Find the mean variance and standard deviation using short-cut method
Height
in cms No. of children
70-75 3
75-80 4
80-85 7
85-90 7
90-95 15
95-100 9
100-105 6
105-110 6
110-115 3

Question

Find the mean variance and standard deviation using short-cut methodHeightin cmsNo. of children70-75375-80480-85785-90790-951595-1009100-1056105-1106110-1153

Filo · Accepted Answer

Class intervalfi​  xi​ ui​=hxi​−A​ ui2​fi​ui​fi​ui2​   70-75 3 72.5 -4 16 -12 48 75-80 4 77.5 -3 9 -12 36 80-85 7 82.5 -2 4 -14 28 85-90 7 87.5 -1 1 -7 7 90-95 15 92.5 0 0 0 0 95-100 9 97.5 1 1 9 9 100-105 6 102.5 2 4 12 24105-110  6 107.5 3 9 18 54 110-115 3 112.5 4 16 12 48 Total 60    6 254We have N=∑fi​=60 Width of class h=5Assumed mean  A=92.5(say)Mean, xˉ=A+N∑i=19​fi​ui​​×h=92.5+606​×5=92.5+0.5=93⇒xˉ=93Variance σ2=h2⎣⎡​N∑i=19​fi​ui2​​−(N∑i=19​fi​ui​​ )2⎦⎤​σ2=52⎣⎡​60254​−(606​ )2⎦⎤​=52(60)2[60×254−62] ​=360025​[15240−36]=360025​×15204σ2=105.58Standard Deviation =Variance​  σ=105.58​σ=10.27

Question Text	Find the mean variance and standard deviation using short-cut method
Answer Type	Text solution:1
Upvotes	150

Find the mean variance and standard deviation using short-cut method
Height
in cms No. of children
70-75 3
75-80 4
80-85 7
85-90 7
90-95 15
95-100 9
100-105 6
105-110 6
110-115 3

Text solutionVerified

Practice questions from similar books

Height in cms	No. of children
70-75	3
75-80	4
80-85	7
85-90	7
90-95	15
95-100	9
100-105	6
105-110	6
110-115	3

Class interval	$f_{i}$	$x_{i}$	$u_{i} = \frac{x _{i} - A}{h}$	$u_{i}^{2}$	$f_{i} u_{i}$	$f_{i} u_{i}^{2}$
70-75	3	72.5	-4	16	-12	48
75-80	4	77.5	-3	9	-12	36
80-85	7	82.5	-2	4	-14	28
85-90	7	87.5	-1	1	-7	7
90-95	15	92.5	0	0	0	0
95-100	9	97.5	1	1	9	9
100-105	6	102.5	2	4	12	24
105-110	6	107.5	3	9	18	54
110-115	3	112.5	4	16	12	48
Total	60				6	254