Week 1

Question 1

What is statistics?

Answer 1

Statistics is the science of collecting, organizing, interpreting and learning from data.

Question 2

What are the three aspects of statistics?

Answer 2

Design: Planning how to obtain data to answer the question of interest.

Description: Summarizing the data that are obtained.

Inference: Using sample data to learn about the population.

Question 3

Population

Answer 3

The population is a collection of units of interest, such as all adults in the United States, alligators in the everglades, iPads from a factory.

Question 4

Subject

Answer 4

Subjects are the individual units of a population, such as an adult, an alligator, an iPad.

Question 5

Sample

Answer 5

A sample is a subset of the units of a population.

Question 6

What makes a good sample?

Answer 6

A sample should be representative of the population. This can be obtained by selecting sample subjects randomly.

Question 7

Where do statistical methods come in?

Answer 7

1. Use DESIGN to obtain an appropriate sample from the population. 2. DESCRIBE the sample data with graphical and numerical summaries. 3. Perform STATISTICAL INFERENCE.

Question 8

Statistical Inference

Answer 8

The procedure of using a sample to learn about a population is called statistical inference.

Question 9

Parameter

Answer 9

A parameter is a number that describes a population. It is usually unknown.

Question 10

Statistic

Answer 10

A statistic is a number that describes a sample. It can be computer from data, therefore, it is known.

Question 11

We use a ____ to estimate a ______.

Answer 11

We use a sample statistic to estimate a population parameter.

Question 12

Variable

Answer 12

A variable is any characteristic of a subject in a population.

Question 13

Categorical (Qualitative) Variable

Answer 13

Classifies subjects as belonging to a certain group/category. For example, gender, race, political party, issue positions, etc.

Question 14

Quantitative Variable

Answer 14

Takes on numerical values that represent different magnitudes. For example, height, weight, age, IQ, income, temperature, etc.

Question 15

A quantitative variable can either be _____ or _____.

Answer 15

A quantitative variable can either be discrete or continuous.

Question 16

Discrete

Answer 16

The possible values of a discrete quantitative variable form a set of separate numbers that can be listed or counted. For example, age in years, number of tattoos, etc.

Question 17

Continuous

Answer 17

The possible values of a continuous quantitative variable form an interval. That is, there is an infinite continuum of possible values. For example, height, weight, income, time, etc.

Question 18

Graphical Summaries for Categorical Variables

Answer 18

Graphical summaries of categorical variables help us visualize the distribution of the data among the separate categories. Before constructing the graphical summary, we first organize the categorical data into a frequency table.

Question 19

Frequency Table

Answer 19

A frequency table is a listing of possible values for a variable, together with the number of observations for each value. (Note that we can also construct frequency tables for quantitative variables.)

Question 20

Proportion

Answer 20

A proportion of observations that fall in a certain category is the count of observations in that category divided by the total number of observations.

Question 21

Two Graphical Summaries for Categorical Variables

Answer 21

Pie Charts and Bar Graphs

Question 22

Pie Chart

Answer 22

A circle is drawn with a “slice of pie” representing each category’s % of observations

Question 23

Bar Graph

Answer 23

A bar is drawn for each category with the bar’s height representing the % or count of observations

Question 24

Pie Charts vs. Bar Graphs

Answer 24

1. Pie charts emphasize a category’s relation to the whole, but make it difficult to compare categories to each other!
2. Bar graphs compare the sizes of each group of a categorical variable (not in relation to the whole).
3. Bar graphs are easier to read and more flexible than pie charts.

Question 25

Distribution

Answer 25

A distribution of data shows the values a variable takes and how often they occur.

Question 26

Features of distributions visualized by graphical summaries:

Answer 26

1. Overall Pattern (bell-shaped, skewed, bimodal, etc.)
2. Center and spread
3. Outliers (unusually large or small observations)

Question 27

Two graphical summaries for quantitative variables:

Answer 27

Stem-and-leaf Plots and Histograms

Question 28

Histogram

Answer 28

Histograms break up the range of values of a variable into classes and display the count (or percent) of the observations that fall into each class

Question 29

Steps to Construct a Histogram

Answer 29

1. Divide the range of data into intervals of equal width. (We want to choose a width that gives us a good picture of the distribution of the data. The number of intervals should not be too many or too few.)
2. Count the number of observations that fall into each interval.
3. On the horizontal axis, mark the scale of the variable. On the vertical axis, mark the scale for counts or percents.
4. Above each interval, draw a bar whose height is either the corresponding count or percent for that interval.

Question 30

Common Distribution Shapes

Answer 30

symmetric (normal, unimodal, bell-shaped), e.g. IQ, height, weight; right-skewed, e.g. income; left-skewed, e.g. lifespan, product failure rate; bimodal, e.g., height of men AND women (two populations); uniform, e.g. commute time

Question 31

n

Answer 31

The number of observations in a sample

Question 32

Mean

Answer 32

(x bar) the average of all observations. sum the observations and divide by n.

Question 33

Median

Answer 33

(M) the middle number when measurements are ordered from smallest to largest (the 50th percentile; when n is odd, M = the middle value; when n is even, M = the average of the two middle values

Question 34

Which measure of center is resistant to outliers?

Answer 34

The median.

Question 35

Resistant

Answer 35

A numerical summary of the observations is resistant if extreme observations have little, if any, influence on its value. The mean is affected by outliers, while the median is resistant to the skewing affects of outliers.

Question 36

Mean vs. Median

Answer 36

In symmetric distributions, the mean and median are approximately equal. In right-skewed distributions, the mean is greater than the median. In left-skewed distributions the mean is less than the median.

Question 37

Measures of Spread

Answer 37

It’s important to look at measures of spread in addition to measures of center to get a better understanding of the data.

Question 38

What are three measures of spread?

Answer 38

Range, interquartile range and standard deviation.

Question 39

Range

Answer 39

The range is the difference between the largest and smallest observations. That is, the maximum value - the minimum value = the range. While the range is a simple measure of spread that is easy to calculate, it is only calculated using the most extreme values of a data set. Therefore, it can be misleading and is not resistant to outliers.

Question 40

Interquartile Range

Answer 40

The interquartile range is the difference between the first and third quartiles. That is, it captures the middle 50% of the data.

Question 41

Percentile

Answer 41

The pth percentile of a distribution is the value below which p% of the observations fall.

Question 42

Notes about IQR

Answer 42

1. The larger the IQR, the more spread out the data is.
2. IQR is resistant to outliers since it’s calculated using only the middle 50% of the data set (outliers tend to be outside this range).

Question 43

5-number summary

Answer 43

The 5-number summary is a brief numerical description of the center and spread of a distribution. It is the max, Q3, median, Q1, and min values. It can be displayed in R with summary() and fivenum()

Question 44

Detecting Potential Outliers

Answer 44

As a rule of thumb, an observation is marked as a potential outlier if it falls more than 1.5xIQR below Q1 or 1.5xIQR more than Q3.

Question 45

Box Plot

Answer 45

The box plot is a plot of the five number summary. Not only do box plots provide a picture of the center and spread of a distribution, they also give us an idea as to the shape or skew of the distribution.