AP Stats Unit 1 Notes

Individuals

people, animals, or objects of a data set that is the focus; who/what is the data focused on?

2 main types of variables and their definitions

Categorical: values that are category names or labels

Quantitative: values that use numerical values for a measured or counted quantity

How do we represent categorical data in a table form?

Frequency or Relative Frequency tables

Frequency and Relative Frequency tables/graphs

Frequency: shows number of cases in each category

Relative Frequency: gives proportion of percentage of cases in each category

Bar Chart

Used for graphing categorical data, uses evenly spaced apart bars with height displaying frequency amount

Pie Chart

Used for graphing categorical data, uses sections of a circle to show amount, requires a legend to connect categories and pieces

Almost 3 times the amount of people chose A as B means…

A = 3B,

Discrete variables:

A quantitative variable that can only take on whole, countable numbers for values (no decimals, gaps)

Continuous variables

A quantitative variable whose values are infinite, decimals and whole numbers (no gaps)

Dotplot:

A graph that displays a quantitative variable, height of dots displays frequency (no dots = 0, 1 dot = 1)

Advantages(same as stem and leaf): shows every individual value, Easy to see shape of distribution

Disadvantage: Can take a long time for large data set

Stem and Leaf plot:

(vertical dot plot in a way), a graph that displays a quantitative variable; numbers on left are tens place and numbers on right are the ones place (44, 46, 47, 49)(key needed to show this); tens place can be split up if need be (must be consistent)

Advantages (same as dot plot): shows every individual value, easy to see shape of distribution

Disadvantages (same as dot plot): hard to make for large data sets

Histograms

(bar chart for quantitative variable), a type of graph for displaying the frequency of a quantitative variable, horizontal distance of bars represents range of values, functions like a bar chart but bars are right next to each other

Advantages: easiest for large data sets, easiest for showing shape of distribution

Disadvantages: doesn’t show every individual value of set

What is the acronym used for describing distributions? And what does each of its letters stand for?

SCOV

Shape- how does it look?

Center- what values happen most?

Outliers- what points are farthest?

Variability- how closely packed or far apart are values?

Shape- Symmetric

One peak in the middle and values on left and right are roughly equal, like a parabola

Shape- Skewed Left

When data is more packed on the upper side of the data set, tail is on the left, hump is on the right

Shape- Skewed Right

When data is more packed on the lower side of the data set, tail is on the right, hump is on the left

Shape- unimodal

When a graph has one peak of values

Shape- bimodal

When a graph has two peaks of values

Shape- Uniform

When a graphs values have roughly equal frequencies

Center- Mean

Mean: the average, found by sum of all values and dividing by n (number of values), heavily affected by outliers and skewness (non-resistant to them), good for symmetric distribution

Center- Median

Median: the middle number, if n= even, the average of the values of ((n/2)’th number and (n/2 + 1)’th number) = , if n= odd, do n/2 and round up = median’th number, resistent to skewness and outliers- perfect for the

Variability- standard deviation

measures the average distance from the mean, (sd)² is variance; “The center typically varies by SD from the mean of (x)

Q1

1st quartile, the median of the values before median of the data set

Q3

3rd quartile, the median of the values after the median of the data set

Variability: IQR

Q3 - Q1, the length of the box in a box plot, higher IQR = Bigger box = more variance

5 number sum

Min, Q1, Median, Q3, Max

1.5 x IQR Method (+ SD version)

Low outliers: x < Q1 - 1.5(IQR)

Low outliers (SD): x < Mean - 2(SD)

High outliers: x > Q3 + 1.5(IQR)

High outliers (SD): x > Mean + 2(SD)

Boxplot

uses 5-number sum, a type of graph used for quantitative variables, box is IQR, bigger box = higher variability = larger IQR