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When a histogram is drawn from a table with unequal class widths, the bar heights must first be converted to frequency density. For finding the MEDIAN from the same unequal-width table:

Class 10Median of Grouped DataStatistics and Probability
  • Aall classes must first be made equal in width
  • Bevery frequency must first be divided by its class width
  • Cno adjustment is needed, because the formula uses only the median class's own l, f and h
  • Dthe median cannot be found at all when the widths are unequal

Step-by-Step Solution

Median = reads four things off the median class — its lower boundary , its own frequency , its own width — plus and the cumulative frequency of the class before it. Nothing is ever compared ACROSS classes, so unequal widths cause no distortion. A histogram is different: there the AREA of each bar must be proportional to its frequency, which is exactly why unequal widths force frequency density. Dividing the frequencies by the widths would wreck the cumulative count that is matched against, and merging classes to equal widths throws away information the table already gives.
Answer: C) no adjustment is needed, because the formula uses only the median class's own l, f and h

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