Question

Calculate mean median mode marks 0 10 20 30 40 50 60 70 80 no of student 150 140 100 80 80 70 80 14 0

Answer 1

Solution :-

Class --------- Fi ------------ Xi ----FiXi------- CF

0 - 10 ---------150 ---------- 5 -----750------- 150

10 - 20 --------140 ---------- 15 -----2100-----290

20 - 30 --------100 ---------- 25 ----2500----390

30 - 40 -------- 80 ---------- 35 -----2800----470

40 - 50 --------- 80 ---------- 45 -----3600----550

50 - 60 ---------70 ---------- 55 -----3850-----620

60 - 70 ---------80 ---------- 65 -----5200-----700

70 - 80 --------- 14 ---------- 75 -------1050----714

⅀ Fi = 714. ⅀FiXi = 21850

so,

→ Mean = ⅀FiXi / ⅀Fi = 21850/714 = 30.60 (Ans.)

now,

→ n = 714 .

So,

→ (n/2) = 357 .

Then, Cumulative frequency greater than 357 is 390, corresponds to the class 20 - 30.

Therefore,

→ Class 20 - 30 is the median class.

Now,

• Median = l + [{(n/2) - cf} / f] * h

from data we have :-

• l = lower limit of median class = 20
• n = total frequency = 714
• cf = Cumulative frequency of class before median class = 290 .
• f = frequency of median class = 100 .
• h = size of class = 10 .

Putting all value we get :-

→ Median = 20 + [(357 - 290)/100] * 10

→ Median = 20 + (67/100) * 10

→ Median = 20 + 6.7

→ Median = 26.7 (Ans.)

then,

→ Mode = 3 Median - 2 Mean

→ Mode = 3 * 26.7 - 2 * 30.6

→ Mode = 80.1 - 61.2

→ Mode = 18.9 (Ans.)

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