Discrete data
Continuous data
What is the difference between discrete and continuous data?
Discrete data may take on exact values, while continuous data lies in a range.
Types of sampling
- Simple
- Convenience
- Systematic
- Quota
- Stratified
Simple sampling
- Achieving randomness by a simple, completely random process.
- You choose items out of a hat or you use a random number generator to pick items from a list.
Convenience sampling
- Choosing a sample based on how easy it is to find the data.
- You ask the first twenty people who walk past you to answer your survey.
Systematic sampling
- If data is listed, selecting a random starting point and then choosing the rest of the sample at a consistent interval in the list.
- You roll a die and get a 6, so you start with the 6th item and then choose every 10th item in the list after that.
Quota sampling
- Choosing a sample that is only comprised of members of the population that fit certain characteristics.
- You want a sample of 50, but they must all be ladies between the ages of 16 and 25. The selection is not random, a convenience method can be used.
Stratified sampling
- Choosing a random sample in a way that the proportion of certain characteristics matches the proportion of those characteristics in the population.
- The population is 45% male and 55% female, so you make a random sample of 100 people that has 45 men and 55 women in it.
Nathanael decides to change his sampling strategy. He is now choosing randomly ten percent of the students from each class.
State the type of sampling Nathanael is using now.
- Stratified
- Because Nathanael is constructing his random sample in proportion to the size of each class, he is using stratified sampling.
A discrete numerical variable takes an ___
Exact number value
The higher the standard deviation or variance, the more ___
Spread out the data is
The maths students in a school count their money and calculate the mean to be μ=€15. Everyone in the class agrees to donate €5 to a local charity.
Find the mean amount of money the students have now.
μ=€10
Since every student is donating €5, the money each one has is decreased by 5. Since they have subtracted 5 from all of the data, the mean will also decrease by 5.
Equations used to find out if something is an outlier
If it falls outside of the range:
Q1 - 1.5 x IQR
or
Q3 + 1.5 x IQR
Diagram showing Q1 and Q3 on a bell curve
What do different r values mean?
0 -> 0.5 or 0 -> -0.5 = no correlation
- 5 -> 0.75 or -0.5 -> -0.75 = weak correlation
- 75 -> 1 or -0.75 -> -1 = strong correlation
If a data set gets multiplied by 5, what happens to the mean, standard deviation, and variance?
Mean: gets multiplied by 5
Standard deviation: gets multiplied by 5
Variance: new standard deviation squared
What happens to the mean and standard deviation if you add 5 to a data set?
Mean: increses by 5
Standard deviation: doesn’t change (spread is the same)
Normal distribution curve with IQRs shown
