Question

TYPE PLEASE find statistical parameters (mean, median and standard deviation).14, 28, 72, 86, 99, 19, 109, 12

Answer 1

The Data in ascending order is 12,14,19,28,72,86,99,109

Mean: Sum of observations/Total observations = (12+14+19+28+72+86+99+109)/8 = 439/8 = 54.875

Median: Since the number of observations is even, the median is the average of the (n/2)th and its next value = average of 8/2 = 4th and 5th values = (28+72)/2 = 100/2 = 50

Standard Deviation: Since we are talking about statistical parameters (not population parameters), then standard deviation is given by SQRT[Sum(x-)²/n-1]. The calculations are as below.

#	X	Mean	(x - mean)2
1	12	54.875	1838.26563
2	14	54.875	1670.76563
3	19	54.875	1287.01563
4	28	54.875	722.265625
5	72	54.875	293.265625
6	86	54.875	968.765625
7	99	54.875	1947.01563
8	109	54.875	2929.51563
Total	439		11656.875

Sum(x-)² = 11656.875, n - 1 = 7,

Therefore the standard deviation deviation = Sqrt(11656.875/7) = 40.8077