# The Following is the Distribution of Height of Students of a Certain Class in a Certain City: Find the Average Height of Maximum Number of Students. - Mathematics

The following is the distribution of height of students of a certain class in a certain city:

 Height (in cm): 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.

#### Solution

 Height(exclusive) Height(inclusive) No. of students 160 - 162 159.5-162.5 15 163 - 165 162.5-165.5 118 166 - 168 165.5-168.5 142 169 - 171 168.5-171-.5 127 172 - 174 171.5-174.5 18

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

L = 165.5, h = 168.5 – 165.5 = 3, f = 142, f1 = 118, f2 = 127

Mode rArr=l+(f-f1)/(2f-f1-f2)xxh

=165.5+(142-118)/(2xx142-118-127)xx3

=165.5+(24xx3)/39

= 165.5 + 72/39

= 165.5 + 1.85

= 167.35 cm

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#### APPEARS IN

RD Sharma Class 10 Maths
Chapter 15 Statistics
Exercise 15.5 | Q 6 | Page 46