Standard Deviation - Example
 

Worked example

The table below shows the number of minutes to the nearest minute, that 50 trains were late on the King's Cross to Newcastle line during one week in December 1994

2	4	14	5	10	3	17	3	5	10
14	21	34	14	22	5	3	9	36	5
13	8	7	4	41	23	22	15	23	6
8	5	43	13	26	33	6	34	17	8
12	19	10	4	23	23	24	5	13	4

Group the data into intervals 0- , 5-, 10 -, etc... and construct a frequency table.

Find the mean and standard deviation of the distribution.

Group	Tally	Frequency, f	Midpt, x	fx	fx2
0 -	1111  1111	9	2.5	22.5	56.25
5 -	1111  1111  1	11	7.5	82.5	618.75
10 -	1111  1111  1	11	12.5	137.5	1718.75
15 -	1111	4	17.5	70	1225
20 -	1111  111	8	22.5	180	4050
25 -	1	1	27.5	27.5	756.25
30 -	111	3	32.5	97.5	3168.75
35 -	1	1	37.5	37.5	1406.25
40 -	11	2	42.5	85	3612.5
		Sf = 50		Sfx = 740	Sfx2 = 16612.5

 

Mean =	740	= 14.8 mins.	Standard deviation = 10.64 mins.
	50