Question

An expert reviews a sample of 10 scientific articles (n = 10) and records the following number of errors in each article: 8, 9, 6, 5, 3, 5, 9, 1, 2, and 4. Compute SS, variance, and standard deviation for this sample using the definitional and computational formula. (Round your answers to two decimal places.) SS variance standard deviation errors

Answer 1

(1)

Defiitional Formula:

(a)

To find Sum of Squares (SS):

Mean = ) = 52/10 = 5.2

x	x -	(x - )2
8	2.8	7.84
9	3.8	14.44
6	0.8	0.64
5	- 0.2	0.04
3	- 2.2	4.84
5	= 0.2	0.04
9	3.8	14.44
1	- 4.2	17.64
2	- 3.2	10.24
4	- 1.2	1.44
Total =		71.6

So,

Sum of Squares (SS) = 71.6

(b)

Variance (s²) is given by:

(c)

Standard Deviation (s) is given by:

(2)

Computational Formula:

(a)

To find Sum of Squares (SS):

x	x2
8	64
9	81
6	36
5	25
3	9
5	25
9	81
1	1
2	4
4	16
Total = 52	342

So,

Sum of Squares (SS) = 342

(b)

Variance (s²) is given by:

(c)

Standard Deviation (s) is given by: