Find the mean and standard deviation using short-cut method. xi 60 61 62 63 64 65 66 67 68 fi 2 1 12 29 25 12 10 4 5

The data is obtained in tabular form as follows. xi f i fi = `(X_i - 64)/1` yi2 fiyi fiyi2 60 2 –4 16 –8 32 61 1 –3 9 –3 9 62 12 –2 4 –24 48 63 29 –1 1 –29 29 64 25 0 0 0 0 65 12 1 1 12 12 66 10 2 4 20 40 67 4 3 9 12 36 68 5 4 16 20 80 100 220 0 286

Find the Mean and Standard Deviation Using Short-cut Method.60 61 62 63 64 65 66 67 68 - Mathematics

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

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Solution

The data is obtained in tabular form as follows.

x_i	f i	f_{i = `(X_i - 64)/1`}	y_i²	f_iy_i	f_iy_i²
60	2	–4	16	–8	32
61	1	–3	9	–3	9
62	12	–2	4	–24	48
63	29	–1	1	–29	29
64	25	0	0	0	0
65	12	1	1	12	12
66	10	2	4	20	40
67	4	3	9	12	36
68	5	4	16	20	80
	100	220		0	286