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Mathematics

Consider the following table :

Diameter of heart (in mm)Number of persons
1205
1219
12214
1238
1245
1259

The median of the above frequency distribution is :

  1. 122 mm

  2. 122.5 mm

  3. 122.75 mm

  4. 123 mm

Measures of Central Tendency

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Answer

Cumulative frequency distribution table is as follows :

Diameter of heart (in mm)Number of personsCumulative frequency
12055
121914 (5 + 9)
1221428 (14 + 14)
123836 (28 + 8)
124541 (36 + 5)
125950 (41 + 9)

Here n = 50, which is even.

By formula,

Median = n2 th observation+(n2+1) th observation2\dfrac{\dfrac{\text{n}}{2} \text{ th observation} + \Big(\dfrac{\text{n}}{2} + 1\Big) \text{ th observation}}{2}

=502 th observation+(502+1) th observation2=25 th observation+(25+1) th observation2=25 th observation+26 th observation2=122+1222=2442=122 mm.= \dfrac{\dfrac{50}{2} \text{ th observation} + \Big(\dfrac{50}{2} + 1\Big) \text{ th observation}}{2} \\[1em] = \dfrac{25 \text{ th observation} + \Big(25 + 1\Big) \text{ th observation}}{2} \\[1em] = \dfrac{25 \text{ th observation} + 26 \text{ th observation}}{2} \\[1em] = \dfrac{122 + 122}{2} \\[1em] = \dfrac{244}{2} \\[1em] = 122 \text{ mm}.

Since, all observations from 25th to 26th corresponds to 122 mm.

Hence, Option 1 is the correct option.

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