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Question

The following table gives production yield in kg per hectare of wheat of 150 farms in a village. Calculate the mean, median and mode production yield.

Production Yield505353565659596262656568687171747477(kg per hectare)Number of Farms381430362816105

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Solution

(i) Mean

Production YieldNumber of FarmsMid -ValueA=63.5d=XAcfd5053351.5124125356854.5932456591457.5622859626060.5313062653663.500065682866.5+3+12868716169.5+6+23271741072.5+9+3307477575.5+2+420Totalf=150fd=16

¯¯¯¯¯K=A+fdf×c

=63.5+16150×3

=63.5+0.32

=63.82 kg per hectare

(ii) Median

Class Interval Frequencycf505333535681156591425596230556265369165682811968716113571741014574775150Totalf=150

Median class =Size of (N2) th item

= size (1502) th= 75th item

75th item lies in the 91st cumulative frequency and the corresponding class interval is 62 - 65.

Median = L+N2cffX4

=62+755536×3

=62+2036×3

= 63.67 kg per hectare

(iii) Mode

Grouping Table

Class Interval IIIIIIIVVVI5053353568112225528056591459623044669462653665682864448054687161717410261531747755

Analysis Table

Mode class = 62-65

Mode = L+f1f02f1f0f2X4

=62+36302×363028×3

=62+6723028×3

=62+614×3

=62+1814

=63.29 kg per hectare.


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