The following is the distribution of height of students of a certain class in a certain city:
Height (in cms): 160-162 163-165 166-168 169-171 172-174
No. of students: 15 118 142 127 18
Find the average height of maximum number of students.

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Solution

Heights(exclusive) 160-162 163-165 166-168 169-171 172-174

Heights (inclusive) 159.5-162.5 162.5-165.5 165.5-168.5 168.5-171.5 171.5-174.5

No of students 15 118 142 127 18

Here the maximum frequency is 142, then the corresponding class 165.5 – 168.5 is the modal class

l = 165.5, h = 168.5 – 165.5 = 3, f = 142, , $f_{1} = 118, f_{2} = 127$
$Mode space equals space straight l plus fraction numerator straight f â�� straight f 1 over denominator 2 straight f â�� straight f 1 minus straight f 2 end fraction cross times straight h space space space space space space space space space space space space equals space 165.5 plus fraction numerator 142 â�� 118 over denominator 2 cross times 142 â�� 118 â�� 127 end fraction cross times 3 space space space space space space space space space space space space equals space 165.5 space plus space 72 over 39 space space space space space space space space space space space space equals space 165.5 space plus space 1.85 space space space space space space space space space space space space space space equals space 167.35 space cm$

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Heights(exclusive)	160-162	163-165	166-168	169-171	172-174
Heights (inclusive)	159.5-162.5	162.5-165.5	165.5-168.5	168.5-171.5	171.5-174.5
No of students	15	118	142	127	18

The following is the distribution of height of students of a certain class in a certain city: Height (in cms): 160-162 163-165 166-168 169-171 172-174 No. of students: 15 118 142 127 18 Find the average height of maximum number of students.

The following is the distribution of height of students of a certain class in a certain city:
Height (in cms): 160-162 163-165 166-168 169-171 172-174
No. of students: 15 118 142 127 18
Find the average height of maximum number of students.