Question

1/22/2020 BSAD63220 Homework #3 Variance, St. Deviations, Z-scores, and Empirical Rule Show your work, do not use a spread sheet. 1. Corn Production. The following data represent the number of corn plants in randomly sampled rows (a 17-foot by 5-inch strip) for various types of plot. Compute the sample variance and standard deviation for each type of plot. Which type has the most dispersion based upon the standard deviation? Plot type Sludge Plot Spring disk No till Spring Chisele Great Lakes Bt Number of Plants 25 27 33 30 28 27 32 30 33 35 34 34 30 26 29 32 25 29 30 32 26 28 31 29 28 32 27 30 29 27 2. Waiting for a Table. The following data represent the number of customers waiting for a table at 6:00pm on Saturday for 40 consecutive Saturdays at Bubba's restaurant. Select a random sample of these waiting times where n=5. Using your randomly selected sample of times, compute the sample variance and the sample st. deviation. Wait times N=40 11

Answer 1

Ans. Sludge Plot

Number (x)	(x - Mean)	(х — Меan
25	-3.33	11.09
27	-1.33	1.77
33	4.67	21.81
30	1.67	2.79
28	-0.33	0.11
27	-1.33	1.77
n = 6		$\Sigma (X-Mean)^2$ = 39.34

Mean = Sum of Numbers / n = 170 / 6 = 28.33

SD = $\sqrt{(X-Mean)^2 / n{_{}}}$ = $\sqrt{39.34 / 6{_{}}}$ = 2.56

Spring Disk

Number (x)	(x - Mean)	(х — Меan
32	-1	1
30	-3	9
33	0	0
35	2	4
34	1	1
34	1	1
n = 6		$\Sigma (X-Mean)^2$ = 16

Mean = Sum of Numbers / n = 198 / 6 = 33

SD = $\sqrt{(X-Mean)^2 / n{_{}}}$ = $\sqrt{16 / 6{_{}}}$ = 1.63

No Till

Number (x)	(x - Mean)	(х — Меan
30	1.5	2.25
26	-2.5	6.25
29	0.5	0.25
32	3.5	12.25
25	-3.5	12.25
29	0.5	0.25
n = 6		$\Sigma (X-Mean)^2$ = 33.50

Mean = Sum of Numbers / n = 171 / 6 = 28.5

SD = $\sqrt{(X-Mean)^2 / n{_{}}}$ = $\sqrt{33.50 / 6{_{}}}$ = 2.36

Spring Chisele

Number (x)	(x - Mean)	(х — Меan
30	0.67	0.45
32	2.67	7.13
26	-3.33	11.09
28	-1.33	1.77
31	1.67	2.79
29	-0.33	0.11
n = 6		$\Sigma (X-Mean)^2$ = 23.34

Mean = Sum of Numbers / n = 176 / 6 = 29.33

SD = $\sqrt{(X-Mean)^2 / n{_{}}}$ = $\sqrt{23.34 / 6{_{}}}$ = 1.97

Great Lakes Bt

Number (x)	(x - Mean)	(х — Меan
28	-0.83	0.69
32	3.17	10.05
27	-1.83	3.35
30	1.17	1.37
29	0.17	0.03
27	-1.83	3.35
n = 6		$\Sigma (X-Mean)^2$ = 18.84

Mean = Sum of Numbers / n = 173 / 6 = 28.83

SD = $\sqrt{(X-Mean)^2 / n{_{}}}$ = $\sqrt{18.84 / 6{_{}}}$ = 1.77

Therefore, the Std Deviation is least in Spring Disk.