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While drawing a frequency polygon, how is the graph brought down to the horizontal axis at both ends?

Class 9StatisticsStatistics and Probability
  • ABy joining it to the class marks of two imaginary classes of zero frequency, one at each end
  • BBy joining the first and last bars straight to the origin
  • CBy drawing a vertical line at the highest class mark
  • DBy joining the largest and the smallest observation

Step-by-Step Solution

One extra class is imagined before the first class and one after the last, each with frequency zero. Joining the polygon to those two class marks closes it neatly on the axis, so the area under it matches the histogram.
Answer: A) By joining it to the class marks of two imaginary classes of zero frequency, one at each end

Key idea: Histogram vs bar graph

Both look like bars, but they differ:

**Bar graph**: For DISCRETE / categorical data (favourite colour, sport, etc.). Bars have GAPS between them. Width has no meaning.

**Histogram**: For CONTINUOUS / grouped data with class intervals. Bars TOUCH (no gaps), reflecting that the class boundaries are continuous. Bar WIDTH represents class size; HEIGHT represents frequency.

**Frequency polygon**: connect the midpoints (class marks) of the tops of histogram bars to form a line graph. Useful for comparing two distributions on the same axes.

**Key rule**: histogram bars must have no gaps; bar graph bars MUST have gaps.

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