29 Jun 2019

ELEMENTARY STATISTICS






Question 1

a)         
Class
Frequency
Upper Boundary
Cumulative Process
Cumulative Frequency
6 - 8
4
≤ 8.5
4
4
9 - 11
6
≤ 11.5
4 + 6
10
12 - 14
10
≤ 14.5
10 + 10
20
15 - 17
3
≤ 17.5
20 + 3
23
18 - 20
12
≤ 20.5
23 + 12
35

Sum = 35



Table 1.1: “Less than or Equal” cumulative frequency polygon

Table 2.2: Cumulative Frequency of types “Less than or equal” polygon
b)          Number of Classes,
K= 1 + 3.3log (n)
K= 1 + 3.3log (40)
K= 6.28 6, or 6 to 7 classes

Class width given = 10
Lower limit given = 50


Number of classes
Class
Counting Tally
Frequency (f)
1st class
50-59
IIII I
6
2nd class
60-69
IIII IIII IIII II
17
3rd class
70-79
IIII III
8
4th class
80-89
IIII IIII
9

Sum

40
Table 1.3: Frequency distribution table



Class
50-59
60-69
70-79
80-89
Frequency (f)
6
17
8
9
Table 1.4: Frequency distribution table







Question 2
           
Class
(Given)
Class mid-point (x)
Frequency (f)
(Given)
1.8 - 2.1
2
4.3
9.245
2.6 – 3.3
4
11.8
34.81
3.4 – 4.1
6
22.5
84.375
4.2 – 4.9
13
59.15
269.1325
5.0 – 5.7
8
42.8
228.98
5.8 – 6.5
3
18.45
113.4675

SUM
36
159
740.01
Table 2.1: Class mid-point, and calculation

Mean


Thus, the mean is 4.4


Mode
Class
Frequency (f)
Class Boundaries
Class width
4.2 - 4.9
13
4.15 - 4.95
(4.15 – 4.95) = 0.8

Calculation of class boundary  and

Class mode with the largest frequency is 4.2 – 4.9 (as per table 2.1).
Lower boundary =4.15
Class width, C = 0.8
 The difference between the frequency of the class mode and the frequency of the class immediately before class mode, that is 13-6 = 7.
 The difference between the frequency of the class mode and the frequency of the class immediately after class mode, that is 13-8 = 5
The mode formula
Thus, the mode is 4.62

Standard Deviation
Therefore, the standard deviation is 1.02
Question 3
a)         Frequency distribution table.
            Number of Class,
K= 1 + 3.3log (n)
K= 1 + 3.3log (40)
K= 6.28 6 to 7 classes

Class width and class limits
Class width     = range / number of classes
                        = Largest number - smallest number / number of classes
                       

Number of Classes
Class
Counting Tally
Frequency (f)
1st Class
4.8 - 7.1
IIII
5
2nd Class
7.2 – 9.5
IIII IIII
9
3rd Class
9.6– 11.9
IIII IIII IIII
15
4th Class
12 – 14.3
IIII
5
5th Class
14.4 – 16.7
III
3
6th Class
16.8 – 19.1
II
2
7th Class
19.2 – 21.5
I
1

SUM

40
Table 3.1: Frequency distribution table



Class
4.8 - 7.1
7.2 – 9.5
9.6 – 11.9
12 – 14.3
14.4 – 16.7
16.8 – 19.1
19.2 – 21.5
Frequency (f)
5
9
15
5
3
2
1
Table 3.2: Frequency distribution table

b)        
Mean
Class
Class mid-point (x)
Frequency (f)
(f) x (x)
4.8 - 7.1
5
29.75
7.2 – 9.5
9
75.15
9.6– 11.9
15
161.25
12 – 14.3
5
65.75
14.4 – 16.7
3
46.65
16.8 – 19.1
2
35.9
19.2 – 21.5
1
20.35

SUM
40
434.80
Table 3.3: Class mid-point calculation




Thus, the mean is 10.87






Mode
Class
Frequency (f)
Class Boundaries
Class width
9.6 – 11.9
15
9.55 – 11.95
11.95 – 9.55 = 2.4

Calculation of class boundary  and
Class mode with the largest frequency is 9.5 – 11.8 (as per table 3.3).
Lower boundary =9.55
Class width, C = 2.4
 The difference between the frequency of the class mode and the frequency of the class immediately before class mode, that is 15-9 = 6.
 The difference between the frequency of the class mode and the frequency of the class immediately after class mode, that is 15-5 = 10

The mode formula

Thus, the mode is 10.45









Median
Class
Frequency (f)
Cumulative Frequency (F)
Class
Boundaries
4.8 - 7.1
5
0+5=5

7.2 – 9.5
9
5+9=14

9.6– 11.9
15
14+15=29
9.45-11.85
=2.4(width)
12 – 14.3
5
29+5=34

14.4 – 16.7
3
34+3=37

16.8 – 19.1
2
37+2=39

19.2 – 21.5
1
39+1=40

SUM
40


Table 3.4: cumulative frequency calculation

i)          The position of the median:
ii)         The class median with a cumulative frequency (f) > 20.5 is the class median
9.6 – 11.9.
iii)        The median  is:
 

Thus, the median is 10.59
Question 4
a)                  The value of :
Thus, the value of x = 4


Question b,c,d and e are based on the table 4.1 below
Class
Number of Students (f)
Cumulative Frequency (F)
Class boundaries
Class width
40 - 44
2
0+2=2


45 - 49
2+4=6


50 - 54
7
6+7=13
49.5 – 54.5
5
55 - 59
13+16=29
54.5 - 59.5
5
60 - 64
29+20=49
59.5 – 64.5
5
65 - 69
2
49+2=51


70 - 74
1
51+1=52







SUM
52



Table 4.1: Coursework Statistic Marks







b)         First Quartile
Step 1

Step 2
Quartile 1
Cumulative frequency (f) of class quartile with F > 13.25, that is F = 29
55-59
16
13+16=29
54.5 - 59.5
5





Step 3
Therefore, the first quartile is 54.58





c)         Median
i)          The position of the median:
ii)         The class median with a cumulative frequency (f) > 26.5 is the class median
55 – 59.
iii)        The median  is:
 

Thus, the median is 58.72.




d)         Third Quartile
Step 1



Step 2
Quartile 3
Cumulative frequency (f) of class quartile with F > 75.75, that is F = 49
60-64
20
29+20=49
59.5-64.5
5


Step 3
Therefore, the third quartile is 62.19



d)         Inter-Quartile Range

IQR ;
 

Therefore, the IQR is 7.61

Lorem ipsum dolor sit amet, consectetuer adipiscing elit, sed diam nonummy nibh euismod tincidunt ut laoreet dolore magna Veniam, quis nostrud exerci tation ullamcorper suscipit lobortis nisl ut aliquip ex ea commodo consequat.

Biar Kami Bantu Anda

Hubungi Kami
Sarah
+60182765083
KUALA LUMPUR