SBST 1303 ELEMENTARY STATISTICS ASSIGNMENT TITLE: STATISTICS Name: MARKUS ADAM Matric Number: 57110135115001 NRIC: 571101-13-5115 Telephone number: 014-6816491 E-mail address: [email protected] Tutor’s name: LAU SIE HOE Learning Centre: OPEN UNIVERSITY MALAYSIA ( KUCHING ) Semester: MAY 2012
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SBST 1303
ELEMENTARY STATISTICS
ASSIGNMENT TITLE:
STATISTICS
Name:
MARKUS ADAM
Matric Number:
57110135115001
NRIC:
571101-13-5115
Telephone number:
014-6816491
E-mail address:
Tutor’s name:
LAU SIE HOE
Learning Centre:
OPEN UNIVERSITY MALAYSIA ( KUCHING )
Semester: MAY 2012
Question 1
The numbers of cars sold per month by a car dealer in 36 months are recorded as follows:
25 20 15 20 17 27 30 15 18
31 35 22 15 16 45 41 25 23
38 18 20 23 36 38 42 40 16
33 35 22 24 25 30 36 41 18
a) Construct a cumulative frequency distribution for the above data.
Class Cars sold per month Frequency Upper
Boundary
Cumulative
Process
Cumulative
Frequency
10-14 0 0 ≤ 14.5 0 0
15-19 15,17,15,18,15,16,18,16,18 9 ≤ 19.5 0+9 9
20-24 20,20,22,23,20,23,22,24 8 ≤ 24.5 8+9 17
25-29 25,27,25,25 4 ≤ 29.5 4+17 21
30-34 30,31,33,30 4 ≤ 34.5 4+21 25
35-39 35,38,36,38,35,36 6 ≤ 39.5 6+25 31
40-44 41,42,40,41 4 ≤ 44.5 4+31 35
45-49 45 1 ≤ 49.5 1+35 36
b) Draw a cumulative frequency polygon of the type “less than or equal to”.
Class Upper Boundary Cumulative
Frequency
10-14 ≤ 14.5 0
15-19 ≤ 19.5 9
20-24 ≤ 24.5 17
25-29 ≤ 29.5 21
30-34 ≤ 34.5 25
35-39 ≤ 39.5 31
40-44 ≤ 44.5 35
45-49 ≤ 49.5 36
0
5
10
15
20
25
30
35
40
14.5 19.5 24.5 29.5 34.5 39.5 44.5 49.5
Cumulative Frequency Polygon of Cars sold per month
Cumulative Frequency Polygon of Cars sold per month
c) From the cumulative frequency polygon, how many months does the dealer sell less than
20 cars?
From the cumulative frequency polygon, it shows that the dealer sell less than 20 cars
is two (2) months in Upper Boundary of 19.5 and 24.5.
d) Calculate the percentage of months with more than 30 cars sold.
Class Cars sold per month Frequency Cumulative
Frequency
10-14 0 0 0
15-19 15,17,15,18,15,16,18,16,18 9 9
20-24 20,20,22,23,20,23,22,24 8 17
25-29 25,27,25,25 4 21
30-34 30,31,33,30 4 25
35-39 35,38,36,38,35,36 6 31
40-44 41,42,40,41 4 35
45-49 45 1 36
The overall cumulative frequency in percentage (%) is shown below.
Class Frequency Cumulative
Frequency
Cumulative
Frequency (%)
10-14 0 0 0
15-19 9 9 25
20-24 8 17 47.2
25-29 4 21 58.3
30-34 4 25 69.4
35-39 6 31 86.1
40-44 4 35 97.2
45-49 1 36 100
The percentage of months with more than 30 cars sold is overall 30.56% as calculated below.
Class Frequency Cumulative
Frequency
Percentage (%)
More than 30 cars
35-39 6 31 16.67
40-44 4 35 11.11
45-49 1 36 2.78
0
10
20
30
40
14.5 19.5 24.5 29.5 34.5 39.5 44.5 49.5
Cumulative Frequency Polygon of Cars sold per month
Cumulative Frequency Polygon of Cars sold per month
Question 2
The following table shows the time (hours) spent by 70 teenagers at a cybercafé daily.
Time
(hours)
Frequency
0 – 0.4 2
0.5 – 0.9 5
1.0 – 1.4 19
1.5 – 1.9 15
2.0 – 2.4 10
2.5 – 2.9 8
3.0 – 3.4 5
3.5 – 3.9 3
4.0 – 4.4 2
4.5 – 4.9 1
a) State the type of variable used.
Continuous Data
Continuous Data is the value of continuous variable that consist of numbers with decimals.
This data usually can be obtained through a measuring process.
b) Construct a histogram for the above data. Hence, describe the distribution.
The most time (hours) spend is 1.0-1.4 hours by 19 teenagers. The Histogram arises
dramatically from 0-0.4 hours and 0.5-0.9 hours and reaches the peak at 1.0-1.4 hours. After
that the histogram slowly deceasing where less teenagers spent longer hours at the cybercafé.
Only 1 teenager spent 4.5-4.9 hours at the cybercafé daily.
0
2
4
6
8
10
12
14
16
18
20
Time (hours) spent by 70 teenager
Time (hours) spent by 70 teenager
c) Find the percentage of teenagers who spent at least 1.0 hours and at most 2.1 hours.
Time
(hours)
Frequency
1.0 – 1.4 19
1.5 – 1.9 15
2.0 – 2.4 10
1.0 ≤ X < 2.1 so:-
Time
(hours)
Frequency Percentage (%)
with
1.0 ≤ X < 2.1
1.0 – 1.4 19 27.14
1.5 – 1.9 15 21.43
The total numbers of teenagers are 70 teenagers. There are 19+15=34 teenagers whom falls
under the category of spent at least 1.0 hours and at most 2.1 hours.
((34/70) X 100% = 48.57%
0
2
4
6
8
10
12
14
16
18
20
Time (hours) spent by 70 teenager
Time (hours) spent by 70 teenager
d) How many teenagers spent less than 30 minutes at the cybercafé daily?
There are 2 teenagers spent less than 30 minutes at the
cybercafé daily.
e) Calculate the following:
i. mean
The mean, µ = 2+5+19+15+10+8+5+3+2+1
10 = 7
ii. mode
1 , 2 , 2 , 3 , 5 , 5 , 8 , 10 , 15 ,19
This set is bimodal data, and the modes are 2 and 5.
Time
(hours)
Frequency
0 – 0.4 2
0.5 – 0.9 5
1.0 – 1.4 19
1.5 – 1.9 15
2.0 – 2.4 10
2.5 – 2.9 8
3.0 – 3.4 5
3.5 – 3.9 3
4.0 – 4.4 2
4.5 – 4.9 1
Time
(hours)
Frequency
0 – 0.4 2
0.5 – 0.9 5
1.0 – 1.4 19
1.5 – 1.9 15
2.0 – 2.4 10
2.5 – 2.9 8
3.0 – 3.4 5
3.5 – 3.9 3
4.0 – 4.4 2
4.5 – 4.9 1
iii. median
Step 1 : 1 , 2 , 2 , 3 , 5 , 5 , 8 , 10 , 15 ,19
Step 2 : In this set there are n = 10 observations. Thus the position of median is at
(10 + 1)/2 = 5.5. This position is at the middle between 5th position and 6th position. The
observation at the 5th position is number 5, and observation at position 6th is number 5.
Step 3 : Thus the median is the average (5 + 5)/2 = 5 which is at the position 5.5.
Median = (5 + 5)/2
= 5
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