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Graphical Representations — Mathematics STD 10 — Question

ICSE BoardEnglish MediumSTD 10MathematicsGraphical Representations5 Marks
Question
Construct a histogram and then a frequency polygon for the following frequency distribution.
Class Interval 11-20 21-30 31-40 41-50 51-60 61-70
Frequency 15 28 50 35 20 12
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Answer

1. Organize the data into equal intervals by subtracting 0.5 from lower limit of each class and add 0.5 to the upper limit of each class .
2. On the $x$-axis, take $1 \mathrm{~cm}$ as 5 units and plot class interval .
3. On the $y$-axis, take $1 \mathrm{~cm}$ as 5 units and plot frequency.
4. Draw rectangles of histogram as per given data.
5. For each rectangle, mark the midpoint of its length at the top part . In this case, points are $(15.5,15),(25.5,28),(35.5,50),(45.5,35),(55.5,20),(65.5,12)$.
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 Interval Frequency
10.5-20.5 15
20.5-30.5 28
30.5-40.5 50
40.5-50.5 35
50.5-60.5 20
60.5-70.5 12
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