AP Statistics Notes:
Aug 7, 2021
Chp1:
Key Vocabulary:
Statistics: Science of data
Individuals: Sets of data contain information about individuals
Variable: Characteristics of the individuals measured
Categorical variable: Variables which can be used to place an individual into a category
Quantitative variable: when a variable is a numeric value which is used for finding averages.
Discrete Variable: variables which are countable/ finite
Continuous Variable: variables which are infinite (i.e - time)
*Distribution: A listing or function showing all possible values or intervals of the data (i.e - normal
distribution/ bell shaped curve)
Inference → 2 types: estimating parameters, hypothesis test
➢ Estimating parameters: making a prediction using data about another parameter
➢ Hypothesis test: Using sample data to answer research questions
Frequency table: Tables displaying the frequency of a particular statistic. Useful for finding patterns
Relative frequency table:the ratio (fraction or proportion) of the number of times a value of the data
occurs in the set of all outcomes to the total number of outcomes.
Bar graph: A graph which uses bars to represent information
Pie chart: Graph shaped like a circle used to represent data
* Marginal relative frequency:
https://www.onlinemath4all.com/how-to-calculate-marginal-relative-frequency.html
Joint relative frequency:
Banana
Mango
Men
14
9
Women
3
20
Bananas are popular among men hence the JRF or that statistic is 14/17.
Conditional relative frequency:
https://www.fusd1.org/cms/lib/AZ01001113/Centricity/Domain/870/Lesson%2011%20Blank%20No
tes%20and%20Homework.pdf
Segmented Bar Graph: used to compare two categories within a data set
Mosaic Plot: A mosaic plot is a graphical display that allows you to examine the relationship among two
or more categorical variables.
Association: shows correlation (or absence of it) between two variables
Mean: avg. found by adding all numbers and dividing by num of values
Median: the middle number in a sorted, ascending or descending, list of numbers
Range: The difference between the lowest and highest values.
Standard Deviation: The Standard Deviation is a measure of how spread out numbers are.
Quartiles: the values that divide a list of numbers into quarters:
Interquartile range (IQR): The range from Quartile 1 to Quartile 3
Five-number summary: The smallest number in the set, largest number, median, Q1, and Q3.
Link to finding these numbers:
https://www.statisticshowto.com/statistics-basics/how-to-find-a-five-number-summary-in-statistics/
Boxplot: a graph that gives you a good indication of how the values in the data are spread out
Individuals and Variables:
Data sets contain info abt individuals
Characteristics of individuals measured → variables
Types of Variables:
2 categories → categorical/ quantitative
Categorical: when variables are used to place an individual into a group/category
Quantitative: when a variable is a numeric value which is used for finding averages.
Displaying Categorical Data:
Frequency table → displays counts/ %s of individuals
Graphical displays > tables (easier to read and highlight important information of distribution)
Pie charts/ Bar graphs → used for displaying categorical data
Dot Plots/ Stemplots →
Pros:
➢ easiest to construct
➢ helpful for describing distributions
➢ Keeps data intact (i.e - individual data can be determined directly from plot)
➢ When comparing data, stemplots/ dot plots of the same scale can be constructed
➢ Plots always require a label for axes and a key
Cons:
➢ Difficult to construct with larger data sets
Histograms → displays frequency of values that fall within equal-width classes. Useful for large data sets
SOCV :
Used to analyze the shape of the data
Shape
Outliers
Center
Variability
Questions asked to analyze:
➢ Is it symmetric or skewed?
➢ Num of peaks?
➢ What is its center?
➢ How variable is the data?
➢ Are values bunched up at center or spread out?
➢ Any outliers?
➢ Any values skewed from the majority?
Exploratory Data Analysis (EDA):
Used to organize, examine, describe data:
➢
➢
➢
➢
➢
Examine each variable by itself
Plot data
Begin with a graph/graphs
Add numeric summaries
Use SOCV
Mean VS Median:
Mean isn’t always an accurate measure of the center of the data as extreme values can influence the mean.
The median is more accurate as it isn;t swayed by extreme values. If the data is more symmetrical the
mean and median should be close to each other. This is why it is important to analyze data before
calculating the center.
Measures of Variability and Boxplots:
Describe variability of a distribution → calculating range (maximum - minimum). Large values can cause
the measure to be inaccurate
Better way to calculate variability → Interquartile range (IQR)
Day 1 Notes:
Definitions
Sample: a subset of individuals in the population from which we collect data.
Convenience Sampling: Collecting data from individuals nearby. Often produces
unrepresentative data.
Simple random sampling A simple random sample (SRS) of size n is chosen in such a way that
every group of n individuals in the population has an equal chance to be selected as the sample.
Voluntary response sampling: Allows people to choose to be part of the sampling
Census: collects data from every individual in the population.
Population: in a statistical study is the entire group of individuals we want information about