B. Com. I Practical No. 4 :Graphical representation of data by using Histogram, Frequency Polygon, Frequency Curve and Locating Modal Value.

Practical No. 4 Graphical representation of data by using Histogram, Frequency Polygon, Frequency Curve and Locating Modal Value

 

Graphical Representation:

The representation of numerical data into graphs is called graphical representation of data. following are the graphs to represent a data

i.                   Histogram

ii.               Frequency Polygon  

iii.              Frequency Curve

iv.        Locating Modal Value

i.   Histogram:

Histogram is one of the simplest methods to representing the grouped (continuous) frequency distribution. And histogram is defined as A pictorial representation of grouped (or continuous) frequency distribution to drawing an adjacent rectangle, the area of rectangle is proportional to the frequency of that class.

For constructing the histogram, we plot the classes on x-axis and the corresponding frequencies on y-axis. The height of the rectangle is proportional to the frequency of that class and the length of all classes are equal then width of the rectangle is equal to the length of the class. If the class width is equal then width of all rectangles is equal but in some cases the width is not equal then rectangle have unequal width that case, we adjust the height of the rectangle and area of the rectangle is proportional to the frequency of that class. The histogram is used to determine the value of mode graphically.  But histogram is not constructed for open- end frequency distribution.

Histogram for Equal class width

e.g., plot the histogram for the following data.

Marks	No. of Students
0-10	1
10-20	14
20-30	19
30-40	20
40-50	36
50-60	40
60-70	30
70-80	16
80-90	5
90-100	4

Histogram for equal class length

 

 Histogram for unequal class width  

If the length of class is unequal then the height of the rectangle is adjusted, in histogram area of a rectangle= height x width then the width of class is double that of normal then height is adjusted as half. And if the width is three times that of normal width then height must be divided by three. And remaining as same.

In this cases the frequency distribution with unequal class width in that case the smallest interval should be assumed to be normal class width.

Or following formula is used

If the length of class is unequal then we use following formula to draw histogram

Frequency Density= (Frequency of class) / (Width of class)

This is to ensure that the area of each bar in histogram is proportional to the frequency of corresponding class.

 

e.g. plot the histogram for the following data.

Marks	No. of Students
0-5	100
5-15	140
15-40	190
40-60	200
60-100	360

 

 

Answer: in this example the classes has unequal width we can use the  area of a rectangle= height x width to draw  histogram

In this example the normal class is  0-5 in normal class width has no change in class frequency we draw histogram as it is, but in unequal class width the are of rectangle is adjusted  Then the adjusted class frequency is

Marks	No. of Students	Adjusted frequency
0-5	100	100
5-15	140	70
15-40	175	35
40-60	200	50
60-100	360	45

 

Now we draw histogram for

Marks	Adjusted frequency
0-5	100
05-15	70
15-40	35
40-60	50
60-100	45

(For histogram we rearrange the classes with normal class width  as to draw histogram

 

Marks	Adjusted frequency
0-5	100
5-10	70
10-15	70
15-20	35
20-25	35
25-30	35
30-35	35
35-40	35
40-45	50
45-50	50
50-55	50
55-60	50
60-65	45
65-70	45
70-75	45
75-80	45
80-85	45
85-90	45
90-95	45
95-100	45

) 

Histogram for unequal class length.

OR 

ii.       Frequency Polygon:

For constructing a polygon the midpoints of the class are taken along the x-axis and the corresponding frequencies on the y-axis, then this point are plotted and joining these points by straight line. And the polygon is extended through half interval on both sides. this type of graph enables us to understand the pattern in the data more clearly

 

e.g. To Draw a Frequency polygon for the following data.

 

Marks	No. of Students
0-10	2
10-20	14
20-30	19
30-40	20
40-50	36
50-60	40
60-70	30
70-80	16
80-90	5
90-100	4

the frequency polygon is

iii. Frequency Curve:

 The frequency polygon is not a smooth curve. The boundary is made up of straight line and it has sharp corners. If the sharp corners are removed and the curve is smooth without changing the area under the frequency polygon, is called frequency Curve.  To draw the frequency curve the midpoints of the class are taken along the x-axis and the corresponding frequencies on the y-axis, then this point is plotted and joining these points by smooth curve.

e.g. To Draw a Frequency Curve for the following data.

 

Marks	No. of Students
0-10	2
10-20	14
20-30	19
30-40	20
40-50	36
50-60	40
60-70	30
70-80	16
80-90	5
90-100	4

the frequency Curve is 

B. Com. I : Practical - I

Expt. No. 4                                                                                      Date:    /    / 2025

Title: Graphical representation of data by using Histogram, Frequency Polygon, Frequency Curve and  Locating Modal Value..

Q.1 The Monthly income of small business owner are given draw histogram to represent the data.

Monthly Income (RS)	0-10	10-20	20-30	30-40	40-50	50-60	60-70	70-80	80-90
No. of Business Owners	2	5	8	12	20	15	10	5	4

 

Q.2 The following table shows weekly sales of grocery shops in market. Draw a histogram to represent the data.

Weekly Sales (Rs)	0-50	50-100	100-150	150-200	200-250	250-300
No. of Shops	10	18	25	20	12	6

 

Q.3 An e-commerce company recorded the number of orders received per week. Represent the data using histogram.

Orders per Week	0-10	10-20	20-30	30-40	40-50	50-60	60-70	70-80	80-90	90-100
No. of Sellers	10	30	70	150	250	200	100	50	40	30

 

Q.4 Draw a histogram and locate the mode graphically from the following data.

Profit (Rs)	0-5	5-10	10-15	15-20	20-25	25-30	30-35
No. of Days	4	8	18	27	21	15	11

 

Q.5 Draw a histogram to represent the following data.

Class	0-5	5-10	10-15	15-20	20-30	30-45	45-65	65-70
Frequency	4	8	18	27	21	15	11	2

 

Q.6 Draw a histogram to represent the following data.

Weight in Kg	1-9	11-19	21-29	31-39	41-49	51-59	61-69
No. of Students	35	49	65	88	105	75	45