From the data given below state which group is more variable, A or B ?
Marks10−2020−3030−4040−5050−6060−7070−80Group A917323340109Group B1020302543157
From the data given below state which group is more variable, A or B ?
Marks10−2020−3030−4040−5050−6060−7070−80Group A917323340109Group B1020302543157
Group A
Mid values Marks xifiu=x−4510fufu210−2015 9−3−278120−302517−2−346830−403532−1−323240−504533 0 0 050−605540 1 404060−706510 2 204070−8075 9 3 2781 150−6342
Mean (¯¯¯¯¯x1)=A+∑fuN×h=45−6150×10=45−0.4=44.6
Standard deviation(σ1)=hN√N∑fu2−(∑fu)2=10150√150×342−(−6)2
=115√51300−36=115×226.41=15.09
Group B
Mid values Marks xifiu=x−4510fufu210−201510−3−309020−302520−2−408030−403530−1−303040−504525 0 0 050−605543 1 434360−706515 2 306070−8075 7 3 2163 150−6366
Mean (¯¯¯¯¯x2)=A+∑fuN×h=45−6150×10=45−0.4=44.6
Standard deviation(σ2)=hN√N∑fu2−(∑fu)2=10150√150×366−(−6)2
=115√5490036=115×234.23=15.61
Since ¯x1=¯x2. So the group which have greater S.D. is more variable. Thus group B is more variable
Group A
Mid values Marks xifiu=x−4510fufu210−2015 9−3−278120−302517−2−346830−403532−1−323240−504533 0 0 050−605540 1 404060−706510 2 204070−8075 9 3 2781 150−6342
Mean (¯¯¯¯¯x1)=A+∑fuN×h=45−6150×10=45−0.4=44.6
Standard deviation(σ1)=hN√N∑fu2−(∑fu)2=10150√150×342−(−6)2
=115√51300−36=115×226.41=15.09
Group B
Mid values Marks xifiu=x−4510fufu210−201510−3−309020−302520−2−408030−403530−1−303040−504525 0 0 050−605543 1 434360−706515 2 306070−8075 7 3 2163 150−6366
Mean (¯¯¯¯¯x2)=A+∑fuN×h=45−6150×10=45−0.4=44.6
Standard deviation(σ2)=hN√N∑fu2−(∑fu)2=10150√150×366−(−6)2
=115√5490036=115×234.23=15.61
Since ¯x1=¯x2. So the group which have greater S.D. is more variable. Thus group B is more variable
