Notesale: Turn your study into money

Document Preview

Extracts from the notes are below, to see the PDF you'll receive please use the links above

---

Author: Adebayo Kassim, Linearkassim@gmail
...
These measures includes
(1)
The Arithmetic mean
(ii)
The Median
(iii) The Mode
(iv)
Harmonic Mean
(v)
Geometric Mean
Arithmetic Mean: This is calculated by summing up all the values in the sample and dividing
this total by the number of observation in the sample
...

Solution:
X1= 582, x 2= 441, x3=475, x 4=525, x5 = 507
X= ∑x = x1 + x2 + x3 …xn
N
n
= 582 + 441 + 475 + 525 + 507
5
= 2530
5
= 506 yards
The Arithmetic Mean of a Frequency Distribution
The definition given above is appropriate only in the case of the figures occurring once
...

X
2
3
4
5
6
F
6
10
8
4
2
Solution
X
F
fx
2
6
12
3
10
30
4
8
32
5
4
20
6
2
12

Author: Adebayo Kassim, Linearkassim@gmail
...
53
∑f 30
Example2: The table below shows the marks of medical students in statistic examination
...
5
8
116
20 – 29
24
...
5
8
276
40 – 49
44
...
5
50 – 59
54
...
5
60 – 69
64
...
5
2
149
70
2565
Mean = ∑fx = 2565 = 36
...
e x –A
In using this formula, the value for assume mean will be given, where it is not given, it can be
obtained as the class midpoints of the median class
...
5, calculate the mean of the table above
Class marks
Frewquency
Class Midpoints
D1= x- A
F1d1
10 - 19
8
14
...
5
- 20
-480
30 - 39
8
34
...
5
0
0
50 - 59
11
54
...
5
20
80
70 - 79
2
74
...
5
X= A + ∑fd
∑f
= 44
...
5 – 7
...
64

Author: Adebayo Kassim, Linearkassim@gmail
...
For that we
added the N values of x and divided their sum by N
...
𝑥2
...

Solution
5
Geometric Mean= √582 𝑥 441 𝑥 475 𝑥 525 𝑥 507
=5
√(3
...
7
Example: Calculate the geometric mean of 7, 8 and 12
...
76
Method 2:
Logarithm of geometric mean= ∑log x
n
Example: Calculate the geometric mean of length of ropes in yards 582, 441, 475, 525 and 507
Solution
Log GM = Log 582 + Log 441 + Log 475 + Log 525 + Log 507
5
= 2
...
644 + 2
...
720 + 2
...
511
5
Log GM = 2
...
7022 Log10
GM= 102
...
7022 + 2
GM= 100
...
037 x 100
= 503
...

Solution
Log GM = Log 7 + Log 8 + Log 12
3
Log GM = 0
...
9030 + 1
...
9424
Log GM = Log 10 0
...
76

Author: Adebayo Kassim, Linearkassim@gmail
...
However it is useful
where two averages are computed under different prevailing conditions
...
73
Median: The median of a set of number is the number that falls in the middle position after
arranging them in ascending or descending order of magnitude
...

Example: Find the median of the numbers 6,5, 9, 8 and 10
...
e least value to the highest value)
5, 6, 8, 9, 10
The median is (5 + 1)𝑡ℎ
2
= 6/ 2
= 3rd position
5, 6, 8, 9, 10
Therefore, Median is 8
Example: Find the median of the numbers 68, 54, 78, 46, 48, 67
Solution
Rearrange 46, 48, 54, 67, 68, 78
Median falls between 3rd and 4th
Median = 54 + 67 = 121 = 60
...

Formula Method:
Median = L1 + ( N/ 2 – Cf ) C
Fm
L1= lower class boundary of the median class
...


Author: Adebayo Kassim, Linearkassim@gmail
...

Example: The following frequency distribution gives the number of defined persons in
successive decades of age
...

Age
0 – 10
10 – 20 20 – 30 30 – 40 40 – 50 50 – 60 60 – 70 70 – 80
Number 1621
1842
1317
1308
1109
964
542
217
of
person
Solution
Age (years)
0 – 10
10 – 20
20 – 30
30 – 40
40 – 50
50 – 60
60 – 70
70 – 80

Class boundary
-0
...
5
9
...
5
19
...
5
29
...
5
39
...
5
49
...
5
59
...
5
69
...
5

Frequency
1621
1842
1317
1308
1109
964
542
217
8920

Cumulative frequency
1621
3463 ( 1621 + 1842)
4780 (3463 + 1317)
6088 (4780 + 1308)
7197 (6088 + 1109)
8161 ( 7197 + 964 )
8703 (8161 + 542)
8920 ( 8703 + 217)

Median = L1 + (N/2 – Cf) x C
Fm
Median class = 8920 = 4460
2
Median = 19
...
5 + ( 4460 – 3463) x 10
1317
Median = 19
...
5 + 7
...
07
Mode: given an array of numbers, the number that occurs most is the mode
...

Marks
50
61
72
80
84
90
Frequency 4
2
6
1
1
2
Solution
Mode = 72, since it occur most
...
com

For group data,
Mode = L1 + 1 x C
1+ 2
L1= Lower class boundary of the modal class
...

2 = Differences between the frequency of the modal class and the class that comes before it
...

Turn
0 – 50 50 –
100 - 150 – 200 - 250 – 300 - 350 – 400 - 450 over
100
150
200
250
300
350
400
450
500
Number 5
8
9
12
18
23
17
14
5
1
of firms
Solution
Turnover p
...
5 + 5 x 50
5+6
=249
...
5 + 22
...
22
= 249
...
5 - 50
...
5 – 100
...
5 – 150
...
5 – 200
...
5 – 250
...
5 – 300
...
5 – 350
...
5 – 400
...
5 – 450
...
5 – 500

---