Representing Data: Statistics for Uninvaritable data - A&A

Discrete Data

Specific to something, think as many details as possible

Continuous Data

Something that is not specific - think: Can change, and the data will fluctuate

Population

Population is a whole- Think: City, class

Sample

A section of the said population → Think: Funny people in a class or red buildings in a city

Convenience

Most accessible members of a population

Simple Random

Any member of a population has an equal chance of being chosen (the random element)

Systematic

Set intervals from points on a list (think: every 10th person)

Stratified

Deciding a population into small groups based on characteristics (strata) - random sample from each strata

Quota

Very similar to stratified→ BUT set sample size take from each strata

Bar chart

Used for discrete data

Histogram

Used for continuous data

Left skewed

Small → large

Normal Distributed

Small → Big → small

Right skewed

Big → Small

Mean

Sum of all data → all data added/by the amount of data points there are

Mode

Most commonly appearing value

Median

Middle of the data - if their is no middle find the mean of the middle

Quartile range

Breaking down the data into 4 equal parts

Q1

25% of the data → Lower quartile

Q2

Or the ½ way point 50% of the data (Median).

Q3

Upper Quartile 75% of the data

Range

The distance between the smallest and largest values in a data set

Inter Quartile Range (IQR)

Q3-Q1

Box plots

Outlier

A very large or small number that will potentially disrupt the data - 1.5 x IQR (above Q3 or bellow Q1)

Cumulative frequency

A running total of how many values are up to a certain point.

Percentiles

A number that tells you what percent of data is below it.

Variance

The average of the squared differences from the mean. It measures how spread out the data is.

Standard Deviation

The square root of the variance. It shows the average distance each value is from the mean.

Effects of Adding or Multiplying to All Values in a Data Set

Adding a number (+a):

• Mean, Median, Mode: +a

• Standard Deviation & Variance: No change

Multiplying by a number (×a):

• Mean, Median, Mode: ×a

• Standard Deviation: ×a

• Variance: ×a²