2-Summarizing data

Tables to organize qualitative data

frequency tables

contingency table

frequency table

organizes and displays frequencies for categories

contingency table

used to display the relationship between 2 categorical variables

Qualitative data organization methods

bar chart

mosiac plot

pie chart

mean

**average

sum of all numbers divided by the amount of numbers

sample mean

a statistic

population mean

a parameter

weighted mean

**weighted average

used when different values contribute unequally to overall total

ex: grades

weighted mean formula

( number * corresponding percent as decimal) + …..

total percents as decimals

Median

**in order from smallest to largest

odd numbered data sets: median is middle value

even numbered data sets: median is average of two middle values

finding median number position

(n+1)/2

Quartiles

• 0th percentile (Q0) - minimum

• 25th percentile (Q1)

• 50th percentile (Q2) - median

• 75th percentile (Q3)

• 100th percentile (Q4) - maximum

Finding Q1 and Q3

• order data from smallest to biggest

• find median

• Q1 is median of 1st half

• Q3 is median of 2nd half

Mode

number that occurs most frequently

** there can be multiple, one or none

Range

difference between max and min

(max)-(min)

**not resistant-may not accurately reflect overall variability in the dataset

Variance

measure of variability

-can be less intuitive to interpret, so standard deviation is better

simple variance

**statistic

sample variance=(data number- sample mean)² / sample size

Population variance

**parameter

population variance= (data value-population mean)² / population size

Standard deviation (s)

measures the spread of data

• always >=0

• larger #s=greater variability in data

• MOST APPROPRIATE FOR SYMMETRIC DISTRIBUTIONS

• not resistant to outliers: one extreme value can drastically increase (s)

Simple standard deviation

**statistic

=square root( (data value-sample mean)² / sample size )

Population standard deviation

**parameter

=square root( (data value-population mean)² / population size )

Interquartile Range (IQR)

measures spread of middle 50% of dataset

**distance from Q1 to Q3

IRQ=Q3-Q1

IQR and outliers

Upper whisker (upper cutoff/ upper fence) = Q3+(1.5*IQR)

Lower whisker (lower cutoff/ lower fence) = Q1-(1.5*IQR)

any data above upper and below lower are considered outliers.

Histogram

Box Plot

box plot- vertical 5 number summary

Distribution of graphs

1. shape: mode symmetry, skewness

2. center: center of mass or midpoint

3. spread: range of values taken by variables

4. unusual observations: outliers

shape based on mode

• 1 mode= unimodial

• 2 modes=bimodial

• 3 or more = multimodial

shape based on symmetry

symmetry: mirrored

skew: leaning to left or right

histograp to box plot