KnowledgeBoat Logo
|

Mathematics

Consider the following table:

ClassFrequency
0 - 58
5 - 1010
10 - 1519
15 - 2025
20 - 258

The upper limit of the median class is :

  1. 10

  2. 15

  3. 20

  4. 25

Measures of Central Tendency

1 Like

Answer

We construct the cumulative frequency distribution table as under :

ClassFrequencyCumulative frequency
0 - 588
5 - 101018 (10 + 8)
10 - 151937 (18 + 19)
15 - 202562 (37 + 25)
20 - 25870 (62 + 8)

Here n = 70, 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}

=702 th observation+(702+1) th observation2=35 th observation+(35+1) th observation2=35th observation+36 th observation2= \dfrac{\dfrac{70}{2} \text{ th observation} + \Big(\dfrac{70}{2} + 1\Big) \text{ th observation}}{2} \\[1em] = \dfrac{35 \text{ th observation} + \Big(35 + 1\Big) \text{ th observation}}{2} \\[1em] = \dfrac{35 \text{th observation} + 36 \text{ th observation}}{2}

As observation from 19th to 37th lies in the class 10 - 15

∴ Median class = 10 - 15, with upper limit = 15

Hence, Option 2 is the correct option.

Answered By

1 Like


Related Questions