Elementary Statistics 11th ed. - M. Triola (Addison-Wesley.2009) BBS.pdfDescripción completa
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ASSIGNMENT SUBMISSION SUBMISSION AND ASSESSMENT ASSESSMENT Elementary Statistics _________________ ________________________ _______________ ________________ ________________ _________________ _________________ ________________ ________ INSTRUCTIONS TO STUDENTS 1.
This assignment contains only FIVE (5) question that is set in English.Answer all FIVE questions. questions.
2.
Answer in English.
3. Students need to submit assignment assignment only in MsWord format unless specified specified otherwise. Please refrain from converting text/phrases into picture format such as .gif / .jpeg / print screen / etc. 4.
Your assignment should be typed using 12 point Times New Roman font and 1.5 line spacing .
5.
Your assignment must be submitted before 10 November November be accepted. 2017will NOT be
6.
Your assignment should be prepared individually. You should not copy another person’s assignment. You should also not plagiarise another person’s work as your own.
2017 . Submission
after
10 November
ASSIGNMENT QUESTION INSTRUCTION: ANSWER ALL QUESTIONS WITH DETAILED EXPLAINNATION
QUESTION 1
Suppose you are working for a company in the music business. They make stereos, musical instruments and produce CD’s. They decide to do a survey on dance preferences by college students. Basically, they wanted to know about college students’ interests and practices on dance music. A survey was administered to a random sample of 37 students and recorded in Table 1: A – Ironic dance
B – Pro dance
C – Sway dance
D – Dad-dance
E – Twerk dance
Table 1
a)
Male
Female
Male
Female
Male
A
A
A
A
E
C
E
C
C
A
A
A
C
B
E
A
C
A
D
D
A
A
B
A
A
C
D
E
B
B
D
A
D
D
A
D
A
Prepare a summary table for dance preferences. Calculate percentage and
(4)
sectarian angle of each type of dance preferred. b)
Represent these figures on a pie chart.
(3)
c)
Draw a bar chart to represent the dance preferences.
(3) [Total: 10 marks]
ANSWERS: a) PERCENTAGE =
FREQUENCY OF EACH DANCE TYPE X 100 TOTAL FREQUENCY
SECTARIAN ANGLE = PERCENTAGE / 100 X 360 o
DANCE TYPE
NUMBER OF STUDENTS
SECTARIAN
MALE+FEMALE PERCENTAGE ANGLE
A
16
43.24 ≈ 43
156
B
4
10.81 ≈ 11
39
C
6
16.22 ≈ 16
58
D
7
18.92 ≈ 19
68
E
4
10.81 ≈ 11
39
TOTAL
37
100
360
b) Dance
Relative Frequency
A
0.43
B
0.11
C
0.16
D
0.19
E
0.11
Dance Frequency 11%
A 43%
19%
B C D
16% 11%
E
c) Dance
Frequency
A
16
B
4
C
6
D
7
E
4
Dance Preferences 18
16
16 14 y c e n q u q e r F
A
12 10
B
8
6
6
7
4
C 4
D
4
E
2 0 A
B
C
D
E
Dance Type
QUESTION 2 Based on Table 1 in Question 1: a)
Prepare a multiple frequency table for dance preferences of both genders.
(2)
b)
Using your frequency table, draw a multiple bar chart to represent the
(4)
information. c)
Briefly discuss and compare the percentage of favorite and least favorite
(4)
dance preferences of both genders. [Total: 10 marks]
c) Both male and female students prefer A the most.41% male and 47% female students
prefer A. Least favorite dance for male is B (only 9% prefer B) and for female is E(only 7 % prefer E)
QUESTION 3 Table 2: Mathematics Score
a)
27
37
30
28
39
25
45
28
32
28
26
38
31
30
47
41
Based on Table 2, organize the data into a frequency distribution by taking
(4)
25 as the lower limit of the first class and 5 as the class width. b)
Construct a “less than or equal” ogive for the frequency distribution
(6)
established in (a) and then approximate the number of candidates who scores below 35.
[Total: 10 marks]
ANSWERS: a) Class
Frequency
Cumulative Frequency
25-30
6
6
30-35
4
10
35-40
3
13
40-45
1
14
45-50
2
16
b)
Cumulative Frequency 18 16 14 y c n e u q q e r F
12 10 8
Cumulative Frequency
6 4 2 0 25-30
30-35
35-40
Class
40-45
45-50
QUESTION 4 A bag contains 3 black balls and 5 white balls. Paul picks a ball at random from the bag and replaces it back in the bag. He mixes the balls in the bag and then picks another ball at random from the bag. a)
Construct a probability tree of the problem.
b)
Calculate the probability that Paul picks:.
(5)
i) two black balls
(2)
ii) a black ball in his second draw
(3)
[Total: 10 marks] ANSWERS: a) First draw
Second draw
Outcomes
3 8
B
( B, B)
W
( B, W)
B
( W,B )
W
( W, W)
3 8
B
5 3
5
W
Probability
9
1
1
9
× = × =
8
8
8 5
× = × =
8
b)
i) two black balls
To find the probability of getting two black balls, first locate the B branch and then follow the second B branch. Since these are independent events we can multipl y the probability of each branch.
( ) = × =
ii) a black ball in his second draw
There are two outcomes where the second ball ca n be black. rom the probability tree diagram, we get:
P(second ball black) = P(B, B) or P(W, B) = P(B, B) + P(W, B)
= = =
9
+
1
24 64
Either (B, B) or (W, B) QUESTION 5 12 workers of an electronic factory were selected to assemble electronic spare parts. The time taken to completely assemble a part are recorded in Table 3. Table 3
a)
18
15
17
22
12
20
19
15
20
25
16
13
Calculate the mean, the median, the mode and the standard deviation of
(7)
assembling time. b)
Calculate the Pearson coefficient of skewness and comment on the
(3)
assembling time distribution. [Total: 10 marks]
ANSWERS: a) MEAN =
∑X / N = 212 / 12 = 17.67
Arrange data in ascending order: 12 13 15 15 16 17 18 19 20 20 22 25 MEDIAN = (17+18) / 2 = 17.5 MODE = 20,15 STANDARD DEVIATION = √ (∑(X - MEAN)2 / N-1) X
X - MEAN
( X – MEAN )2
18
0.33
0.1089
15
-2.67
7.1289
17
-0.67
0.4489
22
4.33
18.7489
12
-5.67
32.1489
20
2.33
5.4289
19
1.33
1.7689
15
-2.67
7.1289
20
2.33
5.4289
25
7.33
53.7289
16
-1.67
2.7889
13
-4.67
21.8089
STANDARD DEVIATION = √(156.6668 / 11) = 3.77
b)Pearson coefficient of skewness = 3 (mean – median) / standard deviation
