Study the following example to know about a histogram and how to draw it.
Ex : The table below shows the net asset value (NAV) per unit of mutual funds of some companies. Draw a histogram representing the information.
|No. of mutual
Solution : The given classes are not continuous. Lets make the classes continuous.
Method of drawing a histogram :
1. If the given classes are not continuous, make them continuous. Such classes are called extended class intervals.
2. Show the classes on the X- axis with a proper scale.
3. Show the frequencies of the Y- axis with a proper scale.
4. Taking each class as the base, draw rectangles with heights proportional to the frequencies.
On the X-axis, a mark `krink` is called the krink mark and it is shown between the origin and the first class. It means, there are no observations upto the first class. The mark can be used on the Y- axis also, if needed. This enables us to draw a graph of optimum size.
The following table is based on the marks of the first term examination of 10th class students. Show the information by a histogram. Also, draw a frequency polygon with the help of the histogram.
|Class-mark of marks||325||375||425||475||525||575|
|No. of students||25||35||45||40||32||20|
The following table shows the investment made by some families. Show
the information by a histogran.
|No. of families||30||50||60||55||15|
|No. of trees planted by each student||1 - 3||4 - 6||7 - 9||10 - 12|
|No. of students||7||8||6||4|
The above data is to be shown by a frequency polygon. The coordinates of the points to show number of students in the class 4-6 are . . . .
|(A) (4, 8)||(B) (3, 5)||(C) (5, 8)||(D) (8, 4)|
|Result (Percentage)||30 - 40||40 - 50||50 - 60||60 -70||70 - 80||80 - 90||90 - 100|
|No. of students||7||33||45||65||47||18||5|
|Electricity bill (Rs)||0 - 200||200 - 400||400 - 600||600 - 800||800 - 1000|
Observe the following frequency polygon and write the answers of the questions below it.
(1) Which class has the maximum number of students ?
(2) Write the classes having zero frequency.
(3) What is the class-mark of the class, having frequency of 50 students ?
(4) Write the lower and upper class limits of the class whose class mark is 85.
(5) How many students are in the class 80-90?
Represent the following data by Histogram:
Price of Sugar per kg
|Number of Weeks|
The following is the frequency distribution of waiting time at ATM centre; draw histogram to
represent the data:
|30 - 60||23|
|60 - 90||64|
|90 - 120||50|
|120 - 150||5|