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| Image Credit: Pixabay.com |
Histogram
We can transform frequency distribution table into bar graphs. Can we do the same with grouped frequency distribution table?We can achieve this through histogram.
In bar graph we draw bars for individual observations but in histogram we draw bars for grouped observations.
Histogram is a type of bar diagram, where the class intervals are shown on the horizontal axis and the heights of the bars show the frequency of the class interval.
The bars are of equal width but there is no gap in between as there is no gap between the class intervals.
If first class interval do not begin with 0, we use jagged (or broken) line along the horizontal line
Try This
Q Observe the histogram 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 the data i.e. ratio of frequency of an observation to the total number of observations.Like in fraction, part to the whole.
The whole circle is divided into sectors. The size of each sector is proportional to 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 the 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
⇒ 1
⇒ 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 = 10/1
Number of CD's for semi classical music = 20/1
Number of CD's for light music = 40/1
Number of CD's for folk music = 30/1
Drawing Pie charts
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 mark the required sectors.
We can use proportionality equation to find the central angle as,
| Central angle | = | Part (Sector) | ||
| 360° | whole (circle) |
| Central angle | = | Quantity in Sector | × | 360° |
| Total Quantity in Circle |
Ex5.2 Q5.
The number of students in a hostel, speaking different languages is given below.Display the data in a pie chart.
| Language | Hindi | English | Marathi | Tamil | Bengali | Total |
| No. of students | 40 | 12 | 9 | 7 | 4 | 72 |
Ans
Central angle for students speaking Hindi = 40/72 × 360° = 200°Central angle for students speaking English = 12/72 × 360° = 60°
Central angle for students speaking Marathi = 9/72 × 360° = 45°
Central angle for students speaking Tamil = 7/72 × 360° = 35°
Central angle for students speaking Bengali = 4/72 × 360° = 20°
| Graphical Representation of Data (I) | |