1 Tabulation means putting data into tables. A table is a matrix - - PowerPoint PPT Presentation

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 Tabulation means putting data into

tables.

 A table is a matrix of data in rows and

columns, with the rows and the columns having titles.

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 converting the set of numbers into the

form of a grouped frequency table.

 This involves dividing the range covered

by the data into classes and counting the numbers of data values which fall into each class.

 These numbers are the class frequencies.

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Class Frequency 25- 34 1 35- 44 2 45- 54 11 55- 64 30 65- 74 36 75- 84 21 85- 94 15 95-104 3 105-114 115-124 1

Lower limits ? Upper limits ? Class boundary ? Class length / width?

• How many classes

should be used but it is usual to arrange for at least 5 and not more than 15.

• If it can be

conveniently arranged for all classes to have the same class width

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Range Cummulative Frequency Less than 34.5 1 Less than 44.5 3 Less than 54.5 14 Less than 64.5 44 Less than 74.5 80 Less than 84.5 101 Less than 94.5 116 Less than 104.5 119 Less than 114.5 119 Less than 124.5 120

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Data in ordered array:

12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58

Class Frequency

10 but under 20 3 .15 15 20 but under 30 6 .30 30 30 but under 40 5 .25 25 40 but under 50 4 .20 20 50 but under 60 2 .10 10 Total 20 1 100 Relative Frequency Percentage

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 In country A there were 22,618,462 dwellings.

Of these 9,875,380 were owner-occupied, 6,765,097 were council rentals, 3,476,907 were private rentals and the remainder were held under a variety of tenures.

 In country B there were 1,846,093 in total and

the numbers in the above categories were 569,043, 903,528 and 278,901, respectively.

 Display this information in a table.

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 The table should be given a clear title  All columns should be clearly labeled  Where appropriate, there should be clear sub-

totals

 A total column may be presented; this would

usually be the right-hand column

 A total figure is often advisable at the bottom

• f each column of figures

 Tables should not be packed with so much

data that reading information is difficult

 Non-essential information should be eliminated

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 Charts often convey the meaning or

significance of data more clearly than would a table.

 Bar charts  Histograms  Ogives  Pie charts

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 A method of data presentation in which

data are represented by

 bars of equal width,  the height / length of the bar

corresponding to the value of the data.

 Axes must be labeled and there must be a

scale to indicate the magnitude of the data.

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Simple Component Compound

• A chart consisting of one
• r more bars
• The actual magnitude of

each item is shown

• The lengths of bars on the

chart allow magnitudes to be compared A bar chart that gives a breakdown of each total into its components. A percentage component = does not show total magnitudes

• two or more separate bars

are used to present sub-divisions of data.

• There is usually no space

between the bars for data in the same category

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 A chart which is used to show pictorially the

relative size of component elements of a

• total. (always be based on percentage

values)

 A complete 'pie' = 360° = 100%

180° = 50%

 Shading and Colour => distinguishes the

segments from each other

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Given : Sales of furniture (£’000) Settees 34 Armchairs 27 Dining sets 38 Shelving 18 Others 12 Category Sales Angle,° Settees 34 95 Armchairs 27 75 Dining sets 38 106 Shelving 18 50 Others 12 34 Total 129 360

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Advantages Disadvantages

• give a simple pictorial display of the

relative sizes of elements of a total

• show clearly when one element is

much bigger than others

• clearly show differences in the

elements of two different totals

• only show the relative sizes of

elements.

• involve calculating degrees of a

circle and drawing sectors accurately

• can be time consuming unless

computer software is used.

• It is often difficult to compare sector

sizes easily.

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› The logic behind this

is that there are 360 degrees total in a

• circle. If you know

that 14,400 is 30 percent of the whole (or 0.30), then you're just trying to figure

• ut what 30% of 360

is.

› Add up all the

degrees you calculate from this

• step. They should

equal 360. If they don't, you've missed something.

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 Remember that all good graphs have a

title and labels.

 Add the name of the sections and the

percent they represent to the chart.

 Color each section of the pie chart a

different color/pattern to easily visualize the results.

 Make sure all angles are accurate.

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› The area of a bar above a class interval is

proportional to the frequency in that class

› AREA not HEIGHT › If there is non-equal size of class interval. Find

the frequency density Height of block = class frequency class width

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The following table shows the ages of 25 children on a school bus: Draw a histogram to represent the above data.

Age Frequency (No. of children) 5 – 10 6 11 – 15 15 16 – 17 4

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Age Frequency Lower boundary Upper boundary Frequency density 5 – 10 6 4.5 10.5 1 11 – 15 15 10.5 15.5 3 16 – 17 4 15.5 17.5 2

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The ages of children entering a theme park in a 1-hour period are recorded in the table: Find the class widths and frequency densities. Then draw a histogram to represent the data.

Age Frequency (No. of children) 0 – 3 12 4 – 10 14 11 – 18 48

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Constructed from a cumulative frequency table by plotting the cumulative frequencies against the corresponding class boundaries and joining the resulting points by straight lines.

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Using the data given below, construct a 'more than' cumulative frequency table and draw the Ogive.

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Marks Lower boundary Upper boundary Cumulative Frequency 0.5 70 1 – 10 0.5 10.5 67 11 – 20 10.5 20.5 49 21 – 30 20.5 30.5 37 31 – 40 30.5 40.5 23 41 – 50 40.5 50.5 13 51 – 60 50.5 60.5 7 61 – 70 60.5 70.5 2 71 – 80 70.5 80.5

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Cumulative frequency Marks

10 20 30 40 50 60 70 80 0.5 10.5 20.5 30.5 40.5 50.5 60.5 70.5 80.5

'More than' Ogive

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Q: Draw a 'less than' ogive curve for the following data: Hence, from the ogive, estimate the number

• f students who has less than 57 marks?

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What is the lower boundary and upper boundary of the classes?

Marks Lower boundary Upper boundary Cumulative Frequency 0 – 10 0.5 9.5 2 10 – 20 9.5 19.5 10 20 – 30 19.5 29.5 22 30 – 40 29.5 39.5 40 40 – 50 39.5 49.5 68 50 – 60 49.5 59.5 90 60 – 70 59.5 69.5 96 70 – 80 69.5 79.5 100

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Cumulative frequency Marks

20 40 60 80 100 120 10 20 30 40 50 60 70 80 90

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 A pictogram is a form of graphical

presentation where repetitions of a picture are used to represent frequencies or other values of a feature.

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Type of employment Construction Housing Fire Service Health Thousands employed 13.1 7.3 5.2 2.5

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