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Exercise 10.2 · Q1

Q.Discuss the difference between bar graph and histogram from charts given in examples of respective concepts.

Yanam CbseNCERTSubjective· 3mImportance★★★★★est
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Bar graphs represent discrete/categorical data with separated bars; histograms represent continuous, grouped (class-interval) data with adjoining bars.

Bar graph: rectangular bars of equal width, one per category, height/length ∝\propto value of that category; bars are drawn with gaps between them since categories are discrete and unordered.

Histogram: rectangles drawn over class-intervals on a continuous numeric axis, width = class width hh, height = frequency (or frequency density if class widths differ); bars are drawn touching each other (no gaps) since the underlying variable is continuous.

  1. Data type: a bar graph is used for qualitative/discrete data (e.g., favourite fruit, exam pass/fail); a histogram is used for continuous quantitative data grouped into class-intervals (e.g., heights of students in 150–155 cm, 155–160 cm, ...).
  2. Gaps: bar graphs leave uniform gaps between bars (categories are independent); histograms have no gaps — adjacent bars share a boundary (the class limits are continuous).
  3. Axis: a bar graph's horizontal axis lists categories (order is arbitrary, can be rearranged); a histogram's horizontal axis is a continuous numeric scale (order is fixed by magnitude).
  4. What height represents: in a bar graph, height directly equals the value/frequency of the category; in a histogram with unequal class widths, the area of the bar, not just its height, represents the frequency.
  5. Example: "Number of students preferring Cricket/Football/Kabaddi" ⇒\Rightarrow bar graph (categorical). "Distribution of 100 students' weights in 5 kg classes" ⇒\Rightarrow histogram (continuous, grouped).
✓Final answer

Bar graph → discrete/categorical data, gapped bars, height = value, bars reorderable. Histogram → continuous grouped data, touching bars on a numeric axis, area (∝ frequency) is the meaningful measure.

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