Chapter 10.5, Problem 16PPS

a.

To determine

To construct graph

Explanation of Solution

Given information:

Blue course: 46,25,62,45,30,43,40,46,33,53,35,38,39,40,52,42,44,48,50,35,32,55,28,58

Red course: 53,49,26,61,40,50,42,35,45,48,31,48,33,50,35,55,38,50,42,53,44,54,48,58

Graph:

Blue course:

  

  

Interpretation:

Data is relatively symmetric in both the histograms.

b.

To determine

To find mean and standard deviation.

Answer to Problem 16PPS

Blue course:

Mean=42.45

Standard deviation=9.21

Red course:

Mean=45.33

Standard deviation=8.76

Explanation of Solution

Given information:

Blue course: 46,25,62,45,30,43,40,46,33,53,35,38,39,40,52,42,44,48,50,35,32,55,28,58

Red course: 53,49,26,61,40,50,42,35,45,48,31,48,33,50,35,55,38,50,42,53,44,54,48,58

Formula used:

Mean= $\frac{{\displaystyle \sum _{i=1}^n{X}_i}}{n}$

Where, n=total number of terms,

  ${\displaystyle \sum _{i=1}^n{X}_i}$ = sum of all terms

Standard deviation, ${\sigma }_{}=\sqrt{\frac{{\displaystyle \sum _{}^{}{(x_i^{}-\mu )}^2}}{N}}$

Where $x_i^{}$ = each value from data

  $\mu$ =mean of data

  $N$ = size of data

Calculation:

Blue course:

Substituting the value,

Mean is,

  $\frac{46+25+62+45+30+43+40+46+33+53+35+38+39+40+52+42+44+48+50+35+32+55+28+58}{24}=\frac{1019}{24}=42.45$

For standard deviation,

Value	Difference= $x_i^{}-\mu$	( $x_i^{}-\mu {)}^2$
46	3.54	12.54
25	-17.45	304.79
62	19.54	381.87
45	2.54	6.46
30	12.45	155.21
43	0.54	0.29
40	-2.45	6.04
46	3.54	12.54
33	-9.45	89.46
53	-10.54	111.1
35	-7.45	55.62
38	-4.45	19.87
39	-3.45	11.96
40	-2.45	6.04
52	9.54	91.04
42	0.45	0.21
44	1.54	2.37
48	5.54	30.71
50	7.54	56.87
35	-7.45	55.62
32	-10.45	109.37
55	12.54	157.29
28	-14.45	209.04
58	15.541	241.54

  ${\displaystyle \sum _{}^{}{(x_{}^{}-\mu )}^2}$ =2127

  $\begin{array}{l}\\ {\sigma }_{}=\sqrt{\frac{{\displaystyle \sum _{}^{}{(x_i^{}-\mu )}^2}}{N}}=9.41\end{array}$

Red course:

  $\frac{53+49+26+61+40+50+42+35+45+48+31+48+33+50+35+55+38+50+42+53+44+54+48+58}{24}=\frac{1088}{24}=45.33$

For standard deviation,

Value	Difference= $x_i^{}-\mu$	( $x_i^{}-\mu {)}^2$
53	7.66	58.77
49	3.66	13.44
26	19.33	373.77
61	15.66	245.44
40	5.33	28.44
50	4.66	21.77
42	3.33	11.11
35	-10.33	106.77
45	-0.33	0.11
48	2.66	7.11
31	-14.33	205.44
48	2.66	7.11
33	-12.33	152.11
50	4.66	21.77
35	-10.33	106.77
55	9.66	93.44
38	-7.33	53.77
50	4.66	21.77
42	-3.33	11.11
53	7.66	58.77
44	-1.33	1.77
54	8.66	75.11
48	2.66	7.11
58	12.66	160.44

  ${\displaystyle \sum _{}^{}{(x_{}^{}-\mu )}^2}$ =1843.76

  ${\sigma }_{}=\sqrt{\frac{1843}{24}}=8.76$