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Calculate mode , given the following dat...

Calculate mode , given the following data set :
`{:("Mid - value",15,25,35,45,55,65,75,85),("Frequency",5,8,12,16,28,15,3,2):}`

Text Solution

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A series with 'mid- vlaue' is first to be expanded as a series with class intervals , as under :

Class interval 50-60 is the one with highest frequency . This is the model class interval , as the frequency are increasing or decreasing in a systematic pattern . the actual value of mode is ,
`Z=l_(1)+(f_(1)-f_(0))/(2f_(1)-f_(0)-f_(2))xxi`
`=50+(28-16)/(2(28)-16-15)xx10`
`=50+(12)/(56-31)xx10`
`=50+(12)/(25)xx10`
`=50+4.8=54.8`
Mode (Z) =54.8.
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