Stat Intro 2

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    STATISTICS

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    CONDUCTING RELIABLE

    INVESTIGATIONS Choose a representative sample from the

    population

    Avoid selecting sample that could lead to bias Plan and draw up questionnaires carefully

    Use closed or open-ended questions in such a

    way that the answers can be analysedproperly

    Avoid questions that could lead to biased

    answers.

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    Example

    Why are these examples not representative and

    describe a method that can result in representative

    sample:

    a) A survey was done to determine the attitude of

    teenagers to smoking in Brunei. The researcher

    visited all school within a 20 km radius of his home

    b) A survey was done to determine whether retired

    persons have sufficient access to health carefacilities. The questionnaire was distributed to 3000

    retired persons, all in retirement villages.

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    Examples

    An open-ended question.

    What kind of movie do you enjoy most?

    Answer: A closed question

    What kind of movie do you enjoy most?

    drama action comedy

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    Rewrite as closed: At what age did you obtain your

    drivers license? What is the total time that youwatch TV on a Saturday?

    Explain why this could lead to biasness:

    A survey was done to determine what skin care

    products teenagers prefer to use. This statement

    appears on the first page of the questionnaire:

    10 respondents will be chosen to have a free

    makeover and make-up lesson. Starry white is atechnologically advanced toothpaste. How often do

    you buy Starry White?

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    CATEGORICAL DATA

    Is where the information that is collected is

    about a quality or category for a certain

    variable, usually consisting of descriptions

    using names.

    Example, for favourite colour- blue, red, green,

    yellow, brown, black, purple.

    Graphing is either by pictogram, pie charts,

    bar charts, etc.

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    CONTINUOUS DATA

    Data that is not categorical.

    Numbers (numerical values) obtained from

    measurements heights, weights, marks Data display histogram, line graphs, ogives

    ects.

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    Example

    How would you represent these data (thenumber of people in 100 cars that passes a

    certain traffic light) in a table form?

    1 3 4 2 5 2 4 3 2 1

    3 1 3 4 2 3 2 2 5 4

    3 2 2 4 3 5 4 3 2 3

    4 5 1 2 4 2 2 4 1 3

    2 3 4 5 2 3 5 4 3 2

    5 2 4 3 2 1 3 2 2 41 2 3 2 4 3 2 4 2 3

    3 4 5 2 2 2 1 3 4 2

    4 2 3 5 4 3 4 2 1 2

    2 5 2 3 3 2 3 2 1 2

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    # of people Tally Frequency( f)

    1 //// ////

    2 //// //// //// //// ////

    //// ////

    3 //// //// //// //// ////4 //// //// //// ////

    5 //// ////

    Total 100Suggesta suitable representation for this

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    Complete the table

    sleep read televisi

    on

    sport Total

    Boys 11 3 49

    Girls 4 9

    Total 25 24 100

    Number of students according to their preferred relaxation activity

    How would you graph this?

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    PICTOGRAM

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    Example

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    Example

    1. What is the world population in 1650?

    2. How many more people were there in 1999 than in

    1975?

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    1. Some people are surveyed on their choice of drinks. The following pictogram

    shows the results of the survey.

    a. How many people are surveyed?

    b. How many more people chose coffee over tea?

    c. What percentage of the people liked hot chocolate?

    d. What percentage of the people did not choose milk as their choice?

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    Answer

    a. 20 * 25 = 500 people

    b. Coffee = 20 * 8 = 160 people

    tea = 20 * 6 = 120 peoplePeople chose coffee over tea = 160 120

    = 40 people.

    Or 8 6 cups = 2 cups.Therefore, 20 * 2 = 40 people.

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    Answer

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    1. A survey of how people travel to work was recorded.Mode of travel Number of people

    MRT 48Walk 30

    Taxi 9

    Bus 36

    Car 21a. Draw a pictogram to represent the given data, using one picture to

    represent 6 people.

    b. Which mode of travel is the most commonly used?c. What is the total number of people involved in the survey?d. What fraction of the total number of people took a bus to work?e. What are the advantages and disadvantages of using

    pictogram?

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    Answer

    b. Mode of travel is MRT.

    c. Total number is 144.

    d. 36/144 =

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    Mode of travel Number of people

    MRT

    Walk

    Taxi

    Bus

    Car

    Key: = 6 people

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    PIE CHARTS

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    Another way of representing data is using a pie

    chart which uses a circle to show and comparethe fractional parts to the whole.

    As = , the angle of the

    sector is also proportional to the area of the sector. To find angle of each sector:

    Total of data corresponds to 360. Let x= the angleat the centre for item A, then

    x = x 360

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    Nex , ra a large ir le a use a pro ra or o measure

    he require a gles of se ors. Fi ally, label he pie har

    omple ely.

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    BAR CHARTS

    Single and compound

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    Example

    Country Gold Silver Bronze

    USA 35 29 29

    China 32 17 14Russia 27 27 38

    Australia 17 16 16

    The table shows the medal tally at Athens Olympics2004:

    a) Construct a bar chart with the countries on the

    horizontal axis

    b) Comment on the similarities and differences

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    Example

    A school recorded the number of form 6

    candidates who achieved the following grades

    in mathematics:

    A: 23 B: 92 C: 89 D: 57 E: 31

    Represent the data on:

    a. A bar chart

    b. A compound bar chart

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