Mock test : 1 -

[Dhiman Sengupta]

Last question --

Did anyone solve the 1st question ? 

A statistician, who is not good at math, wants to represent the relative frequencies of the 1010 different categories of a categorical variable in a pie chart. He calculated the relative frequency of each category. In order to make a pie chart representing categories, he calculated the angle of slices for the first 99 categories using the wrong formula π∗riπ∗ri radians, where riri represents the relative frequency of the ithith category. Since he knows that the sum of angles of slices must be 2π2π radians, he calculated the angle of the tenth slice as 2π−π∗∑9i=1ri2π−π∗∑i=19ri.

If the total frequency is equal to 500500 and the angle of the tenth category using the above formula is 1.02π1.02π radians in the pie chart, then what is the actual frequency of the tenth category?  

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Thanks,

Dhiman Sengupta

Bangalore

Ph: +91 7338130710

[Hussain Khambati]

Since summation of all relative frequency is equal to 1, the summation of all relative frequencies from 1 to 9 can be written as: 1-r10(r10 is the relative frequency of the 10th variable)

therefore a given in the question,

1.02π=  2π−π∗(1-r10)

1.02 π=2 π- π+ π r10

1.02 π=  π+ πr10

1.02 π= π(1+r10)

1.02=1+r10

r10=0.02

since total frequency is 500, the 10th frequency is r10*500=0.02*500=10