Data Analysis and Modeling Distributions

What do we need to include in our graphs?

1. title

2. labeled axes

3. consistent scale

graphs MUST stand alone (they can be explained without background knowledge)

What are the three types of distribution shape?

1. roughly/fairly symmetrical

2. skewed to the right

3. skewed to the left

distribution with ONE bump

unimodal

distribution with TWO bumps

bimodal

distribution with THREE bumps

trimodal

uniform distribution

where the frequency for all values is the same (aka approximately symmetric)

what are the three measures of center (averages)?

1. mean

2. median

3. mode

mode

the number that occurs the most

Ex. 4455558888888899

the mode is 8

median

value where 50% of the values are above it and 50% are below it

Ex. 55688 → the median is 6

Ex. 55567888 → add up the two middle numbers together and divide by two (get the average) to get the median → (6+7)/2 = 13/2 = median

mean

all the numbers added up divided by the total number of trials/categories there are

expressed as x̄ (x-bar)

what is the distribution of a variable?

the values taken by a variable and how many times those values occur

what do we need to describe the distribution of a variable?

1. context

   1. variable name and units

2. complete sentences

   1. NO BULLETED SENTENCES

3. SOCS

   1. shape

   2. outliers

   3. center

   4. spread

Dot plot

Stem plot

organize the data from least to greatest

ALWAYS CREATE A KEY (ex. 6|9 = 69,000 units, 7|1 = 71 apples)

ALWAYS do from least to greatest

you can also split between the upper half of a ten and the lower half

• Ex. 1 | 589

• 1 | 014

Boxplots

use the calculator to find the Min, Q₁, Median, Q₃, and the max by entering all the values into one column and using one variable statistics

statistical advantage

using a random process to select a sample and generalize

what do statistically significant results allow us to see?

a cause and effect relationship between the explanatory and response variables. this is only possible if we have a well designed experiment that contains Randomization, Replication, and Control

Bar graphs

we use proportions (decimals/fractions)

contains the bar graph, segment graph, and mosaic graph

two way table

table of counts that summarizes data on the relationship of two categorical variables

marginal totals

the sums of rows and the sums of columns for two way tables

joint relative frequency

gives the proportion of individuals that have a specific value for one categorical value and another

• answers questions involving both variables

• cell total/grand total

conditional relative frequency

proportion of indivs that have a specific value for one categorical variable among indivs who share the same value of another categorical variable

mosaic plot

what measure of center do you use when the shape of the distribution is skewed to the left or right? why?

use the median because it is resistant to extreme values

what measure of center do you use when the shape of the distribution is symmetrical?

the mean

what happens to the mean when the shape of the distribution is skewed to the left?

the mean becomes smaller

what happens to the mean when the shape of the distribution is skewed to the right?

the mean gets bigger

what happens when the shape of the distribution is symmetrical?

the mean equals the median

what type of spread do we use when the shape of the distribution is skewed to the left or right?

the IQR (interquartile range)

IQR

interquartile range, measures the spread of the middle ½ of data (Q₃ - Q₁)

what type of spread do we use if the shape of the distribution is roughly symmetrical?

standard deviation (mean is always accompanied with standard deviation)

standard deviation

quantifies the average distance from the mean (