data collection understand data collection process

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Data Collection •Understand data collection process

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Page 1: Data Collection Understand data collection process

Data Collection

•Understand data collection process

Page 2: Data Collection Understand data collection process

Refresh

• Test the questionnaire on a few people first to see if it works OK or needs amending.

Pilot survey:

Sample Size and Type:• Decide on the size and type of the sample that you intend to use. Will it be a simple random sample or a stratified random sample?

Simple Random Sampling

After producing a questionnaire for your survey (see Questionnaires and Surveys) you will need to organise a sample.

Page 3: Data Collection Understand data collection process

Simple Random SamplingSamples and

Populations.

In our earlier work on surveys we produced questionnaires to be given out to students in a school. The number of students in the school is called the population and the number of students that receive the questionnaire is called the sample. However, in statistics the word population has a much broader meaning and can be taken to be a group of anything (for example objects as well as people).

The sample is that part of the population under consideration. For instance the population could be the number of light bulbs produced by a manufacture during a day and the sample could be every 50th light bulb produced. Samples are taken by manufacturers of products to ensure that the quality is up to the required standard.

Page 4: Data Collection Understand data collection process

Population Possible Samples

TV’s produced by a factory.. Every 20th TV

Children’s trousers made in a factory. Every 30th pair

Punctuality of buses in a city.

Check punctuality for 10 different routes

Tyre produced by manufacturer.

5% of all tyres produced

Page 5: Data Collection Understand data collection process

Why do we take a Sample?

Simple Random Sampling

•Too expensive and too time consuming to survey an entire population.•If the population under consideration is a set of objects such as car tyres/nuts and bolts etc then they may need to be tested to destruction.

After producing a questionnaire for your survey (see Questionnaires and Surveys) you will need to organise a sample.

Page 6: Data Collection Understand data collection process

Precautions with the Sample

Simple Random Sampling

• The sample taken should be representative of the whole population under consideration. A sample that is not representative is said to be biased.

After producing a questionnaire for your survey (see Questionnaires and Surveys) you will need to organise a sample.

Page 7: Data Collection Understand data collection process

Simple Random SamplingDiscuss why the following samples may not be

representative (i.e. biased) of the populations.

1. Stuart’s group are going to carry out a survey about the average time spent on homework by students in their school.

They decide to give a questionnaire about this to every one in their class2. Sara’s group are going to carry out a survey about peoples views on reading books and whether this improves spelling standards.

They decide to sample the views of students as they enter the library.

3. A retail outlet wants to get views on what people think about digital TV’s.They decide to ring up the first fifty people in the phone book.

4. A car manufacture wants to check the quality of doors made for its cars by one of their five “door teams” (teams A,B,C,D and E) in the factory.It decides to check 10% of all doors made by team B on a Friday afternoon.

Page 8: Data Collection Understand data collection process

Simple Random Sampling

Simple Random Sampling

• In a simple random sample every member of the population under consideration has an equal chance of being chosen.

After producing a questionnaire for your survey (see Questionnaires and Surveys) you will need to organise a sample.

• We will look at the methods of simple random sampling in the context of a school survey on homework.

Page 9: Data Collection Understand data collection process

Hat

Simple Random Sampling

324 538 214 43

Method 1

Example: Out of a school of 618 students forty are to be selected to take part in a survey on Homework.

1. Assign a three digit number from 001 to 618 to each student.

2. Write each number on a piece of paper (or use raffle tickets), place in a hat and mix up.

3. Draw the forty numbers from the hat.

Page 10: Data Collection Understand data collection process

Random Number Table

Simple Random Sampling

Method 2

23 02 63 03 81 67 96 40 59 84 30 03 67 17 42 35 94 12 74 87

23 19 09 66 05 40 19 36 47 16 86 52 63 27 26 54 24 50 34 35

39 32 73 36 41 90 96 69 02 18 08 35 62 30 67 23 06 27 89 74

55 15 54 03 20 75 53 95 20 94 19 34 10 65 10 41 82 91 83 17

38 75 86 68 55 60 84 07 25 93 24 37 63 76 18 04 78 03 41 01

29 80 86 34 42 45 71 46 62 76 42 52 95 18 24 74 07 97 27 10

05 74 23 23 52 34 12 13 90 50 85 28 89 46 37 63 36 87 48 35

55 89 75 14 36 58 56 19 51 77 34 78 55 17 96 35 69 14 88 31

15 43 81 09 53 14 33 58 69 36 19 01 68 61 35 87 97 09 01 86

39 30 62 86 60 40 19 03 97 34 12 28 33 73 33 37 20 57 08 84

07 13 22 06 71 60 10 01 41 45 11 08 60 27 98 42 56 74 58 62

78 14 38 54 73 98 33 09 90 51 02 55 72 75 01 39 82 77 27 90

03 87 01 90 81 59 05 80 47 15 24 31 28 91 91 25 64 30 54 63

44 57 69 09 67 13 91 85 83 23 26 52 30 64 84 20 02 56 57 85

32 81 42 42 50 75 29 26 16 63 78 34 79 31 27 55 96 69 32 64

36 55 18 28 51 78 52 35 70 72 29 04 66 58 89 55 35 62 32 29

50 74 02 76 86 17 78 64 06 26 93 27 55 84 51 91 61 28 28 55

07 04 45 91 11 56 07 45 87 93 94 75 25 87 32 66 81 71 15 43

95 42 80 83 56 95 23 63 85 94 25 03 88 24 26 27 46 29 64 35

01 85 45 66 68 41 54 91 56 44 33 34 58 53 81 73 60 79 63 75

Use a random number table. You can start anywhere (i.e. randomly) in the table and go in any direction left, right, up or down in groups of 3 digits until all 40 numbers are chosen. In this example we start by going down then left.

Starting from this 5

587 153

113 092

570 254

915 644

333Remove unwanted digits and continue until you have your 40 numbers.

Page 11: Data Collection Understand data collection process

Simple Random Sampling

23 02 63 03 81 67 96 40 59 84 30 03 67 17 42 35 94 12 74 87

23 19 09 66 05 40 19 36 47 16 86 52 63 27 26 54 24 50 34 35

39 32 73 36 41 90 96 69 02 18 08 35 62 30 67 23 06 27 89 74

55 15 54 03 20 75 53 95 20 94 19 34 10 65 10 41 82 91 83 17

38 75 86 68 55 60 84 07 25 93 24 37 63 76 18 04 78 03 41 01

29 80 86 34 42 45 71 46 62 76 42 52 95 18 24 74 07 97 27 10

05 74 23 23 52 34 12 13 90 50 85 28 89 46 37 63 36 87 48 35

55 89 75 14 36 58 56 19 51 77 34 78 55 17 96 35 69 14 88 31

15 43 81 09 53 14 33 58 69 36 19 01 68 61 35 87 97 09 01 86

39 30 62 86 60 40 19 03 97 34 12 28 33 73 33 37 20 57 08 84

07 13 22 06 71 60 10 01 41 45 11 08 60 27 98 42 56 74 58 62

78 14 38 54 73 98 33 09 90 51 02 55 72 75 01 39 82 77 27 90

03 87 01 90 81 59 05 80 47 15 24 31 28 91 91 25 64 30 54 63

44 57 69 09 67 13 91 85 83 23 26 52 30 64 84 20 02 56 57 85

32 81 42 42 50 75 29 26 16 63 78 34 79 31 27 55 96 69 32 64

36 55 18 28 51 78 52 35 70 72 29 04 66 58 89 55 35 62 32 29

50 74 02 76 86 17 78 64 06 26 93 27 55 84 51 91 61 28 28 55

07 04 45 91 11 56 07 45 87 93 94 75 25 87 32 66 81 71 15 43

95 42 80 83 56 95 23 63 85 94 25 03 88 24 26 27 46 29 64 35

01 85 45 66 68 41 54 91 56 44 33 34 58 53 81 73 60 79 63 75

Use your printed random table to take a random sample of size 20 from a school population of 450.

Page 12: Data Collection Understand data collection process

Calculator

Simple Random Sampling

Method 3

Use a random number generator. Using a scientific calculator press Shift/Inv key followed by the RND/random key to generate three digit numbers from 0.001 to 0.999

0.386 0.525 0.023 0.874 0.702 0.123

386 525 023 874 702 123

Ignore the decimal points and simply read as a 3 digit number.

Page 13: Data Collection Understand data collection process

Simple Random Sampling

0.386 0.525 0.023 0.874 0.702 0.123

386 525 023 874 702 123

Ignore the decimal points and simply read as a 3 digit number.

Use your calculator to obtain a random sample of size 25 from a school population of 580.

Page 14: Data Collection Understand data collection process

Worksheet

23 02 63 03 81 67 96 40 59 84 30 03 67 17 42 35 94 12 74 87

23 19 09 66 05 40 19 36 47 16 86 52 63 27 26 54 24 50 34 35

39 32 73 36 41 90 96 69 02 18 08 35 62 30 67 23 06 27 89 74

55 15 54 03 20 75 53 95 20 94 19 34 10 65 10 41 82 91 83 17

38 75 86 68 55 60 84 07 25 93 24 37 63 76 18 04 78 03 41 01

29 80 86 34 42 45 71 46 62 76 42 52 95 18 24 74 07 97 27 10

05 74 23 23 52 34 12 13 90 50 85 28 89 46 37 63 36 87 48 35

55 89 75 14 36 58 56 19 51 77 34 78 55 17 96 35 69 14 88 31

15 43 81 09 53 14 33 58 69 36 19 01 68 61 35 87 97 09 01 86

39 30 62 86 60 40 19 03 97 34 12 28 33 73 33 37 20 57 08 84

07 13 22 06 71 60 10 01 41 45 11 08 60 27 98 42 56 74 58 62

78 14 38 54 73 98 33 09 90 51 02 55 72 75 01 39 82 77 27 90

03 87 01 90 81 59 05 80 47 15 24 31 28 91 91 25 64 30 54 63

44 57 69 09 67 13 91 85 83 23 26 52 30 64 84 20 02 56 57 85

32 81 42 42 50 75 29 26 16 63 78 34 79 31 27 55 96 69 32 64

36 55 18 28 51 78 52 35 70 72 29 04 66 58 89 55 35 62 32 29

50 74 02 76 86 17 78 64 06 26 93 27 55 84 51 91 61 28 28 55

07 04 45 91 11 56 07 45 87 93 94 75 25 87 32 66 81 71 15 43

95 42 80 83 56 95 23 63 85 94 25 03 88 24 26 27 46 29 64 35

01 85 45 66 68 41 54 91 56 44 33 34 58 53 81 73 60 79 63 75

Worksheet

Page 15: Data Collection Understand data collection process

Discrete and Continuous Data

Discrete data can only take on certain individual values.

Continuous data can take on any value in a certain range.

Example 2

Length of a film is a continuous variable.

Example 1

Number of pages in a book is a discrete variable.Example 3

Shoe size is a Discrete variable. E.g. 5, 5½, 6, 6½ etc. Not in between.

Example 4

Temperature is a continuous variable.

Example 5

Number of people in a race is a discrete variable.

Example 6

Time taken to run a race is a continuous variable.

Page 16: Data Collection Understand data collection process

Volume of a cereal

box

Population of a town

Number of goals in a

season

Number of matches in

a box

Length of a

crocodileShirt

collar size

Speed of a car

Temperature of oven

Discrete? Continuous?

Group the following as either discrete or continuous data.

Page 17: Data Collection Understand data collection process

Volume of a cereal

box

Population of a town

Number of goals in a

season

Number of matches in

a box

Length of a

crocodile

Shirt collar size

Top speed of a car

Temperature of oven

Discrete Continuous