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
Answers
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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