# Chapter 7Statistics - organising data - Palgrave

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```					    Chapter 8

Statistics

Organising data

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qNot many people find long sheets of data
particularly interesting or easy to understand.

qLarge sets of data are generally presented
either by means of tables, or by drawing
diagrams, or both.

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What do We Mean By Statistics?

qStatistics are facts usually expressed numerically.

qThe science of statistics is generally
taken to include the systematic:
§Collecting
§Classifying
§Analysing
§Presenting
of data in order to get a better
understanding of some given situation.

qThis may mean summarising the data in
tabulated, graphical or numerical form.

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qIn business, we may be interested in a set of
data in its own right.

§ In this case we could just describe our data, both
numerically and graphically, in the most
appropriate manner – descriptive statistics

§ We have all the data we are interested in – the
whole population

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qAlternatively we may be interested a far
wider picture than that presented by our set
of data.
§ We may be interested in forecasting future
demands from our current demands or past
demands.

§ We may be interested in the opinions of the whole
population when we have surveyed only a sample
from them – inferential statistics

§ The data we have only represents a sample from
the whole population.

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qSources of data

q Government statistics include a vast amount of
business, economic and sociological information. These
are gathered by the Government, and are published
both in various hard-copy formats and on-line.

q The website of National Statistics is
http://www.statistics.gov.uk/.

q On the international level, the United Nations
Statistics Division produces similar information on
http://unstats.un.org/unsd/default.htm

q (More references to data sources on the companion
website)
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qPublished statistics such as those published
by the government are known as secondary
data.
q If you need to analyse information which is specific
to your own organisation, this needs to be collected
directly and is known as primary data. Useful data
may be on:
§ Your firm's products, costs, sales or services
§ Their competitors' products, costs, sales or
services
§ Measurement of industrial processes

q It may be collected from the firm’s accounts or
records or, if it concerns items such as public
opinions, it may need to be gathered from a survey
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qTypes of data
§ Data may be qualitative - they may be
describing something such as the colour of
a car

§ Data may be quantitative – they may be
measuring something

§ If they are quantitative, the measurements
may be discrete or continuous - they may
be counting descrete people or measuring
continuous weght.

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qPresenting data in tables
§ Most people are put off by the sight of a page
filled with numbers. It is necessary to summarise
them into a table or by a diagram so that they can
be more easily understood.

§ Qualitative or descrete quantitative data may be
summarised by its frequencies.

§ Quantitative continuous data will be grouped
together into intervals and the the frequencies
within those intervals found.

§ Summarised quantitative data is always presented
in numerical order.
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Example 1
§ The number of employees working in the
different areas of a supermarket at any
one time:

Area    Staff
Office      18
Shop area    32
Check out     12
Car park     6

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q Example 2
§ The supermarket staff may be described
by their sex as well as where they work
using cross-tabulation.

Area    Males   Females
Office      7       11
Shop area        24       12
Check out         2       10
Car park     6        0

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Example 3
§ Mileages recorded for a sample of hired vehicles
during a given week yield the following data:
138   164   150   132   144   125   149   157

146   158   140   109   136   148   152   144

168   126   138   186   163   109   154   165

146   183   105   108   135   153   140   135

161   145   135   142   150   156   145   128

§ There are so many numbers in this sample that it
seems reasonable to collect them as interval data.

§ Nine intervals of width 10 miles seems reasonable

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§ Collecting these data into an interval frequency
table:
Class Interval   Frequency
100 & < 120         4
120 & < 130         3
130 & < 140         7
140 & < 150         11
150 & < 160         8
160 & < 170         5
170 & < 190         2

§ Note that all the intervals do need to have the
same width
§ We shall revisit this data later

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Example 4

q If our data is described by two variables, such as the car
driver’s sex as well as mileage travelled, it is cross-tabulated:

Mileage         Male     Female
100 & < 120          1         3
120 & < 130          1         2
130 & < 140          4         3
140 & < 150          8         3
150 & < 160          4         4
160 & < 170          3         2
170 & < 190          2         2

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qCumulative frequency

§ We may be interested to know how many
people fit into a category of less than a
particular value.

§ How many, or what percentage of patients’
waiting times are within the government’s
target times?

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Example 5
§ How many of the hired car drivers covered less
than the mileage included in the hire fee, 150
miles? What percentage of the drivers was that?
Class Interval   Frequency   Cumulative frequency   % C.F.
100 & < 120            4                 4           10.0
120 & < 130            3                 7           17.5
130 & < 140            7                14           35.0
140 & < 150            11               25           62.5
150 & < 160            8                33           82.5
160 & < 170            5                38           95.0
170 & < 190            2                40          100.0

25 drivers, 62.5%, kept within their allowance.

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q Graphical representation of data

§ Data is more easily understood if represented by diagrams
§ The simplest of these are:

Type of data              Type of diagram

Qualitative               Pie chart or bar chart

Bar chart, Pie chart if only a few
Quantitative descrete
categories

Quantitative continuous   Histogram

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q Example 6           Supermarket data

q In the pie chart the angle of a sector is proportional to the number of staff
working in that department.

q In the bar chart the height of the bar is proportional to the number of staff
working in that department.

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Example 7                  Car hire data
§ In a histogram the area of the bar, rather than its
height, is proportional to the cars in the bar.
§ A histogram does not need to have equal intervals
Cars per 10 mile interval
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5

0
100   110   120      130 140 150          160   170   180   190
Mileages travelled

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