Question

Calculate the mean deviation about median for the following data:
Class. Frequency
0-10. 6
10-20 7
20-30 15
30-40. 16
40-50. 4
50-60. 2​

Answer 1

Solution :-

we have,

→ N = 50

so,

→ Median class = (N/2)th term = 50/2 = 25th term => 20 - 30 .

now, we know that,

• Median = L + [(n/2 - CF) / f] * h

we have,

• L = Lower limit of median class = 20 .
• (n/2) = 25 .
• CF = cumulative frequency of class before median class = 13 .
• f = frequency of median class = 15 .
• h = class size = 10 .

then,

→ Median = 20 + {(25 - 13)/15} * 10

→ Median = 20 + (12/15) * 10

→ Median = 20 + (120/15)

→ Median = 20 + 8

→ Median = 28 .

now, from image we get,

• ⅀Fi * |Xi - M| = 508 .
• ⅀Fi = 50 .

therefore,

→ Mean deviation about median = ⅀Fi * |Xi - M| / ⅀Fi = 508 / 50 = 10.16 (Ans.)

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