Bar Graphs and Histograms - Statistics, Class 9, Mathematics PDF Download

BAR GRAPH (OR COLUMN GRAPH OR BAR CHART)
A bar graph is a pictorial representation of numerical data in the form of rectangles (or bars) of equal width and varying heights.
These rectangles are drawn either vertically or horizontally.
The height of a bar represents the frequency of the corresponding observation.
The gap between two bars is kept the same.

Ex.7 The following table shows the number of students participating in various games in a school.

Draw a bar graph to represent the above data.

Sol. Take the games along x-axis and the number of students along Y-axis.

Along y-axis, take the scale 1 cm = 6 students. The bar-graph may, thus, be drawn as shown alongside.

Ex.8 Given below are data showing number of students of a school using different modes of travel to school.

Draw a bar graph to represent the above data.

Sol. Take the mode along x-axis and the number of students along y-axis.
Scale : Along y-axis, take 1 cm = 40 students.
The bars of equal width and proportionate heights with same gap between the two consecutive bars, may be drawn as shown below.
Shading for boys and girls may be done as under :

HISTOGRAM
A histogram is a graphical representation of a frequency distribution in an exclusive form in the form of rectangles with class intervals as bases and the corresponding frequencies as heights, there being no gap between any two successive rectangles.

METHOD OF DRAWING A HISTOGRAM

Step 1 : If the given frequency distribution is in inclusive form, convert it into an exclusive form.

Step 2 : Taking suitable scales, mark the class-intervals along x-axis and frequencies along y-axis.
Note that the scales chosen for both the axes need not be the same.

Step 3 : Construct rectangles with class-intervals as bases and the corresponding frequencies as heights.

Ex.9 Draw a histogram to represent the following data :

Sol. Draw rectangles with bases 30 – 36, 36 – 42, 42 – 48, 48 – 54 and 54 – 60 and heights 15, 25, 20,
30 and 10 respectively.

Note : Since the scale on x-axis starts at 30, we make a kink ( ) in the beginning.

Ex.10 Draw a histogram for the following data :


Sol. The given table is in inclusive-form. So, we first convert it into an exclusive form, as given below.

Now, we may draw the histogram, as shown below.
Note : Since the scale on x-axis starts at 0.5, a kink is shown near the origin.