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 Yield50−5353−5656−5959−6262−6565−6868−7171−7474−77(kg per hectare)Number of Farms381430362816105
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 Yield50−5353−5656−5959−6262−6565−6868−7171−7474−77(kg per hectare)Number of Farms381430362816105
(i) Mean
Production YieldNumber of FarmsMid -ValueA=63.5d=X−Acfd50−53351.5−12−4−1253−56854.5−9−3−2456−591457.5−6−2−2859−626060.5−3−1−3062−653663.500065−682866.5+3+12868−716169.5+6+23271−741072.5+9+33074−77575.5+2+420Total∑f=150∑fd=16
¯¯¯¯¯K=A+∑fd∑f×c
=63.5+16150×3
=63.5+0.32
=63.82 kg per hectare
(ii) Median
Class Interval Frequencycf50−533353−5681156−59142559−62305562−65369165−682811968−716113571−741014574−775150Total∑f=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+N2−cffX4
=62+75−5536×3
=62+2036×3
= 63.67 kg per hectare
(iii) Mode
Grouping Table
Class Interval IIIIIIIVVVI50−53353−568112225528056−591459−623044669462−653665−68286444805468−716171−741026153174−7755
Analysis Table
Mode class = 62-65
Mode = L+f1−f02f1−f0−f2X4
=62+36−302×36−30−28×3
=62+672−30−28×3
=62+614×3
=62+1814
=63.29 kg per hectare.
(i) Mean
Production YieldNumber of FarmsMid -ValueA=63.5d=X−Acfd50−53351.5−12−4−1253−56854.5−9−3−2456−591457.5−6−2−2859−626060.5−3−1−3062−653663.500065−682866.5+3+12868−716169.5+6+23271−741072.5+9+33074−77575.5+2+420Total∑f=150∑fd=16
¯¯¯¯¯K=A+∑fd∑f×c
=63.5+16150×3
=63.5+0.32
=63.82 kg per hectare
(ii) Median
Class Interval Frequencycf50−533353−5681156−59142559−62305562−65369165−682811968−716113571−741014574−775150Total∑f=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+N2−cffX4
=62+75−5536×3
=62+2036×3
= 63.67 kg per hectare
(iii) Mode
Grouping Table
Class Interval IIIIIIIVVVI50−53353−568112225528056−591459−623044669462−653665−68286444805468−716171−741026153174−7755
Analysis Table
Mode class = 62-65
Mode = L+f1−f02f1−f0−f2X4
=62+36−302×36−30−28×3
=62+672−30−28×3
=62+614×3
=62+1814
=63.29 kg per hectare.
