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Exercises · Q3

Q.Ogives can be helpful in locating graphically the

(i) mode
(ii) mean
(iii) median
(iv) none of the above
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✓ Free question

Ogives help locate the median graphically — option (iii). The two ogives ('less than' and 'more than') cut each other at a point whose X-value is the median.

Concept first: what an ogive is

An ogive is a cumulative frequency curve. There are two kinds:

  • 'Less than' ogive — plot cumulative frequency against the upper class limits; the curve rises left to right.
  • 'More than' ogive — plot cumulative frequency against the lower class limits; the curve falls left to right.

Locating the median graphically

Method 1 — the two ogives: Draw both the 'less than' and 'more than' ogives on the same axes. They intersect at one point. Drop a perpendicular from that point to the X-axis; the value there is the median.

Method 2 — a single ogive: Mark N/2 on the cumulative-frequency (Y) axis, move across to the ogive, then drop down to the X-axis to read the median.

OptionVerdict
(i) mode✗ located from a histogram
(ii) mean✗ not read from an ogive
(iii) median✓ Correct
(iv) none of the above✗
✓Final answer

(iii) median — ogives (cumulative frequency curves) locate the median graphically; the X-coordinate of the intersection of the 'less than' and 'more than' ogives gives the median.

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