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A histogram is drawn with equal class widths. The classes and frequencies are 0–20: 9, 20–40: 14, 40–60: 22 and 60–80: 11. Which class has the tallest bar, and what is its class mark?

Class 9StatisticsStatistics and Probability
  • A40–60, class mark 50
  • B40–60, class mark 20
  • C60–80, class mark 70
  • D20–40, class mark 30

Step-by-Step Solution

The greatest frequency is 22, so the tallest bar is the class 40–60. Its class mark = . The number 20 is the class size, not the class mark.
Answer: A) 40–60, class mark 50

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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