6.1 - Intro to Stats

Fill in the Blank

Warm-up #1: Find the mean of {13, 9, 7, 12, 15, 19, 2}

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Warm-up #2: Find the mode of {4, 1, 5, 5, 7}

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Warm-up #3: Find the median of {9, 2, 3, 8, 5, 7}

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As you read through the slides, fill in your 6.1 notes handout

6.1 Sampling Techniques

SL 4.1

I can classify
different sampling
techniques and
identify potential
biases.

Types of Data

Quantitative (Numerical) Data

Describes information that can be counted or measured

Quantitative data can be discrete or
continuous

Discrete Data

Each data value is distinct from the others and there are no
“gaps” between data values. Examples include:

● The number of pets in your house
● The result of rolling a number cube
● A personʼs shoe size

Continuous Data

Not restricted to certain fixed values, can occupy any value within
a continuous range. Its values are often expressed using fractions
or decimals. Examples:

● The mass of an object
● The time it takes you to get to school

Categorize

Options (4)

The number of computers you have owned

The number of laptop bags that you have

The length of a computer monitor

The weight of your computer

Example #1: Classify each as either discrete or continuous.

Discrete

Continuous

Categorical Data

Types of data which can be divided into groups. Examples
include:

● Race
● Sex
● Age Group
● Educational Level

Categorize

Options (6)

Type of Car

Breed of Dog

ZIP Code

Weekly wage

Plane fares

Petrol prices

Example #2: Classify the following data as quantitative or categorical

Categorical

Quantitative

Categorize

Options (5)

Shoe size

Time taken to get home from school

The number of relatives you have

The lengths of the rooms in your home

The number of computers that your classmates have owned

Example #3: Classify the following numerical data as continuous or discrete

Continuous

Discrete

Populations & Samples

Population vs. Sample

Population: Every member of the
group that you want to find out
about

Sample: subset of the population
that will give you information about
the population as a whole

Selecting an Appropriate Sample

Lots of methods for sampling exist. When selecting a sample, you should always try to select a method that gives you a sample that is the best approximation for the population as a whole.

Reliability of Data

●

Data is reliable if the process of data collection can be repeated to obtain
similar findings
○

Two factors which can cause unreliable data are:
■

Missing Data: lack of responses or it not being possible to record
the data

■

Errors in handling data: for instance, the data is entered
incorrectly

●

Data is sufficient if there is enough data to support your conclusions

Sampling Bias

This occurs when you take a sample from a population and some members of the
population are not as likely to be chosen as others.

When sampling bias occurs, the sample might not give an accurate representation of the population, so inappropriate conclusions may be drawn.

Sampling Methods

● Convenience Sampling
● Simple Random Sampling
● Systematic Sampling
● Stratified Sampling
● Quota Sampling

Convenience Sampling

Easiest method for obtaining a sample: select the members of the
population who are most easily accessible or readily available.

Example: to find the mean length of time spent doing homework, you survey the students who are in the same class as you

Simple Random Sampling

Each member of the population has an equal chance of being
selected. A sample is chosen by drawing names for a hat, or
assigning numbers to the population and using a random number
generator.

Example: to find the mean length of time spent doing homework, you might put the names of every student into a
hat and draw out the names of 100 students to form a
sample

Systematic Sampling

List the members of the population and select a sample
according to a random starting point and a fixed interval.

Example: if you wanted to create a systematic sample of 100
students at a school with an enrolled population of 1000, you
would choose every tenth person from a list of all students

Stratified Sampling

This involves dividing the population into smaller groups known
as strata. The strata are formed based on membersʼ shared
characteristics. You then choose a sample from each stratum, and
put them together to form your sample.

Example: in a high school of 1000 students, you could choose 25
students from each grade-level to form a sample of 100 students

Quota Sampling

Like stratified sampling, this involves taking a sample size from
each stratum that is in proportion to the size of the stratum.

Example: in a high school of 1000 students where 60% of the
students are female and 40% are male, your sample should also
be 60% female and 40% male

Drag and Drop

A sample of 100 students is taken by organizing the students’ names by classification (freshman, sophomore, junior, senior) and then selecting 25 students from each classification.​ ​

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A random name is chosen. Starting with that student, every 50th student is chosen until 80 students are included in the sample.​

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A completely random method is used to select 100 students. Each student has the same probability of being chosen at any stage of the sampling process.​

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The population of the school consists of 70% mathematicians and 30% non-mathematicians. Seven mathematicians and three non-mathematicians are chosen from each grade.​

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Drag these tiles and drop them in the correct blank above

Stratified Random Sample

Systematic Random Sample

Simple Random Sample

Convenient Sample

Quota Sample

Assignment:
6.1 on Canvas