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Mathematics

For the following distribution :

ClassFrequency
0 - 510
5 - 1015
10 - 1512
15 - 2020
20 - 259

The sum of lower limits of the median class and modal class is

  1. 15

  2. 25

  3. 30

  4. 35

Measures of Central Tendency

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Answer

We construct the cumulative frequency distribution table as under :

ClassFrequencyCumulative frequency
0 - 51010
5 - 101525
10 - 151237
15 - 202057
20 - 25966

Here n (total no. of observations) = 66.

As n is even,

∴ Median = (n2\dfrac{n}{2}th observation + (n2+1\dfrac{n}{2} + 1)th observation) / 2

=662+(662+1)2=33th observation+34th observation2= \dfrac{\dfrac{66}{2} + \Big(\dfrac{66}{2} + 1\Big)}{2} \\[1em] = \dfrac{33\text{th observation} + 34\text{th observation}}{2}

As observation from 26th to 37th lie in the class 10 - 15,

∴ Median class = 10 - 15.

Since the class 15 - 20 has highest frequency i.e. 20.

∴ Modal class = 15 - 20.

Sum of lower limit of median and modal class = 10 + 15 = 25.

Hence, Option 2 is the correct option.

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