(Ans: 26.07 m 11. The frequency distribution of heights of 110 male workers in a factory is given below. Height (inches): 60-62 63-65 66-68 69-71 72-74 No. of workers: 5 18 42 27 18 Find the mean height of the workers by using: (a) Direct Method (b) Short-cut Method (c) Step Deviation Method Ans: 67.95
Answers
Solution :-
a) Direct Method :-
Height -------------- Fi --------- Xi -------- FiXi
59.5-62.5 ----------- 5 --------- 61 ------- 305
62.5-65.5 ----------- 18 ---------64 ------ 1152
65.5-68.5 ----------- 42 --------67 ------ 2814
68.5-71.5 ----------- 27 ---------70 ----- 1890
71.5-74.5 ----------- 18 ---------73 ------ 1314
---------------------⅀Fi = 110 ⅀ FiXi = 7475
so,
→ Mean = ⅀ FiXi / ⅀ Fi
→ Mean = 7475/110
→ Mean = 67.95
b) Short-cut Method :-
Height -------- Fi ----- Xi -----Di(Xi-A)----- FiDi
59.5-62.5 -----5 ------61 ------- (-6) --- (-30)
62.5-65.5 -----18 -----64 ------ (-3) ---- (-54)
65.5-68.5 -----42 ---67(A) --- 0 ----- 0
68.5-71.5 ------27 ----70 ------ 3 ----- 81
71.5-74.5 ------18 -----73 ------ 6 ----- 108
-----------------⅀Fi = 110------ ⅀ FiDi = 105
so,
→ Mean = A + (⅀ FiDi / ⅀ Fi)
→ Mean = 67 + (105/110)
→ Mean = 67 + 0.95
→ Mean = 67.95
c) Step Deviation Method :-
→ h = class size = 3
→ Ui = (Xi - A) / h
Height -------- Fi ----- Xi -----Ui----- FiUi
59.5-62.5 -----5 ------61 ----(-2) --- (-10)
62.5-65.5 -----18 -----64 ---(-1) ---- (-18)
65.5-68.5 -----42 ---67(A)--0 ----- 0
68.5-71.5 ------27 ----70 --- 1 ----- 27
71.5-74.5 ------18 -----73 ----2 ----- 36
-----------------⅀Fi = 110-----⅀ FiUi = 35
so,
→ Mean = A + h(⅀ FiUi / ⅀ Fi)
→ Mean = 67 + 3(35/110)
→ Mean = 67 + (105/110)
→ Mean = 67 + 0.95
→ Mean = 67.95
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