Question

whats the mean deviation, standard deviation and range for these set of numbers 47,47,66,50,78,61

Answer 1

Solution:

The required formulas are given as below:

Mean deviation = ∑|X – mean|/n

Standard deviation = Sqrt[∑(X - mean)^2 / (n – 1)]

Range = Maximum – Minimum

The calculation table is given as below:

No.	X	|X - mean|	(X - mean)^2
1	47	11.16667	124.6945189
2	47	11.16667	124.6945189
3	66	7.83333	61.36105889
4	50	8.16667	66.69449889
5	78	19.83333	393.3609789
6	61	2.83333	8.027758889
Total	349	61	778.8333333

From above table, we have

Sample size = n = 6

Mean deviation = ∑|X – mean|/n = 61/6 = 10.16667

Standard deviation = Sqrt[∑(X - mean)^2 / (n – 1)]

Standard deviation = Sqrt(778.8333333/(6 - 1))

Standard deviation =12.48065

Maximum = 78

Minimum = 47

Range = 78 – 47 = 31