Question

Sarah D is a guitar player. Her guitar has an under-saddle pezio-electric pick up. This device uses a 9 volt battery. She has recorded a sample of the hours of guitar use she has gotten from has last 13 batteries.

	1	2	3	4	5	6	7	8	9	10	11	12	13
Hours	15	18	12	21	15	13	9	16	14	20	19	12	15

Given this data, calculate the:

a. Sample Average Hours

b. Sample Median Hours

c. Sample Model Hours

d. Sample Variance

f. Sample Standard Deviation

Answer 1

(a)

Sample Average () is given by:

So,

Sample Average is given by:

15.3077 Hours

(b)

Arranging data in ascending order, we get:

9, 12, 12, 13, 14, 15, 15, 15, 16,18, 19, 20, 21

n = 13

Median = (13+1)/2th item = 7th item = 15

So,

Sample Median is given by:

15 Hours

(c)

Sample Mode is given by:

15 Hours,

because 15 occurs maximum number of times

(d)

x	(x - )	(x - )2
15	- 0.3077	0.0947
18	2.6923	7.2485
12	- 3.3077	10.9408
21	5.6923	32.4024
15	- 0.3077	0.0947
13	- 2.3077	5.3254
9	- 6.3077	39.7870
16	0.6923	0.4793
14	- 1.3077	1.7101
20	4.6923	22.0178
19	3.6923	13.6331
12	- 3.3077	10.9408
15	- 0.3077	0.0947
Total =		144.7692

Sample Variance (s²) is given by:

So,

Sample Variance is given by:

12.0641

(f)

Sample Standard Deviation (s) is given by:

So,

Sample Standard Deviation is given by:

3.4733