From the data given below state which group is more variable $A$ or $B$
Marks 10-20 20-30 30-40 40-50 50-60 60-70 70-80
Group A 9 17 32 33 40 10 9
Group B 10 20 30 25 43 15 7

Question

From the data given below state which group is more variable A or B Marks10-2020-3030-4040-5050-6060-7070-80Group A917323340109Group B1020302543157

Filo · Accepted Answer

Class fi​ xi​ui​=hxi​−A​  ui2​ fi​ui​fi​ui2​  10-20 9 15 -3 9 -27 8120-30 17 25 -2 4 -34 68 30-40 32 35 -1 1 -32 32 40-5033  45 0 0 0 0 50-60 4055  11  40 4060-70  10 65 2 4 20 4070-80  9 75 3 9 27 81 Total 150    -6 342Here h=10,N=150Let assumed mean A=45Mean xˉ=A+N∑i=17​fi​ui​​×h=45+150(−6)×10​=45−0.4=44.6Variance (σ12​ )=N2h2​⎣⎡​Ni=l∑7​fi​ui2​−(i=l∑7​fi​ui​)2⎦⎤​=22500100​[150×342−(6)2] =2251​(51264) =227.84∴ Standard deviation (σ1​)=227.84​=15.09  Group B: Class fi​ xi​ui​=hxi​−A​  ui2​ fi​ui​fi​ui2​  10-20 10 15 -3 9 -30 9020-30 20 25 -2 4 -40 80 30-40 30 35 -1 1 -30 30 40-5025 45 0 0 0 0 50-60 4355  11  43 4360-70  15 65 2 4 30 6070-80  7 75 3 9 2163 Total 150    -6 366Here h=10,N=150Let assumed mean A=45Mean xˉ=A+N∑i=17​fi​ui​​×h=45+150(−6)×10​=45−0.4=44.6Variance (σ22​ )=N2h2​⎣⎡​Ni=l∑7​fi​ui2​−(i=l∑7​fi​ui​)2⎦⎤​=22500100​[150×366−(6)2] =2251​(54864) =243.84∴ Standard deviation (σ2​)=243.84​=15.61 Since, the mean of both the groups is same the group with greater standard deviation will be more variable. Thus group B has more variability in the marks.

Question Text	From the data given below state which group is more variable $A$ or $B$
Answer Type	Text solution:1
Upvotes	150

From the data given below state which group is more variable $A$ or $B$
Marks 10-20 20-30 30-40 40-50 50-60 60-70 70-80
Group A 9 17 32 33 40 10 9
Group B 10 20 30 25 43 15 7

Text solutionVerified

Practice questions from similar books

Marks	10-20	20-30	30-40	40-50	50-60	60-70	70-80
Group A	9	17	32	33	40	10	9
Group B	10	20	30	25	43	15	7

Class	$f_{i}$	$x_{i}$	$u_{i} = \frac{x _{i} - A}{h}$	$u_{i}^{2}$	$f_{i} u_{i}$	$f_{i} u_{i}^{2}$
10-20	9	15	-3	9	-27	81
20-30	17	25	-2	4	-34	68
30-40	32	35	-1	1	-32	32
40-50	33	45	0	0	0	0
50-60	40	55	1	1	40	40
60-70	10	65	2	4	20	40
70-80	9	75	3	9	27	81
Total	150				-6	342