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standrad deviation short cut method formula proof

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Calculate the standard deviation by :

(A) Actual mean method

(B) Direct method

(C) Short cut method.

3, 4, 6, 7, 10

Q. Find the Variance and Standard Deviation of the values

4, 4, 4, 4, 4, 4

using short-cut method.

Q. Find the mean and standard deviation using short-cut method

$X_{i}$	60	61	62	63	64	65	66	67	68
$f_{i}$	2	1	12	29	25	12	10	4	5

Q. Find the mean and standard deviation using short-cut method.x60662 63 64 65 66 67 68f 21 12 29 252 10456.

Q. 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

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