UPSC NDA I 2016 Mathematics Solved Paper

Concept:In a histogram, each rectangle’s area represents the frequency of the class interval, and the frequency polygon connects the midpoints of the top edges of these rectangles.Explanation:Statement 1: The frequency polygon is drawn by joining the midpoints of the tops of the histogram rectangles.The area under the frequency polygon (above the x‑axis) equals the total area of all the rectangles in the histogram.Hence, statement 1 is correct.Statement 2: For a histogram with equal class intervals, the height of each rectangle is the frequency.When class intervals are unequal, the height is the frequency density = $\frac{\text{frequency}}{\text{class width}}$.Then, area of rectangle = class width × height = class width × $\frac{\text{frequency}}{\text{class width}}$ = frequency.Thus, the area of each rectangle is directly proportional to (actually equal to) the frequency.So statement 2 is also correct.Answer:Both statements 1 and 2 are correct. Hence, option C is correct.