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Question
The following table gives the literacy rate (in percentage) of 35 cities. Find the mean literacy rate by step deviation method.
Literacy rate (in percentage)45−5555−6565−7575−8585−95Number of cities3101183
The following table gives the literacy rate (in percentage) of 35 cities. Find the mean literacy rate by step deviation method.
Literacy rate (in percentage)45−5555−6565−7575−8585−95Number of cities3101183
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Solution
The correct option is B 69.43
The class size(h) is 55 – 45 = 10
(upper class limit - lower class limit)
Class mark(xi)=upper limit+lower limit2
Let the assumed mean(a) be 70 (Choose the number in order to get minimum values of d)
Class IntervalNumber of Frequency(fi)Class mark(xi)di=xi−aui=dihfiui45−55350−20−2−655−651060−10−1−1065−75117000075−85880101885−953902026Total∑fi=35∑fiui=−2
Mean (¯¯¯u)=a+(∑fiui∑fi)×h
=70+(−2 35)×10
=(70−0.57)
=69.43
The class size(h) is 55 – 45 = 10
(upper class limit - lower class limit)
Class mark(xi)=upper limit+lower limit2
Let the assumed mean(a) be 70 (Choose the number in order to get minimum values of d)
Class IntervalNumber of Frequency(fi)Class mark(xi)di=xi−aui=dihfiui45−55350−20−2−655−651060−10−1−1065−75117000075−85880101885−953902026Total∑fi=35∑fiui=−2
Mean (¯¯¯u)=a+(∑fiui∑fi)×h
=70+(−2 35)×10
=(70−0.57)
=69.43
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