### 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

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

Standard deviation

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

Cumulative frequency

Box and whisker plot

## 7.4. Bivariate statistics

For analysis of data with two variables.

On GDC use LinReg(ax+b).

Scatter diagrams

Perfect positive
No correlation
Weak negative

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.

Correlation does not mean causation.