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Exercises · Q2

Q.Data represented through a histogram can help in finding graphically the

(i) mean
(ii) mode
(iii) median
(iv) all the above
Andaman Nicobar CbseNCERTSubjective· 1mImportance★★★★★est
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✓ Free question

A histogram helps find the mode graphically — option (ii). The mode lies inside the tallest (modal) rectangle and is located by drawing two cross-diagonals and dropping a perpendicular to the X-axis.

Concept first: histogram and the mode

A histogram is a set of adjacent rectangles whose areas are proportional to the class frequencies; for equal class intervals the heights are proportional to the frequencies. The modal class is the class with the highest frequency — i.e. the tallest rectangle.

Locating the mode graphically

  1. Identify the tallest rectangle (the modal class).
  2. From its top-left corner, draw a line to the top-left corner of the rectangle on its right.
  3. From its top-right corner, draw a line to the top-right corner of the rectangle on its left.
  4. These two diagonals intersect inside the modal rectangle.
  5. Drop a perpendicular from the point of intersection to the X-axis. The value at its foot is the mode.
OptionVerdict
(i) mean✗ not read from a histogram
(ii) mode✓ Correct
(iii) median✗ located from an ogive, not a histogram
(iv) all the above✗
✓Final answer

(ii) mode — a histogram locates the mode graphically via the cross-diagonals of the tallest (modal) rectangle and a perpendicular dropped to the X-axis.

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