AP Statistics Ch 1 Role of Statistics and the Data Analysis Process

The 6 Data Analysis Process Steps

1. Understanding the nature of the problem: knowing goals and what we hope to answer
2. Deciding what to measure and how to measure it: carefully define variables
3. Data collection: existing/new data
4. Data summarization and preliminary analysis: summarize graphically and numerically
5. Formal data analysis: select and apply statistical methods
6. Interpretation of results: What can we learn? What conclusion can we draw? How can results guide further research?

population

the entire collection of individuals or objects about which information is desired

census method

collecting data about the entire population

sample

subset of the population selected for study

variable

a characteristic whose value may change from one observation to another

data

a collection of observations on one or more variables

independent variable

variable whose variation DOES NOT depend on that of another

dependent

variable whose variation DOES depend on that of another

categorical data set

qualitative data

numerical data set

quantitative data (can be discrete or continuous)

discrete (numerical) variables

possible values of the variable correspond to isolated points on the number line; takes finite or countably infinite values. (EX: number of books, number rolled on a die)

continuous (numerical) variables

set of possible values forms an entire interval on the number line; cannot be accurately precise. (EX: height=1.722222... meters)

descriptive statistics

includes numerical, graphical, and tabular methods for organizing and summarizing data

inferential statistics

involves generalizing a sample to the population and assessing the reliability of such generalizations

univariate data

a data set consisting of observations on a single characteristic

bivariate data

data of two variables (EX: ice cream sales vs. temperature outside)

multivariate data

data of three or more variables; two or more dependent variables

frequency distribution for categorical data

a table that displays the possible categories along with the associated frequencies and/or relative frequencies

frequency

the number of times the category appears in the data set

relative frequency

frequency/number of observations in the data set
(shown as a percentage)

The proportion of the observations that belong to that category

relative frequency distribution

a frequency distribution that includes relative frequencies

bar chart

graph of frequency distribution of categorical data. Each category is a bar/rectangle, and the area of each bar is proportional to the corresponding frequency or relative frequency.

dotplot

a simple way to display numerical data when the data set is reasonably small. Each observation is represented by a dot above the location corresponding to its value on a horizontal measurement scale.