angle for students speaking Marathi = \frac{9}{72} × 360°

= 45°

Central angle for students speaking Tamil = \frac{7}{72} × 360°

= 35°

Central angle for students speaking Bengali = \frac{4}{72} × 360°

= 20°

Now, required pie chart can be drawn as following,

pie chart

Histogram and Pie Chart – Problems with Solutions

⏪ Graphical Representation of Data (I) Line Graphs ⏩

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