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Question

In a retail market, fruit vendors were selling mangoes kept in packing boxes. These boxes contained varying number of mangoes. The following was the distribution of mangoes according to the number of boxes.

Number of mangoes50525355565859616264Number of boxes1511013511525

Find the mean number of mangoes kept in a packing box. Which method of finding the mean did you choose?


Solution

Number of mangoesNumber of boxes505215535511056581355961115626425

We may observe that class intervals are not continuous. There is a gap of 1 between two class intervals. So we have to add 12 to upper class limit and subtract 12 from lower class limit of each interval.
The class mark (xi) may be obtained by using the relation:

xi =Upper class limit  + lower class limit2

Class size h of this data = 3

Since, the given data is large, we will use Assumed Mean Method to find the mean. This method helps in reducing the calculations and results in small numerical values. We will choose the assumed mean (a) in such a way so that the the value obtained in di,cancel out each other.

Now, taking 57 as assumed mean (a); we may calculate di,ui,fiui as following –

Class intervalfixidi=xi57fidi49.552.51551630652.555.511054316255.558.5135570058.561.511560318061.564.525636378Total400  90

Now, we may observe that:

fi=400fidi=90Mean ¯x=a+(fidifi)=57+90400=57+0.225=57.225=57.2

Clearly, mean number of mangoes kept in a packing box is 57.2.


Mathematics

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