Quantitative Variables

3 main things we want to measure about Quantitative variables:

“Can Spiders Spit“

3 main things we want to measure about Quantitative variables:

“Can Spiders Spit“

center of data, spread of data, & shape of data

Ways of measuring the center of a data set:

Mean and Median

Mean/Average (Symbol: x̄ OR μ)

add the #’s together & divide by the amount of data points

• Sample: x̄

• Population: μ

This symbol __ is used when talking of population mean/average

μ

This symbol __ is used when talking of sample mean/average

x̄

Median (Symbol: M)

organize the #’s into ascending order & find middle #. Has 2 special cases:

1. If we have an odd # of data pts then middle # is median

2. If we have an even # of data pts then median is the average of the 2 middle numbers

IS RESISTANT

Median will always cut our data set in ____

half

Ex) What is the mean & median of this sample.

{ 42, 77, 49, 90, 67 }

Mean (x̄) = (42+77+49+90+67)/5 = 325/5 = 65

Median: 42, 49, 67, 77, 90 —> 67

Statistical Measure

is said to be resistant if it not greatly impacted by the presence of extreme values

• mean is NOT a resistant measure of center

• median is IS a resistant measure of center

The 5 Number Summary includes:

• Minimum

• Q1 (median of ALL numbers less than true median)

• Q2/Median/M

• Q3 (median of ALL numbers greater than true median)

• Maximum

3 ways of Measure of Spread

Range, Standard Deviation, Interquartile Range (IQR)

Range

tells how spread out the data is from lowest to highest value

Formula: Maximum - Minimum

IS NOT resistant measure of variability

Standard Deviation/SD

measures how spread out the data is from the average

Population: σ (IS ALWAYS less than the sample)

Sample: s

IS NOT resistant measure of variability since based on mean

Interquartile Range/ IQR

Measures how spread out the middle 50% of data is

Formula: Q3 - Q1

IS A RESISTANT measure of variability