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Chapter 7Statistics - organising data - Palgrave

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Chapter 7Statistics - organising data - Palgrave Powered By Docstoc
					    Chapter 8




 Statistics


Organising data




                  1
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.




                                               2
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.



                                                       3
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




                                                         4
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.

                                                     5
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)
                                                        6
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
   § Your firm's workforce

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
                                                         7
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.

                                                 8
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.
                                                         9
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


                                              10
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


                                              11
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

                                                         12
§ 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

                                                     13
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




                                                                      14
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?



                                                15
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.

                                                              16
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




                                                                 17
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.




                                                                                  18
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
     10




     5




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

                                                                           19

				
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