# Draw Frequency Polygons for Each of the Following Frequency Distribution: (A) Using Histogram (B) Without Using Histogram - Mathematics

Sum

Draw frequency polygons for each of the following frequency distribution:

(a) using histogram

(b) without using histogram

 C.I 10 - 30 30 - 50 50 - 70 70 - 90 90 - 110 110 - 130 130 - 150 ƒ 4 7 5 9 5 6 4

#### Solution

using histogram

 C.I ƒ 10 - 30 4 30 - 50 7 50 - 70 5 70 - 90 9 90 - 110 5 110 - 130 6 130 - 150 4

Steps:

1. Draw a histogram for the given data.
2. Mark the mid-point at the top of each rectangle of the histogram drawn.
3. Also, mark the mid-point of the immediately lower class-interval and mid-point of the immediately higher class-interval.
4. Join the consecutive mid-points marked by straight lines to obtain the required frequency polygon.

Without using Histogram:

Steps:

1. Find the class-mark (mid-value) of each given class-interval.
classmark = mid-value = " Upper limit + Lower  limit"/2
2. On a graph paper, mark class-marks along X-axis and frequencies along Y-axis.
3. On this graph paper, mark points taking values of class-marks along the X-axis and the values of their corresponding frequencies along Y-axis.

4. Draw line segments joining the consecutive points marked in step (3) above.
 C.I. Class-mark f -10 - 10 0 0 10 - 30 20 4 30 - 50 40 7 50 - 70 60 5 70 - 90 80 9 90 - 110 100 5 110 - 130 120 6 130 - 150 140 4 150 - 170 160 0

Concept: Graphical Representation of Data
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#### APPEARS IN

Selina Concise Mathematics Class 9 ICSE
Chapter 18 Statistics
Exercise 18 (B) | Q 5.1 | Page 233