Math 3020 lesson 3

descriptive statistics

numerical and graphical methods

Exploratory Data Analysis or descriptive statistics consists of

• Organizing and Summarizing Raw Data

• Discovering Features/Patterns and Deviations from those Features/Patterns

• Interpreting findings IN CONTEXT

Exploratory Data Analysis or descriptive statistics are useful for

• Describing Distributions

• Investigating Relationships

• Checking Data for Errors

• Checking Assumptions for more complex analyses

Distribution of a variable

• What values does the variable take?

• How often does the variable take those values?

Measures of center

mean and median

measures of variance

standard deviation, variance, range, and IQR

sample mean

population mean

Z-score

z-score definition

The z-score for a given observation represents how far that observation is from the mean in standard deviations. The sign of the -score indicates the direction (above or below the mean).

Measures of position

• Z-Scores

• Percentiles

• Quartiles

IQR

Q3 - Q1

Histogram

Graphical displays

• Stem-and-Leaf [R: stem]

• Histogram [R: hist]

• Boxplot [R: boxplot]

Boxplot

Stem and leaf plot

Fences

Degrees of freedom

n - 1

Standardization

the process of converting different variables to a common scale. It transforms raw data into z-scores by centering the mean at 0 and scaling the standard deviation to 1. This allows for the fair comparison of variables measured in different units or ranges. [1, 2, 3, 4, 5]

Five-Number Summary

• The minimum

• Q1 First quartile 25th Percentile

• Q2 Median or Second quartile 50th Percentile

• Q3 Third quartile 75th Percentile

• The maximum.

histogram modality