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. 2

 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. 3

Lower limits ? Upper limits ? Class boundary ? Class length / width? Class Frequency • How many classes 25- 34 1 should be used but it is usual to arrange for 35- 44 2 at least 5 and not 45- 54 11 more than 15. 55- 64 30 65- 74 36 • If it can be 75- 84 21 conveniently 85- 94 15 arranged for all classes to have the 95-104 3 same class width 105-114 0 115-124 1 4

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 5

Data in ordered array: 12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58 Relative Frequency Percentage 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 6

 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. 7

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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 of each column of figures  Tables should not be packed with so much data that reading information is difficult  Non-essential information should be eliminated 9

 Charts often convey the meaning or significance of data more clearly than would a table.  Bar charts  Histograms  Ogives  Pie charts 10

 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. 11

Simple Component Compound • A chart consisting of one A bar chart that gives a • two or more separate bars are used to or more bars breakdown of each total • The actual magnitude of into its components . present sub-divisions of each item is shown data. • The lengths of bars on the A percentage component • There is usually no space chart allow magnitudes to = does not show total between the bars for data be compared magnitudes in the same category 12

 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 13

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 14

Advantages Disadvantages • give a simple pictorial display of the • only show the relative sizes of relative sizes of elements of a total elements. • show clearly when one element is • involve calculating degrees of a much bigger than others circle and drawing sectors • clearly show differences in the accurately elements of two different totals • can be time consuming unless computer software is used. • It is often difficult to compare sector sizes easily. 15

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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 out 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. 18

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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. 25

› 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 26

The following table shows the ages of 25 children on a school bus: Age Frequency (No. of children) 5 – 10 6 11 – 15 15 16 – 17 4 Draw a histogram to represent the above data. 27

Lower Upper Frequency Age Frequency boundary boundary 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 28

The ages of children entering a theme park in a 1-hour period are recorded in the table: Age Frequency (No. of children) 0 – 3 12 4 – 10 14 11 – 18 48 Find the class widths and frequency densities. Then draw a histogram to represent the data. 29

Constructed from a cumulative frequency table by plotting the cumulative frequencies against the corresponding class boundaries and joining the resulting points by straight lines. 30

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Using the data given below, construct a 'more than' cumulative frequency table and draw the Ogive. 32

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 0 33

'More than' Ogive 80 70 60 Cumulative frequency 50 40 30 20 10 0 0.5 10.5 20.5 30.5 40.5 50.5 60.5 70.5 80.5 Marks 34

Q: Draw a 'less than' ogive curve for the following data: Hence, from the ogive, estimate the number of students who has less than 57 marks? 35

What is the lower boundary and upper boundary of the classes? Marks Lower Upper Cumulative boundary boundary 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 36

120 100 80 Cumulative frequency 60 40 20 0 0 10 20 30 40 50 60 70 80 90 Marks 37

 A pictogram is a form of graphical presentation where repetitions of a picture are used to represent frequencies or other values of a feature. 38

Type of Construction Housing Fire Service Health employment Thousands 13.1 7.3 5.2 2.5 employed 39