Data Presentation and Collection Week 2 Prepared by: Nurazrin Jupri

Types of data Data Quantitative Qualitative Discrete Continuous Primary Data Secondary

Primary data Secondary data Data collected especially for the Data which have already been purpose of whatever survey is being collected elsewhere, for some other conducted. purpose, but which can be used or adapted for the survey being Raw data are primary data which conducted. have not been processed at all, and which are still just a list of numbers. For example from government, banks, newspapers, the Internet. The main sources of primary data are personal investigation, teams of Secondary data sources may be investigators, interviews, satisfactory in certain situations, or questionnaires and telephone they may be the only convenient surveys. means of obtaining an item of data. It is reliable as you know where the data has come from and are aware It is essential to ensure secondary of any inadequacies or limitations. data used is accurate and reliable. However, it can take time to collect relatively inexpensive and quick to and is expensive. obtain

Discrete data • Can only be whole numbers, • e.g. people, • houses 4

Continuous data Can take on all values: examples include • Change in speed (acceleration) of a car • Change in height of a person • Change in age of a person 5

Discrete data Continuous data are the number of goals include the heights of all the scored by Arsenal against members of your family, as Chelsea in the FA Cup Final: these can take on any Arsenal could score 0, 1, 2, 3 value: 1.542m, 1.639m and or even 4 goals ( discrete 1.492m for example. variables = 0, 1, 2, 3, 4), but Continuous variables = they cannot score 2.1 or 2.5 1.542, 1.639, 1.492 goals.

Look through the following list of surveys and decide whether each is collecting qualitative data or quantitative data. If you think the data is quantitative, indicate whether it is discrete or continuous. Qualitative Discrete Continuous Statement (a) A survey of accountancy textbooks, to determine how many diagrams they contain. (b) A survey of greetings cards on a newsagent's shelf, to determine whether or not each has a price sticker on it. (d) A survey of swimmers to find out how long they take to swim a kilometre.

• 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. 8

FREQUENCY DISTRIBUTIONS • 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. 9

Tally Chart for defective items Age in months Tally Frequency (F) ıı 0 and under 5 2 ııı 5 and under 10 3 Iııı ıı 10 and under 15 7 Iııı Iııı 15 and under 20 9 Iııı ıııı ıııı ıııı 20 and under 25 20 Iııı ıııı ıııı Iı 25 and under 30 17 Iııı ıııı ıııı ıııı ıı 30 and under 35 22 Total 80 10

Frequency table for defective items by age of machine Age in months Frequency 0-5 2 5-10 3 10-15 7 15-20 9 20-25 20 25-30 17 30-35 22 80 11

Class intervals • used in grouped data • e . g. 0 - 9 • 10 - 19 • 20 – 29 12

Class boundaries • the values at which different class intervals meet; e.g. for the second class interval • 9.5 is the lower class boundary 10 -19 • 19.5 is the upper class boundary • What are the class boundaries of the third class interval ? • 19.5 is the lower class boundary 20 -29 • 29.5 is the upper class boundary 13

Class size (class widths) • the difference between the upper and lower class boundaries (e.g. 10 in our example) 14

Class frequencies • the number of times an observation occurs in a class interval 15

Lower boundary ? T Upper boundary ? R Class length / width? Class interval? Y • How many classes should be used but it is usual to arrange for at Class Frequency least 5 and not more 25- 34 1 than 15. 35- 44 2 45- 54 11 • If it can be conveniently 55- 64 30 arranged for all classes 65- 74 36 to have the same class width 75- 84 21 85- 94 15 95-104 3 105-114 0 CUMMULATIVE 16 115-124 1 TABLE

Histogram – Set of rectangles (bars), giving a picture of the distribution – Base of each bar : equal to class size (width) – Height of each bar : equal to class frequency (or proportional where class size varies – 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 17

Number of students 40 30 20 10 0 0 20 40 60 80 100 Score on final exam (maximum 100) 18

Histogram (Frequency density) 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. 19

Solution: 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 20

Try this! The ages of children entering a theme park in a 1- hour period are recorded in the table: Age Frequency (No. of children) 1 – 3 12 4 – 10 14 11 – 18 48 Find the class widths and frequency densities. Then draw a histogram to represent the data. 21

Frequency curve • Connecting the mid-points of the tops of each rectangle in the histogram by straight lines gives the frequency polygon. • Area beneath the frequency polygon is identical to that of the histogram • If we ‘smooth’ the straight lines to form ‘curves’ then a frequency curve results 22

Frequency polygon 23

Frequency Curve 24

cumulative frequency table 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 FREQUENCY TABLE 25

Cumulative frequency • the running total of the figures shown in the frequency column of a frequency table. Can be • Cumulative less than • OR Cumulative more than 26

‘More than’ Ogive Using the data given below, construct a 'more than' cumulative frequency table and draw the Ogive. 27

Solution: 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 28

'More than' Ogive 80 70 60 50 Cumulative frequency 40 30 20 10 0 0.5 10.5 20.5 30.5 40.5 50.5 60.5 70.5 80.5 Marks 29

‘Less than’ Ogive Draw a 'less than' ogive curve for the following data: 30

Solution: 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 31 100

120 100 80 Cumulative frequency 60 40 20 0 0 10 20 30 40 50 60 70 80 90 Marks 32

Percentiles • A particular value below (or above) which a given percentage of the distribution lies • Lower quartile: that value below which 25% of the distribution lies • Upper quartile: that value above which 25% of the distribution lies • Median: that value below/above which 50% of the distribution lies 33

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Stem-and-leaf • Order the raw data in an array (e.g. lowest to highest) • Stems: often the tens • Leafs: often the units • Example: 80, 83, 84, 86, 87, 89, 90, 94, 95, 97, 99 8 : 0 3 4 6 7 9 9 : 0 4 5 7 9 35

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Bar charts 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. 37

Simple Component Compound • A chart consisting of one or • two or more separate bars A bar chart that gives a more bars breakdown of each total are used to • The actual magnitude of into its components . present sub-divisions of each item is shown data. • The lengths of bars on the • There is usually no space A percentage component = chart allow magnitudes to be does not show total between the bars for data in compared magnitudes the same category 38

number of students 0 1 2 3 4 5 6 7 8 China Turkey Ukraine Kyrgyzstan Bar chart nationalities of students India Pakistan Oman Saudi Arabia Ivory Coast Thailand 39

Pie Chart • Circular ‘pie’ diagram using sectors to show distribution • A complete 'pie' = 360° = 100% 180° = 50% • Shading and Colour => distinguishes the segments from each other • Sector angle : fraction of total in sector x 360° 40

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