Ch 1: Intro to Statistics and Data Analysis

What is statistics?

The main objective of statistics is to make an inference about a population based on the information given in a sample

Population

a set of units (people, days, etc.) that we are interested in studying

Sample

A subset selected from a population

Most common sampling method

simple random sample (SRS)

Branches of Stats

-Descriptive Stats

-Inferential Stats

Methods of Descriptive Stats

-graphical methods

-numerical methods

Two Types of Data

-quantitative (measure numerically)

-qualitative (think categories)

Quantitative Data Types

-discrete data (countable)

-continuous data

Graphs used for qualitative data

pie charts and bar charts

Stem-and-Leaf Plots

split digits to create a pattern we can see

Frequency Table

Relative Frequency Table

Frequency Histogram

Branches of Numerical Methods

-measures of central tendency

-measures of variability

Measures of Central Tendency

-sample mean

-sample median

-sample mode

Measures of Variability

-range

-interquaratile range (IQR)

-sample variance (S²)

-standard deviation (S)

sample size notation

n (can be m, n1, n2, etc)

value in sample

x

first value in sample

x₁

second value in sample

x₂

n^th value in sample

x_n

sample representation

x₁, x₂, …, x_n

Sample Mean

Sample v. Population Mean

Sample Median

*Sample MUST be in order

-the middle

Sample Mode

-the value(s) that appears the most

Sample Range

largest sample value - smallest sample value

Sample Variance (S²)

Step 1: Find x̄

Step 2: Variance Formula

Sample Standard Deviation (S)

Step 1: Find Sample Variance (S²)

Step 2: Square root S²

Box Plots

IQR Formula

Q3 - Q1

1.5 x IQR Rule

finds the inner and outer fence to find outliers

partially suspected outlier

*

highly suspected outlier

o

How does changing the min/max affect the box plot?

IQR is not affected, but there may be outliers

Finding min/max for box plot

use smallest/largest value WITHIN the inner fence

Based on a graph, how can you tell if the mean or median is larger?

-if skewed left, the mean is bigger because most of the values are on the higher end, making the average larger

-if skewed right, the median is bigger

-if symmetric, both are the equal

Empirical Rule

-only works for mound-shaped graphs

-approximate rule to interpret standard deviation

First Standard Deviation (Empirical)

~68% of data

Second Standard Deviation (Empirical)

~95% of data

Third Standard Deviation (Empirical)

~99.7%