Consider the following distribution of the number of mangoes being packed in cardboard boxes where these boxes contain varying number of mangoes. Find the mean number of mangoes kept in a packing box using assumed mean method?
Number of mangoes50−5253−5556−5859−6162−64Number of boxes1511013511525
Consider the following distribution of the number of mangoes being packed in cardboard boxes where these boxes contain varying number of mangoes. Find the mean number of mangoes kept in a packing box using assumed mean method?
Number of mangoes50−5253−5556−5859−6162−64Number of boxes1511013511525
The correct option is C 57.18
The class intervals are not continuous. There is a gap of 1 between 2
intervals. So 0.5 has to be added to the upper class limit of each
interval and 0.5 has to be subtracted from the lower class limit of
each interval to make class intervals continuous.
Let the assumed mean(a) be 57 (Choose the number in order to
get minimum deviation(d) in table shown below)
Class IntervalNumber of Mangoes(fi)Class mark(xi)di=xi−afidi49.5−52.51551−6−9052.5−55.511054−3−33055.5−58.5135570058.5−61.511560334561.5−64.525636150Total∑fi=400∑fidi=75
Mean (¯¯¯x)=a+∑fidi∑fi
=57+75400
=57.1875
57.18
The class intervals are not continuous. There is a gap of 1 between 2
intervals. So 0.5 has to be added to the upper class limit of each
interval and 0.5 has to be subtracted from the lower class limit of
each interval to make class intervals continuous.
Let the assumed mean(a) be 57 (Choose the number in order to
get minimum deviation(d) in table shown below)
Class IntervalNumber of Mangoes(fi)Class mark(xi)di=xi−afidi49.5−52.51551−6−9052.5−55.511054−3−33055.5−58.5135570058.5−61.511560334561.5−64.525636150Total∑fi=400∑fidi=75
Mean (¯¯¯x)=a+∑fidi∑fi
=57+75400
=57.1875
