stats unit 1 quiz 1

Statistics

The science of data

Data analysis

The process of organizing, displaying, summarizing, and asking questions about data

Individuals

Objects described by a set of data

Variable

Any characteristic of an individual

Categorical variable

Places an individual into one of several groups or categories

Quantitative variable

Numerical values and can be used to find an average

Distribution

What value a variable takes and how often it takes them

Process from data analysis to inference

Collect data from a representative sample, perform data analysis while keeping probability in mind, make an inference about the population

Frequency table

Displays the counts (frequencies) of items in each category

Relative frequency table

Displays the percent of items in each category

Why does the total in a frequency table add up to 99.9% and not 100%

Roundoff error

Roundoff error

When rounding causes slight differences in data, doesn’t mean there are mistakes it’s just effect of rounding

2 ways to display categorical data

Bar graph or Pie chart

Pie Chart

Displays data to emphasize each category’s relation to the whole

Bar graph

Represents each category as a bar, bar height shows the category counts or percents

What’s one of the most important things when making a bar graph?

Make the bars equally wide

2 things to watch out when making a bar graph

Making a pictograph and making sure the scales start from 0

Two-way table

Describes 2 categorical variables organizing counts according to a row variable and a column variable

Marginal distribution (one of the categorical variables)

Distribution of values of that variable among all individuals described by the table

What’s more informative than counts when comparing groups of different sizes?

Percents

How to examine marginal distribution?

1. calculate marginal distribution in percents of the row and column totals using the data

2. Make graph to display marginal distribution

Conditional distribution

Describes the values of that variable among individuals who have a specific value of another variable

How to examine or compare conditional distributions?

1. Select rows or columns of interest

2. Use data in table to calculate the conditional distribution in percents of the rows or columns

3. Make a graph to display the conditional distribution by using a side by side or segmented bar graph

Association

If knowing the value of one variable helps predict the value of the other

Dotplots

Each data value is shown as a dot above its location on a number line

How to examine distribution of a quantitative variable?

Look for overall pattern and striking departures from that pattern and describe the overall pattern using SOCS

SOCS

shape, outliers, center, spread

Outliers

Individual values that fall outside the overall pattern

Center

The middle value (midpoint/median)

Shape

Clustering of data around a certain data point

Spread

How the data varies

What do you focus on what describing a distributions shape

Symmetry or clear slowness

Symmetric

Left and right sides are approximately mirror images of each other

Skewed to the right

Right side is much longer than left

skewed to the left

If the left side is much longer than the right

Stem plots (stem and leaf plots)

Gives picture of distribution while including actual numerical values

Histogram