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Mathematics

Construct the following frequency distribution :

ClassFrequency
0 - 513
6 - 1110
12 - 1715
18 - 238
24 - 2911

The upper limit of the median class is

  1. 17

  2. 17.5

  3. 18

  4. 18.5

Measures of Central Tendency

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Answer

Converting the discontinuous interval into continuous interval.

Adjustment factor = (Lower limt of one class - Upper limit of previous class) / 2

=11102=12=0.5= \dfrac{11 - 10}{2} \\[1em] = \dfrac{1}{2} \\[1em] = 0.5

We construct the cumulative frequency distribution table as under :

Classes before adjustmentClasses after adjustmentFrequencyCumulative frequency
0 - 50 - 5.51313
6 - 115.5 - 11.51023
12 - 1711.5 - 17.51538
18 - 2317.5 - 23.5846
24 - 2923.5 - 29.51157

Here n (total no. of observations) = 57.

As n is odd,

Median =n+12th observation=57+12=582=29th observation\therefore \text{Median } = \dfrac{n + 1}{2} \text{th observation} \\[1em] = \dfrac{57 + 1}{2} \\[1em] = \dfrac{58}{2} \\[1em] = 29 \text{th observation}

As observation from 24th to 38th lies in the class 11.5 - 17.5

∴ Median class = 11.5 - 17.5, with upper limit = 17.5

Hence, Option 2 is the correct option.

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