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The table below gives the percentage dis...

The table below gives the percentage distribution of female teachers in the primary schools of rural areas of various states and union territories (U.T.) of India. Find the mean percentage of female teachers by all the three methods discussed in this section.

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`{(CI,x_i,fi,x_i fi),(15-25,20,6,120),(25-35,30,11,330),(35-45,40,7,280),(45-55,50,4,200),(55-65,60,4,240),(65-75,70,2,140),(75-85,80,1,80),(,,sumf_i=35,sumf_i*x_i=1390):}`
`x_i= ("lower class + upper class")/2`

`"(a.) Using Direct Method"`
`barx=(sumf_i*x_i)/(sumf_i) = 1390/35 = 39.714`

`"(b.)Using assumed mean method"`
Here `a=50 , d_i=x_i-50`
`barx=a+(sumf_i*d_i)/(sumf_i) = 50+ (-360)/(35) = 39.714`

`"(c.)Using step-deviation method"`
`a=50 , h=10 , u_i=(x_i-50)/10`
`barx=a+(sumf_i*u_i)/(sumf_i) xx h= 50+ (-36)/(35)xx10 = 39.714`
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