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Graphical Representations — Mathematics STD 10 — Question

ICSE BoardEnglish MediumSTD 10MathematicsGraphical Representations4 Marks
Question
Construct a frequency polygon without using a histogram for the following frequency distribution :
Class Interval 1-10 11-20 21-30 31-40 41-50
Frequency 8 12 10 16 6
✓

Answer

Steps:
1. Make the class intervals continuous by subtracting 0.5 from the lower limit of each class and add 0.5 to the upper limit of each class.
2. Find class mark by calculating the average of the class interval.
3. On the $x$-axis, take $1 \mathrm{~cm}$ as 5 units and plot class interval.
4. On the $y$-axis, take $1 \mathrm{~cm}$ as 5 units and plot frequency.
5. Plot the points on the graph. $(5.5,8),(15.5,12),(25.5,10),(35.5,16),(45.5,6)$.
6. Mark two more midpoints of zero frequency on $x$-axis at the start and at the end.
7. Now connect the points using straight lines.
Class IntervalClass MarkFrequency
0.5-10.5$
=\frac{0.5+10.5}{2}=5.5
$		8
10.5-20.5$
=\frac{10.5+20.5}{2}=15.5
$		12
20.5-30.5$
=\frac{20.5+30.5}{2}=25.5
$		10
30.5-40.5$
=\frac{30.5+40.5}{2}=35.5
$		16
40.5-50.5$
=\frac{40.5+50.5}{2}=45.5
$		6

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