Definitions
Population the entire group from which statistical data is drawn (and which the statistics obtained represent).
Sample the observations actually selected from the population for a statistical test.
Random Sample a sample that is selected from the population with no bias or criteria; the observations are made at random.
Discrete finite or countable number of possible values (e.g. money, number of people)
Continuous infinite amount of increments (e.g. time, weight)
Note: continuous data can be presented as discrete data, e.g. if you round time to the nearest minute or weight to the nearest kilogram.
7.1. Descriptive statistics
For 1 variable data with frequency use 1-Var Stats on GDC.
Mean the average value
![mean](https://revisiontown.com/wp-content/uploads/2023/03/Screenshot-2023-03-26-at-5.50.23-PM.png)
Mode the value that occurs most often
Median when the data set is ordered low to high and the number of data points is:
- odd, then the median is the middle value;
- even, then the median is the average of the two middle values.
Range largest x-value−smallest x-value
Variance
![variance](https://revisiontown.com/wp-content/uploads/2023/03/Screenshot-2023-03-26-at-5.55.21-PM.png)
Standard deviation
![standard deviation](https://revisiontown.com/wp-content/uploads/2023/03/Screenshot-2023-03-26-at-5.57.48-PM.png)
Grouped data data presented as an interval. Use the midpoint as the x-value in all calculations.
Q1 first quartile = 25th percentile
Q2 median = 50th percentile
Q3 third quartile = 75th percentile
Q3 – Q1 interquartile range (IQR) = middle 50 percent
7.3. Statistical graphs
Frequency the number of times an event occurs in an experiment
Cumulative frequency the sum of the frequency for a particular class and the frequencies for all the classes below it
Histogram
![histogram](https://revisiontown.com/wp-content/uploads/2023/03/Screenshot-2023-03-26-at-6.05.03-PM.png)
Cumulative frequency
![Cumulative frequency](https://revisiontown.com/wp-content/uploads/2023/03/Screenshot-2023-03-26-at-6.05.11-PM.png)
![Box and whisker plot](https://revisiontown.com/wp-content/uploads/2023/03/Screenshot-2023-03-26-at-6.05.21-PM.png)
7.4. Bivariate statistics
For analysis of data with two variables.
On GDC use LinReg(ax+b).
Scatter diagrams
![Perfect positive](https://revisiontown.com/wp-content/uploads/2023/03/Screenshot-2023-03-26-at-6.14.12-PM.png)
![No correlation](https://revisiontown.com/wp-content/uploads/2023/03/Screenshot-2023-03-26-at-6.14.21-PM.png)
![Weak negative](https://revisiontown.com/wp-content/uploads/2023/03/Screenshot-2023-03-26-at-6.14.29-PM.png)
Regression Line (r = ax + b) Can be used to interpolate unknown data.
Interpretation of r -values
The correlation between the two sets of data. Can be positive or negative.
![Bivariate statistics](https://revisiontown.com/wp-content/uploads/2023/03/Screenshot-2023-03-26-at-6.25.31-PM.png)