Unit 1: One Variable Statistics

Categorical Variable

Measures characteristics that are sorted into categories. 

• Gender, color, or brand names

Nominal variable

Unordered Categories

• Blonde, brown, black

• USA, Canada, Japan

Ordinal Variable

Ordered Categories

• Dissatisfied, Neutral, Satisfied.

• Elementary School, Middle School, High School

Binary

Two Specific Categories

• Pass, Fail

• Yes, No

Describing a Distribution

CSOCS

1. Context - What the data represents

2. Spread - Give the least and highest value in the data set

• Range = Maximum - Minimum

3. Outliers - are there any values that stand out as unusual

• 2 standard deviations away or 1.5 × 1QR

4. Shape - does the graph symmetry or is it skewed

Shape of a Distribution

Five-Number Summary

1. Minimum: The lowest value in the dataset

2. First Quartile: The 25th percentile, or median of the lower half of the data.

3. Median: The middle value of the dataset.

4. Third Quartile: The 75th percentile, or median of the upper half of the data.

5. Maximum: The highest value in the dataset

The Mean (x)

The average of the data

• (sum of values) / (amount of numbers)

Median

The middle value of a data set, arranged from highest to lowest

→If the number of observations is odd, the Median is the center of the list (n+1)/2

→If the number of observations even, the center position can be found at (n/2)

Box Plots

Its a graph of the five-number summary

Interquartile Range (IQR)

Represents the 50% of a data set

• IQR = Q₃ - Q₂

Outliers

1.5 × 1QR

• Q₁ - 1.5 × 1QR → anything below this boundary is an outlier

• Q₂ + 1.5 × 1QR →anything above this boundary is an outlier

Standard Deviation (S or Sx)

How far dat is away from the mean

Normal Distribution

• Within one SD - 68%

• Within two SD - 95%

• Within three SD - 99.7%