Summer Assignment Key Terms

Question 1

What is Statistics?

Answer 1

Statistics is the art and science of collecting and analyzing data and making inferences from data.

Question 2

What are data?

Answer 2

Data are any collected information. Data can be numbers or words but with context like 10.5 pounds or brown eyes.

Question 3

Individuals are…

Answer 3

the objects described by a set of data. Individuals can be people, animals or things.

Question 4

Variable

Answer 4

any characteristic of an individual. A variable can take different values for different individuals. Variables can be categorical or quantitative.

Question 5

Categorical variable

Answer 5

Places an individual into one of several groups or categories.

Question 6

Quantitative variable

Answer 6

Takes on numerical values for which it makes sense to find an average. Not all numbers are quantitative data: SAT scores are quantitative, zip codes are categorical.

Question 7

Distribution

Answer 7

Distribution

Question 8

Frequency

Answer 8

The number of times a data value or range of values is observed

Question 9

Relative frequency

Answer 9

The percent of times a data value or range of values is observed

Question 10

What are the 4 parts of statistics in our book?

Answer 10

Data production; data analysis; probability; inference

Question 11

Data production

Answer 11

Taking a sample from a larger group and recording data or doing an experiment in order to record data.

Question 12

Data analysis

Answer 12

Making graphical and numerical summaries of the data

Question 13

Probability

Answer 13

Determine the chances an event will occur

Question 14

Inference

Answer 14

Drawing conclusions from the data analysis and probability calculations. In statistics we look at a sample and make conclusions about a population.

Question 15

Why take a sample instead of a census? A census gives the exact information about a population and a sample will always have some error.

Answer 15

Example: If I make a large pot of soup, I will taste a few spoonfuls (the sample) and then make a conclusion about the whole pot of soup (the population, all spoonfuls). We do not take a census to get accurate information about the population because that would be like consuming all the soup in order to determine how the whole pot of soup will taste. First, there would be no soup left. Second, it would take a very long time for one person to consume the entire pot of soup, and third a few spoonfuls does give accurate information about how the entire pot of soup tastes as long as we stir the soup thoroughly before each spoonful is taken (random sampling).
Likewise, if we wanted to know what % of Californians approve of splitting Ca into three states, we do not attempt to ask every single Ca resident (a census), we ask a random sample because it is doable and very accurate (not precise but as close to precise as we are willing to get based on time and cost).

Question 16

What is a sample?

Answer 16

A subset of individuals of a much larger group called the population

Question 17

What is a population?

Answer 17

All individuals in a group that you are interested in

Question 18

What is a census?

Answer 18

An attempt to get information from every individual in the population of interest

Question 19

Parameter

Answer 19

A numerical summary of a population like a mean (μ), standard deviation , median, …

Question 20

Statistic

Answer 20

A numerical summary of a sample like a mean, standard deviation, median, …
(remember this course is called “Statistics” not parameters)
Statistics come from Samples
Parameters come from Populations (census)

Question 21

Suppose we are interested in the mean wait time in the drive through at In-N-Out. You randomly choose cars throughout the day (or some time period) and calculate an average wait time of 7.1 minutes.What is the population?What is the sample? What is the parameter of interest? What is the statistic?

Answer 21

The population is all wait times for cars in that time period. The sample is the wait times that you observed/recorded. The parameter is the average(mean) of all the wait times for that time period. The statistic is mean of all the observed wait times in our sample.
We use the statistic as an estimate of the parameter. We would also calculate and add on error to our statistic knowing that it will not be exactly equal to the parameter.
You might ask “why don’t they just get the time for every car?”
See if you can come up with some reasons why a census does not make sense. And how would we design a sampling method to get this info?