Skip to content

CMA Foundation · Fundamentals of Business Mathematics and Statistics · Statistical Representation of Data

A histogram of marks has continuous classes of width 10 starting at 0. Frequencies are 4, 10, 16, 12, 8 for classes 0-10 up to 40-50. A frequency polygon is drawn by joining mid-points and closing it at both ends on the x-axis with additional classes. The area of the polygon equals the area of the histogram. What is that total area, and what are the two extra end points?

The area is 500 and the end points are (−5, 0) and (55, 0). Total frequency is 50 and each class has width 10, so area is 500. The polygon is closed with zero-frequency classes −10-0 and 50-60, whose mid-points are −5 and 55.

  1. AArea 500; end points (−5, 0) and (55, 0)Correct
  2. BArea 50; end points (5, 0) and (45, 0)
  3. CArea 500; end points (0, 0) and (50, 0)
  4. DArea 500; end points (−5, 0) and (50, 0)

Explanation

Total frequency = 4+10+16+12+8 = 50; histogram area = 50 × width 10 = 500. The polygon is closed using imaginary classes −10-0 and 50-60 with zero frequency, whose mid-points are −5 and 55. Option 2 forgets the width and uses wrong points.

Did you get it right without looking?

One question tells you little. A timed set on Statistical Representation of Data shows your real accuracy, how long you take and where you lose marks.

Practise Statistical Representation of DataFree diagnostic mock

More Statistical Representation of Data questions