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Question
The table shows the Distribution of the Scores obtained by 155 shooters in a shooting competition. Using the step - deviation method find the mean.
ScoresNo. of shooters0−101010−201220−301530−40840−502050−602460−70770−801180−903090−10018
The table shows the Distribution of the Scores obtained by 155 shooters in a shooting competition. Using the step - deviation method find the mean.
ScoresNo. of shooters0−101010−201220−301530−40840−502050−602460−70770−801180−903090−10018
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Solution
The correct option is B 55.77
ClassMid valueFrequencyμ=x−ah fiuiInterval(xi)(fi)0−10510−5−5010−201512−4−4820−302515−3−4530−40358−2−1640−504520−1−2050−6055=a240060−706571770−80751122280−90853039090−1009518472Total∑fi=155∑fiui=12
Let, the assumed mean (a) = 55.
Class width (h) = 10
∴Mean=a+ΣfuΣf×h
=55+12155×10
=55+0.77
=55.77
ClassMid valueFrequencyμ=x−ah fiuiInterval(xi)(fi)0−10510−5−5010−201512−4−4820−302515−3−4530−40358−2−1640−504520−1−2050−6055=a240060−706571770−80751122280−90853039090−1009518472Total∑fi=155∑fiui=12
Let, the assumed mean (a) = 55.
Class width (h) = 10
∴Mean=a+ΣfuΣf×h
=55+12155×10
=55+0.77
=55.77
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