Post on 07-Apr-2018
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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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