# HOW TO DRAW FREQUENCY POLYGON WITHOUT HISTOGRAM

## About "How to draw frequency polygon without histogram"

How to draw frequency polygon without histogram :

Here we are going to see how to draw frequency polygon without histogram.

Step 1 :

Obtain the frequency distribution and compute the mid points of each class interval.

Step 2 :

Represent the mid points along the X-axis and the frequencies along the Y-axis.

Step 3 :

Plot the points corresponding to the frequency at each mid point.

Step 4 :

Join these points, by straight lines in order.

Step 5 :

To complete the polygon join the point at each end immediately to the lower or higher class marks (as the case may be at zero frequency) on the X-axis.

## Frequency polygon example problems

Example 1 :

Draw a frequency polygon for the following data without using histogram.

 Class interval10 - 2020 - 3030 - 4040 - 5050 - 6060 - 7070 - 8080 - 90 Frequency46810121475

Solution :

 Class interval0 - 1010 - 2020 - 3030 - 4040 - 5050 - 6060 - 7070 - 8080 - 9090 - 100 Mid points5152535455565758595 Frequency0468101214750

Mark the class intervals along the X-axis and the frequency along the Y-axis. We take the imagined classes 0-10 at the beginning and 90-100 at the end, each with frequency zero. We have tabulated the data as shown.

Using the adjacent table, plot the points A (5, 0), B (15, 4), C (25, 6), D (35, 8), E (45, 10), F (55, 12), G (65, 14), H (75, 7), I (85, 5) and J (95, 0).

We draw the line segments AB, BC, CD, DE, EF, FG, GH, HI, IJ to obtain the required frequency polygon ABCDEFGHIJ, which is shown in the picture given below.

Scale :

X - axis 1 cm = 10 units

Y - axis 1 cm = 2 units Example 2 :

Draw a frequency polygon for the following data without using histogram

 Age (in years)0 - 1010 - 2020 - 3030 - 4040 - 5050 - 6060 - 70 Number of persons611253518126

Solution :

 Class interval0 - 1010 - 2020 - 3030 - 4040 - 5050 - 6060 - 7070 - 80 Mid points515253545556575 Frequency6112535181260

Mark the class intervals along the X-axis and the frequency along the Y-axis. We take the imagined classes 0-10 at the beginning and 60-70 at the end, each with frequency zero. We have tabulated the data as shown.

Using the adjacent table, plot the points A (5, 6), B (15, 11), C (25, 25), D (35, 35), E (45, 18), F (55, 12), G (65, 6), and H (75, 0)

We draw the line segments AB, BC, CD, DE, EF, FG, GH, HI to obtain the required frequency polygon ABCDEFGHI, which is shown in the picture given below.

Scale :

X - axis 1 cm = 10 units

Y - axis 1 cm = 5 units  After having gone through the stuff given above, we hope that the students would have understood "How to draw frequency polygon without histogram".

Apart from the stuff "How to draw frequency polygon without histogram" given in this section, if you need any other stuff in math, please use our google custom search here.

You can also visit our following web pages on different stuff in math.

WORD PROBLEMS

Word problems on simple equations

Word problems on linear equations

Algebra word problems

Word problems on trains

Area and perimeter word problems

Word problems on direct variation and inverse variation

Word problems on unit price

Word problems on unit rate

Word problems on comparing rates

Converting customary units word problems

Converting metric units word problems

Word problems on simple interest

Word problems on compound interest

Word problems on types of angles

Complementary and supplementary angles word problems

Double facts word problems

Trigonometry word problems

Percentage word problems

Profit and loss word problems

Markup and markdown word problems

Decimal word problems

Word problems on fractions

Word problems on mixed fractrions

One step equation word problems

Linear inequalities word problems

Ratio and proportion word problems

Time and work word problems

Word problems on sets and venn diagrams

Word problems on ages

Pythagorean theorem word problems

Percent of a number word problems

Word problems on constant speed

Word problems on average speed

Word problems on sum of the angles of a triangle is 180 degree

OTHER TOPICS

Profit and loss shortcuts

Percentage shortcuts

Times table shortcuts

Time, speed and distance shortcuts

Ratio and proportion shortcuts

Domain and range of rational functions

Domain and range of rational functions with holes

Graphing rational functions

Graphing rational functions with holes

Converting repeating decimals in to fractions

Decimal representation of rational numbers

Finding square root using long division

L.C.M method to solve time and work problems

Translating the word problems in to algebraic expressions

Remainder when 2 power 256 is divided by 17

Remainder when 17 power 23 is divided by 16

Sum of all three digit numbers divisible by 6

Sum of all three digit numbers divisible by 7

Sum of all three digit numbers divisible by 8

Sum of all three digit numbers formed using 1, 3, 4

Sum of all three four digit numbers formed with non zero digits

Sum of all three four digit numbers formed using 0, 1, 2, 3

Sum of all three four digit numbers formed using 1, 2, 5, 6 