Question

Find the Mean, Median and Mode from the ages of married women in the first child birth: First Child 13 14 15 16 17 18 19 20 21 22 23 24 Number of married women 37 162 343 390 256 433 161 355 65 85 59 46

Answer 1

Solution :-

Let assumed mean is = 19 = a

Age(Xi) ----Fi ---- Di(Xi - a) --- Fi*Di ---- CF

13 -----------37 -------(-6) ----- -222 ----- 37

14 ----------162 ----- (-5) ---------810 ------199

15 ---------343 ----- (-4) ------ -1372 ------542

16 -------- 390 ------(-3) ------ -1170 ------ 932

17 ------- 256 ------(-2) ------- -512 ------1188

18 ------- 433 ------ (-1) ------- -433 ------1621

19 ---------161 ------- 0 -------- 0 ------1782

20 ------- 355 ------- 1 ----------355 -----2137

21 ---------65 -------- 2 ----------130 ---- 2202

22 --------85 -------- 3 ----------255 ----2287

23 --------59 ---------4 -------- 236 ----2346

24 ------- 46 -------- 5 ---------230 ----2392

⅀ Fi =2392 -------⅀Fi*Di = (-3313)

so,

→ Mean = a + (⅀Fi*Di / ⅀Fi)

→ Mean = 19 + (-3313/2392)

→ Mean = 19 - 1.385

→ Mean = 17.615

now,

→ (N/2) = 2392/2 = 1196 .

so, CF greater than 1196 is 1621 . then, we can conclude that, this is our median class . Therefore, Median is Xi of median class which is 18 .

now, mode will be with highest frequency which is 433 . Therefore, mode of the data is 18 .

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