Calculate the mean & standard deviation of the following
age distribution of members
Age
(Years) 50-60 60-70 70-80 80-90 90-100 100-110 110-120
Number
of
Members
5 61 132 153 140 51 5
Answers
Answer :-
Class Interval xi fi fixi fi*(xi)²
50−60 55 5 275 15125
60−70 65 61 3965 257,725
70−80 75 132 9900 742,500
80−90 85 153 13005 1,105,425
90−100 95 140 13300 1,263,500
100−110 105 51 5355 562,275
110−120 115 5 575 66125
⅀fi=547 ⅀fixi=46375 ⅀fixi²=4012675
we know that,
- Mean = ⅀fixi / ⅀fi
- variance = (⅀fixi² / ⅀fi) - (Mean)²
- standard deviation = √(variance)
Putting all values now we get :-
→ Mean = (46375/547) = 84.78 (Ans.)
and,
→ variance = (4012675/547) - (84.78)²
→ variance = 7335.78 - 7187.64
→ variance = 148.13 .
Hence,
→ Standard deviation = √(148.13) = 12.17 (Ans.)
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