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The following table shows the ages of the patients admitted in a hospital during a year:

Find the mode and the mean of the data given above. Compare and interpret the two measures of central tendency.

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We may compute class marks (xI) as per the relation

x1 \(=\frac{upper\,class\,limit+lower\,class\,limit}{2}\)

Now, 

let assumed mean (A) = 30

∑fi=80, ∑fidi=430

Mean = A + \(\frac{\sum f_id_i}{\sum f_i}\)

\(=30+\frac{430}{80}=30+5.375\)

=35.38

It represents that on an average the age of patients admitted was 35.38 years. As we can observe that the maximum class frequency 23 belonging to class interval 35-45. 

So, 

modal class= 35-45 

Lower limit (l) of modal class =35 

Frequency (f1) of the modal class=23 

h=10, 

Frequency (f0)of class preceding the modal class=21 

Frequency (f2) of class succeeding the modal class =14

Now,

Mode = \(I+(\frac{f-f_0}{2f-f_0-f_2})h\)

\(=35+(\frac{23-21}{2(23)-21-14})10\)

=35 + 1.81 =36.8years

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