The frequency distribution of the heights (in cm) of 100 students of class X in a school .Find the average height of the students .

Explanation

Here , the class boundaries are 139.5-144.5,149.5,……179.5-184.5. The class mid-values are 142,147,………182 and class-length=5. The mid value 162 of the class interval 160-164 is assumed to be the origin and 5, the class-length is assumed to be the unit, then `u=(x-162)/(5) and barx=162+5baru`
Let us now prepare the following table :

`therefore u=(sum m.f)/(sumf)=(8)/(100)=0.08`
`therefore barx=162+ 5.baru=162+5xx0.08=162+0.40 =162.40 cm` .
`therefore ` The average height of 100 students is 162.4 cm.