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