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
Can the assumed mean be 60?
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
Can the assumed mean be 60?
The correct option is B 57.18, yes
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−afidi50−521551−6−9053−5511054−3−33056−58135570059−6111560334562−6425636150Total∑fi=400∑fidi=75
Mean(x)=a+∑fidi∑fi =57+75400 =57.1875
We could have taken a different assumed mean, for example, 60. The answer would be the same. However, to make the calculations easier, the assumed mean is selected from the middle class interval.
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−afidi50−521551−6−9053−5511054−3−33056−58135570059−6111560334562−6425636150Total∑fi=400∑fidi=75
Mean(x)=a+∑fidi∑fi =57+75400 =57.1875
We could have taken a different assumed mean, for example, 60. The answer would be the same. However, to make the calculations easier, the assumed mean is selected from the middle class interval.
