Question

the mode of the following distribution is 15 the mean of the data and then find the median value of by using empirical formula relating mean,median and mode C.I( 1-5 ,5-9,9-13,13-17,17-21) number of workers (7,2,2,8,1) please answer this question step by step​

Answer 1

Solution :-

CI --------- Fi ---------- Xi ------------- FiXi

1-5 -------- 7 ---------- 3 ------------- 21

5-9 --------2 ---------- 7 ------------- 14

9-13 -------2 ---------- 11 ------------- 22

13-17 -------8 ---------- 15 ------------- 120

17-21 -------1 ---------- 19 ------------- 19

⅀Fi = 20 ⅀FiXi = 196

so,

→ Mean = ⅀FiXi / ⅀Fi = 196/20 = 9.8 .

also, given that,

→ Mode = 15 .

then, using empirical formula we get,

→ 3Median = Mode + 2Mean

→ 3Median = 15 + 2(9.8)

→ 3Median = 15 + 19.6

→ 3Median = 34.6

→ Median = 11.54 (Ans.)

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