Explain clearly and using relevant examples the scales of measurement Measurement is the assigning of numbers to objects according to a set of rules

Explain clearly and using relevant examples the scales of measurement
Measurement is the assigning of numbers to objects according to a set of rules.
Interval scale
This scale deals with differences between objects. In marketing it measures attitudes, opinions and index. In permissible statistics it range, mean and standard. The best example is the Fahrenheit scale for temperature.
Ratio scale
In ratio scale zero point is fixed, ratios of scale values can be compared. An example is weight or height.
Nominal scale
This scale deals with classifying objects and identifying numbers. Nominal scale are qualitative, the main statistic used is percentages and mode. Examples of nominal scale are social security numbers and numbering games players.
Ordinal scale
This scale categorizes and rank orders items. It does not contain equal interval. An example is rating scales and rank orders.
Explain the following methods of data collection
Case studies
Case study refers to a process or a record of research into the development of a single unit such as a person, group or situation over a long period of time.
Diaries
A diary is a book showing information gathered on how individuals spend their time on professional activities. It can record both qualitative and quantitative data
Critical incidents
A critical incident is any actual or alleged situation or event that creates a significant risk of serious harm to the mental or physical health, safety of a researcher.
Portfolios
This is a grouping of financial assets such as bonds, cash and stocks equivalents as well as their funds and counterparts.
In 1995 five firm registered the following economic growth rates 26% , 32%, 41%, 18% and 36%
Work out
Arithmetic mean
Geometric mean
Harmonic mean

Arithmetic mean
(Sum of all values)/(Total number of values)
(26+32+41+18+36)/5 = 153/5

AM = 30.6%

Geometric mean ?(3&a×b×c)

?(26×32×41×18×36) = ?22104576

GM =280.6472

Harmonic mean
HM = n/(1/x1+1/x2+1/x3+?1/x6) =n/(?_i^(n=)??1 1/xi?)

1/26+ 1/32+ 1/41+ 1/18 + 1/36

=0.0385+0.0313+0.0244+0.0556+0.0278
=0.1776

5/0.1776
HM =28.1532

A sample comprises of the following observations 14, 18, 17, 16, 25, 31. Determine the standard deviation of this sample
Standard deviation

X x^2
14 196
18 324
17 289
16 256
25 625
31 961
_________________

??x ?_x?2

121 2651

(( ? ?x)?^2)/n = 121×121
6
= 14641
6
=2440.1667
?_x?2 __ (( ? ?x)?^2)/n = 2651_2440.1667
=210.8333
(210.8333)/(n-1) = (210.8333)/(6-1) =(210.8333)/5 =42.1667
Standard deviation = ?(2&42.1667) = 6.4936
5. The following table shows the part time per hour of a given number of laborers in the month of June 1997
Rate per hour (x) No of labourers
Shs (x) f
230 7
400 6
350 2
450 1
200 8
150 11
______
Total 35
Work out
Coefficient of variation
Coefficient of skewness

Coefficient of variation
x f fx ? x?^2 fx^2
230 7 1610 52900 370300
400 6 2400 160000 960000
350 2 700 122500 245000
450 1 450 202500 20500
200 8 1600 40000 320000
1780 35 8410 600,400 2345300
S.D = ((?f)???(fx^2 )-???( fx)2??)/((?f) (?f-1)
((35)(2345300)-(?8410)?^2)/(35 (35-1))
(82085500 -70728100)/(35×34)
11357400/1190
S.D = 9544.0336
Mean = (?fx)/(?f) = 8410/35
Mean = 240.2857
Coefficient of variation =(standard deviation)/mean×100
Coefficient of variation =?/µ×100
9544.0336/240.2857
=39. 7195 × 100
CV = 3971.7195
Coefficient of skewness
SK = (x ?-Mo)/SD

SK= (mean-mode)/SD

SK = (240.2857-150)/9544.0336

SK = 90.2857/9544.0336

SK = 0.00945