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Question
Find the mean of the data given in the table using step - deviation method.
Class IntervalFrequency0−101010−201220−30730−40640−50550−608
Find the mean of the data given in the table using step - deviation method.
Class IntervalFrequency0−101010−201220−30730−40640−50550−608
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Solution
The correct option is B 26.67
Class InternalMid value (x_i)Frequency (f_i)u=xi−ahfiui0−10510−3−3010−201512−2−2420−30257−1−730−4035=a60040−504551550−60558216Total∑ fi=48∑u=−3∑ fiui=−40
Let's the assumed mean (a) = 35.
Class width (h) = 10 - 0 = 10
∴Mean=a+∑fiui∑fi×h
=35+−4048×10
=35+(−8.33)
=35−8.33
=26.67
Class InternalMid value (x_i)Frequency (f_i)u=xi−ahfiui0−10510−3−3010−201512−2−2420−30257−1−730−4035=a60040−504551550−60558216Total∑ fi=48∑u=−3∑ fiui=−40
Let's the assumed mean (a) = 35.
Class width (h) = 10 - 0 = 10
∴Mean=a+∑fiui∑fi×h
=35+−4048×10
=35+(−8.33)
=35−8.33
=26.67
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