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Question

# The marks obtained (out of 100) by a class of 80 students are given below: MarksNumber of students10−20620−301730−501550−701670−10026 Construct a histogram to represent the data above. (4 marks)

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Solution

## In the given frequency distribution, class sizes are different. So, we calculate the adjusted frequency for each class. Here, minimum size = 20 - 10 = 10 We use the formula, Adjusted frequency of a class =Minimum class sizeClass size of this class×Its frequency The modified table for frequency distribution is given below. MarksNumber ofAdjusted frequencystudents(Frequency)10−2061010×6=620−30171010×17=1730−50151020×15=152=7.550−70161020×16=162=870−100261030×26=263=8.67 Along the horizontal axis, we represent the class intervals of marks on some suitable scale. The corresponding frequencies of the number of students are represented along the Y-axis on a suitable scale. The given intervals start with 10 - 20. It means that there is some break (≈) indicated near the origin to signify the graph is drawn with a scale beginning at 10. Now, we draw rectangles with class intervals as the bases and the corresponding adjusted frequencies as heights. (2 marks) A histogram of the given distribution is given below. (2 marks)

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