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TYPES OF DATA:
1. Continuous Data
2. Discrete Data
3. Categorical Data
1. Continuous Data
(Measured, not counted. Can be any value within a range, often with decimals.)
Examples:
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Height: A person can be 165.3 cm, 180.7 cm, or any value in between.
Weight: An object can weigh 2.54 kg, 15.891 kg, etc.
Time to run a race: A runner's time could be 10.58 seconds, 23.14 seconds,
etc.
Temperature: The temperature outside can be 21.5°C, -3.2°C, or 98.6°F.
Volume of liquid in a bottle: A bottle can contain 0.355 liters, 1.5 liters, or
500.25 ml.
2. Discrete Data
(Counted. Only specific, separate values, usually whole numbers.)
Examples:
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Number of students in a class: You can have 25 students or 26, but not 25.5.
Shoe size: A person wears a size 8, 9, or 10, but not a size 8.25.
Number of pets owned: A family has 0, 1, 2, or 3 pets.
Number of questions answered correctly on a test: You can score 15/20, but
not 15.5/20.
Cars in a parking lot: There are 47 cars, not 47.2 cars.
3. Categorical Data
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(Describes a category or group. Can be numerical labels, but the numbers don't
have mathematical meaning.)
Examples:
 Nationality: American, Canadian, Brazilian, Japanese, Italian
 Eye Color: Brown, Blue, Green, Hazel
 Hair Color: Blonde, Brunette, Black, Red, Gray
 Car color: Red, Blue, Silver, Black, White.
 Blood type: A, B, AB, O.
TYPES OF SAMPLES
1. Random sample
Everyone has an equal chance of being picked.
Example: Put all learners’ names in a hat and pick some out.
2. Systematic sample
Choose people in a regular pattern.
Example: Pick every 5th learner on the class list.
3. Stratified sample
Split people into groups first, then pick fairly from each group.
Example: Pick some learners from each year group so all ages are included.
4. Convenience sample
Choose the people who are easiest to ask.
Example: Just ask learners in your own class.
Continuous Data
1. Height of the cars: e.g. 55.5 inches.
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2. Fuel efficiency (miles per gallon): e.g. 25.3 miles per gallon, 30.85 miles
per gallon).
Discrete Data
1. Number of passengers in each car: e.g. 1, 2, 3.
2. Number of parking spots available: e.g. 10, 15, 20.
Categorical Data
1. Type of car : e.g. sedan, SUV, truck.
2. Car color : e.g. red, blue, green.
1) Use random numbers from the school register to choose 20 students.
2) Select a specific number of students from each year group so that both younger
and older learners are included.
Assign each of the 632 people a unique number from 1 to 632. Use the calculator
or software to generate 50 different random numbers within this range. The people
whose assigned numbers match the generated random numbers are selected for the
sample.
Evaluating Surveys
Q1: When you see a survey result, what five questions should you ask yourself
to check its reliability?
A1:
1. Who did the survey?
2. How was the survey carried out?
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3. How big was the sample?
4. How was the sample chosen?
5. Was it a representative sample?
Q2: What are the steps involved in planning a statistical investigation?
A2:
1. Ask a statistical question.
2. Make a prediction (hypothesis).
3. Plan what data to collect and how to collect it.
4. Choose a sampling method.
5. Conduct a small trial.
6. Use the results to make a generalization.
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For foot size: Use shoe size (discrete data) as it is easy to collect and less
embarrassing than measuring feet directly.
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For hand size: Measure hand span (the distance from the tip of the thumb to
the tip of the little finger when stretched out) or the length from the wrist to
the top of the middle finger (continuous data). This is easier and more
accurate than drawing the hand and counting squares.
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1 a) Write some questions you could ask about estimation.
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Can boys estimate lengths more accurately than girls?
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Do older learners estimate time intervals better than younger learners?
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Are learners better at estimating acute angles or obtuse angles?
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Can learners estimate the number of sweets in a jar more accurately than the
number of paperclips?
1 b) Write some predictions you could test.
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Girls estimate the length of a line more accurately than boys.
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Older learners estimate obtuse angles more accurately than younger learners.
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Learners generally underestimate one minute of time.
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Learners overestimate the number of small items in a jar.
1 c) Describe some different ways of choosing a sample to test one or more of
your predictions.
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Simple random sample: Assign each learner in the school a number and use
random numbers to pick participants.
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Systematic sample: Choose every 10th learner on the school register.
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Stratified sample: Divide learners into groups (e.g., boys and girls, or older
and younger learners) and randomly choose a proportional number from
each group.
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Convenience sample: Choose learners from your own class or nearby
classes.
1 d) Which sample method is best? Give a reason for your answer.
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The stratified sample is best, because it ensures that different groups (such
as gender or age) are fairly represented, which makes the results more
reliable when testing predictions that involve comparing groups.
1 e) Carry out a small trial of your investigation. Can you think of ways to
improve your investigation?
(Example trial) – Ask 10 classmates to estimate how long one minute is without a
stopwatch. Most guesses were between 40 seconds and 1 minute 20 seconds.
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Improvements: Use a bigger sample, test more than one type of estimation
(e.g., both time and length), and record results more carefully using
consistent instructions.
1 f) Use the results of your trial to make a generalisation about learners’
ability to estimate.
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Learners in my school tend to underestimate one minute of time.
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Learners are fairly good at estimating short lengths but less accurate with
angles.
a) Write some questions you could ask about the structure of the school day.
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Are lessons too long or too short?
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Do learners think there are too many lessons in one day?
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Should school start earlier or later?
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Are the breaks long enough?
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Would learners prefer a longer lunch break instead of more short breaks?
b) Write some predictions you can test.
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Learners would prefer shorter lessons.
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Learners want fewer lessons in a day.
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Most learners would prefer school to start later and finish later.
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Learners think the lunch break is too short.
c) Describe some different ways of choosing a sample to test one or more of
your predictions.
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Simple random sample: Choose learners at random from the whole school
list.
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Stratified sample: Divide the learners into groups (e.g., lower school,
middle school, upper school) and select proportionally from each.
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Systematic sample: Pick every 5th learner from the register.
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Convenience sample: Ask learners from your own class only.
d) Which sample method is best? Give a reason for your answer.
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The stratified sample is best because it ensures learners from all age groups
and year levels are included. This makes the results more representative of
the whole school.
e) Carry out a small trial of your investigation. Can you think of ways to
improve your investigation?
(Example trial) – I asked 8 classmates if they wanted the school to start later. Six
said yes, two said no.
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Improvements: Use a bigger and more varied sample (not just my class), ask
more than one question about the school day, and use anonymous
questionnaires to make answers more honest.
f) Use the results of your trial to make a generalisation.
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From my small trial, most learners prefer the school to start later.
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This suggests that if I tested the whole school, many learners would support
a later start time.
a) Questions you could ask about news articles
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Do online news articles use shorter sentences than newspaper articles?
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Are headlines longer in newspapers or online articles?
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Do sports articles use simpler vocabulary than political articles?
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Are online articles shorter in length than printed ones?
b) Predictions you can test
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Online articles have shorter sentences than newspaper articles.
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Newspaper headlines are longer than online headlines.
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Sports articles use fewer difficult words than political articles.
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Online articles are shorter overall than newspaper articles.
c) Different ways of choosing a sample
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Random sampling: Pick articles randomly from a list of newspapers and
news websites.
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Systematic sampling: Choose every 5th article from the homepage of a
news site or from a printed newspaper.
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Stratified sampling: Split articles into categories (e.g., sports, politics,
lifestyle) and pick a few from each group to make it fair.
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Convenience sampling: Use whichever articles are easiest to access (e.g.,
today’s top headlines).
d) Which sampling method is best? Why?
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Stratified sampling is best because it makes sure all types of articles are
included (e.g., politics, sports, lifestyle). This avoids bias that could happen
if you only pick from one category.
e) Small trial of your sampling method
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I chose 6 articles (2 sports, 2 politics, 2 lifestyle).
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I counted the average sentence length in each.
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Sports: 10 words per sentence
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Politics: 18 words per sentence
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Lifestyle: 12 words per sentence
Result: Political articles tend to have longer sentences.
Ways to improve:
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Use a bigger sample size (e.g., 20+ articles).
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Compare multiple news sources instead of just one.
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Look at vocabulary difficulty using a readability tool.
f) Generalisation based on trial results
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Political articles usually have longer, more complex sentences than sports or
lifestyle articles.
Biased Sample
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A biased sample is when the group you choose for your investigation does not
fairly represent the whole population.
This usually happens because:
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Some groups are left out.
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Some groups are chosen more often than others.
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You only ask people who are easy to reach or who agree with you.
Example of a biased sample:
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You want to know what all learners in your school think about lunch.
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But you only ask your friends in your own class.
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This is biased because it doesn’t include learners from other classes or year
groups.
Why it’s a problem:
A biased sample gives unfair or misleading results, because it doesn’t show what
the whole group really thinks.
a) The survey is biased because it only asks people who shop at the supermarket in
the morning on weekdays. This leaves out many people, such as those who are at
work, at school, or busy at that time. It may also include people who don’t use the
library and don’t care about it.
b) To improve the investigation, the survey should be done in different places (e.g.
the town centre, library, bus stop) and at different times (mornings, afternoons,
evenings, weekdays and weekends). This way, you get opinions from a wider range
of people.