stats final 251

Question 1

List three or more categorical variables.

Answer 1

Gender (male, female, other), color, race

Question 2

List three or more quantitative variables.

Answer 2

Age, number of siblings you have, the mass or weight of an object

Question 3

Explain the difference between categorical and quantitative variables.

Answer 3

You can do logical math with quantitative variables since they can be calcified as intervals,

Question 4

Give an example of a numerical value that is NOT quantitative.

Answer 4

Temperature degrees since they can be used logically for math

Question 5

Explain the difference between quantitative variables on the interval scale versus the ratio scale.

Answer 5

quanitative Interval data can have logical operations done between them
while the ratio scale like temerature canot

Question 6

Explain the difference between categorical variables that are nominal versus ordinal.

Answer 6

If there is no ordering that can be done between categories the variable is nominal, but if there is some type of order that can be applied the variable is ordinal.

Question 7

How do you visually display categorical data?

Answer 7

On a horizontal axis with a list of categories.

Question 8

How do you visually display quantitative data?

Answer 8

The horizontal axis contains ranges of numbers that represent a continuum

Question 9

Explain the difference between discrete and continuous distributions.

Answer 9

Discrete distributions use countable unique numbers while continuous distributions have an infinite range of possible values

Question 10

Describe how we can characterize a distribution.

Answer 10

Describe it in terms of where the modes can be found (for uniform this isn’t as useful

Question 11

What are descriptive statistics and what does each one tell us about our data?

Answer 11

They tell us about our data - the mean is average, median is middle, mode is popular, range is spread, and standard deviation is variability. Quartiles and percentiles show data locations and outliers.

Question 12

What are the similarities between bar charts, pie charts, histograms, stem-and-leaf, dotplots, and boxplots?

Answer 12

-Visualization tools for data visuals.
-Used to put together and understand data.
-Helpful for categorical data.

Question 13

What are the diffrences between bar charts, pie charts, histograms, stem-and-leaf, dotplots, and boxplots?

Answer 13

-Bar Charts: Show differences between categories.
-Pie Charts: Display parts usually as a % of a whole
-Histograms: show data distribution.

Question 14

What is metadata?

Answer 14

data that provides info about other data gives details about a dataset or piece of information.

Question 15

What are some examples of descriptive statistics and what do they tell us?

Answer 15

One example of a descriptive statistic would be the mean which gives us the average values of a set of data

Question 15

In this class, are we conducting experiments and/or doing observational studies?

Answer 15

We are analyzing data from said experiments but the experiments must be class related because of the tests we have to do in order to do human trials

Question 16

What are some words you should NEVER use when talking about our studies?

Answer 16

Everyone/no one - generalizations
I/they thinks - facts matter

Question 16

What is a relative frequency?

Answer 16

the proportion or percentage of times a particular event or outcome occurs relative to the total number of observations

Question 17

How many marginal distributions are there?

Answer 17

2 one for each observed frequency

Question 18

How many conditional distributions are there?

Answer 18

There are many but in our M&M experiment for ex we had 10: C,L,M,N,B,BR,G,O,R,Y

Question 19

Explain how to read/interpret a contingency table.

Answer 19

The contingency will have a range of numerical values on the y axis and on the x axis will have whatever the defect, numerical amount, type amount is.

Question 20

Explain what a distribution is.

Answer 20

A distribution in statistics describes how data values are spread or organized.

Question 21

Explain how to distinguish between a sample and a population.

Answer 21

A sample is a subset of a larger group, the population, from which data is collected for analysis

Question 22

Describe the meaning of N(𝛍,𝛔) and the standard normal distribution N(0,1).

Answer 22

This is a normal Gaussian distribution where the standard normal distribution N(0,1) has a mean (meu) of 0 and a standard deviation (sigma) of 1

Question 23

Explain how to interpret histograms

Answer 23

Histograms: show data distribution by side-by-side values and displaying their frequency

Question 24

Explain how to interpret boxplots

Answer 24

Boxplots: summarize data with a box indicating quartiles and ticks showing the data range

Question 25

Explain how to interpret comparative boxplots

Answer 25

Comparative Boxplots: compare distributions of multiple datasets using multiple boxplots side by side

Question 26

What is the meaning of the z-score?

Answer 26

Tells us how many standard deviations above or below the mean our data point is

Question 27

z-score fourmula

Answer 27

Z = (X - μ) / σ

Question 28

what does each one mean
Z = (X - μ) / σ

Answer 28

Z is the z-score.
X is the data point you want to convert.
μ is the mean of the dataset.
σ is the standard deviation of the dataset.

Question 29

Describe how to use the 68-95-99.7 rule to approximate the area under the normal curve between any two data points or z-scores, or to the left of a given z-score, or to the right of a given z-score.

Answer 29

About 68% is within one standard deviation from the mean
About 95% is within two standard deviations
About 99.7% is within three standard deviation
You can use this rule to get a rough estimate between, to the left, or to the right of specific z-scores or data points

Question 30

Explain how to find the area under the normal curve between data points or z-scores.

Answer 30

use a standard normal distribution table or a calculator with statistical functions like R

Question 31

What is a sampling distribution?

Answer 31

A sampling distribution shows how a specific statistic, like the mean, would vary when calculated from random samples taken from the same group.

Question 32

How do you distinguish between distribution of a sample and sampling distribution?

Answer 32

-distribution of a sample refers to the pattern or arrangement of data values within a single sample
-sampling distribution is a theoretical probability distribution that illustrates how a specific statistic varies across multiple random samples drawn from the same population

Question 33

What does “random” mean in statistical terms?

Answer 33

refers to a process or event that occurs without any predictable pattern or bias.

Question 34

How can you ensure your sample is both random and representative? (What strategies could you use and how are they different?)

Answer 34

Random Sampling: Use random methods to select individuals or elements, ensuring each has an equal chance of being chosen.

Systematic Sampling: Select every “k-th” individual from a random starting point, balancing randomness and structure like if you got every 10th person thwart walked into U-REC.

Cluster Sampling: Randomly select clusters and sample all individuals within them, practical for large populations.

Convenience Sampling: not random, based on convenience, and may introduce bias, best for quick data but not ideal for representativeness.

Question 35

Why is it so important to have a sample that is both random and representative?

Answer 35

This is important because it ensures that the findings correctly represent the population this will, minimize bias, and enhance the statistical correctness of the results.

Question 36

Describe the main concept behind the central limit theorem.

Answer 36

States that the more samples you get the more “normal/bell-shaped” the sample will be regardless of the original population’s shape.

Question 37

Explain why the normal model shows up so often & why we spend so much time studying it.

Answer 37

We study the normal distribution often because it shows us many real-world problems and it helps us with statistical analysis it also serves as a foundation for various statistical methods