Stats 200 Chapter 1-3

What is statistics about? Statistics data are used to describe typical values and variability and to _____ _____ that affect everyone of us.

Make decisions

Statistics is to study how to best _____ data, _____ data, and ______ ______ from data

Collect, summarize, draw conclusions

Summarizing data in stats is _____ statistics

Descriptive statistics

Drawing conclusions from data is ______ statistics

inferential

_____ statistics

Use of graphs (histograms, scatterplots, etc.) and numbers (mean, median, standard deviation, correlation, etc.) to summarize and describe the data at hand (sample data) SUMMARIZE DATA YOU HAVE

Descriptive

______ statistics

Analyze a small specific set of data (sample) in order to draw a GENERALIZATION and conclusion about a large, more general group (population)

2 Types

-_______ intervals

- Hypothesis _____

Inferential, confidence, tests

Inferential or descriptive

The Georgia Department of Transportation maintains records concerning all trucks stopped for inspection. A report of these inspections lists the proportion of all trucks stopped, by cargo carried.

Descriptive

Inferential or descriptive

Eric Knudsen, a researcher at Stanford University Medical Center, obtains a random sample of wild owls and measures how far each can turn its neck. The data are used to conclude that an owl can turn its neck more than 120°from the forward position.

Inferential

Inferential or descriptive

A safety inspector in Atlanta selects a sample of apartment buildings and checks the fire ladders on each. The proportion of broken ladders in the sample is used to estimate the proportion of apartment buildings with broken fire ladders in the entire city.

Inferential

Inferential or descriptive

A report from the CDC lists the percentage of people seeing their health care provider for influenza-like illness by state.

Descriptive

________ the entire collection of individuals or objects to be considered or studied (typically very large) THE GROUP YOU WANT TO STUDY

Population

_______ a small selection of individuals or objects taken from the population, (WHO YOU GET DATA FROM)

Sample

________- a characteristic of an individual or object in a population of interest (CHARACTERISTIC YOU MEASURE)

Variable

A new study is concerned with the magnesium level in a slice of whole-grain bread. One hundred slices of whole-grain bread are selected at random from various markets, and the magnesium in each is carefully measured and recorded.

Population-

Sample-

Variable-

Population- All slices of whole grain bread

Sample- 100 slices of whole grain bread randomly selected

Variable- Magnesium level in each slice

Is the magnesium level in each slice considered quantitative or qualitative

Quantitative

A factory purchases a large lot of parts from a supplier. Before accepting the entire lot, a quality control engineer randomly selects 50 parts, identifies whether each part is good or bad, and then makes a decision whether the factory will keep the entire lot or reject it.

Population-

Sample-

Variable-

Population- All of the parts in the entire lot

Sample- 50 parts randomly selected

Variable- Quality (status) of each part

Is the quality of each part considered quantitative or qualitative

Qualitative

_____ study-we observe the response for a specific variable for each individual or object (but do not attempt to influence responses)

NOT IMPOSING ANYTHING ON THEM

Observational

______ study-we DELIBERATELY impose treatments (by manipulating one or more factors) on individuals or objects in the sample and observe their responses. Goal -to see if a treatment is effective or which of several treatments is most effective

Experimental

______ ______ _______ of size 𝒏-a sample selected in such a way that every possible sample of size 𝑛has the same chance of being selected

(EVERY SAMPLE HAS THE SAME CHANCE)

Simple random sample (SRS)

People in the ______ have to be the people or objects getting data from

Sample

The administration at the University of Nebraska in Lincoln is interested in student reaction to a planned parking garage on campus. A dormitory near the proposed site is selected and several Student Senate members volunteer to solicit responses. One Thursday evening, the volunteers each take a specific dorm wing, knock on doors, and record student answers to several prepared questions.

(a)Is this an observational or an experimental study?

(b)Describe the sample in this problem.

(c)Is this a random sample? Justify your answer.

A. Observational study

B. Students who answered/respond to the questions

C. No, a specific dorm, only one dorm and only those where home at a certain time, one evening NOT A RANDOM SAMPLE

Electric and plug-in electric cars are designed to save gasoline and help the environment. The Tesla Model S and Model 3 are designed to have extra safety features, a convenient interior design, and up to an 8-year warranty. Although owning an electric car certainly has some benefits,many people complain about the slow acceleration, repair expense, and overall comfort. Thirty-five passengers are randomly selected. Each is blindfolded and taken for a ride in a traditional combustion-engine automobile and in a comparably sized electric car (over the same route). The passenger is then asked to select the car with the most comfortable ride.

(a)Is this an observational or an experimental study?

(b)What is the variable of interest?

(c)Describe possible sources of bias in these results.

A. Experimental Study (I AM CONTROLLING THE SUBJECTS TREATMENT ) (Imposing people to two different treatments, a traditional car and an electric car)

B. Comfort in car (opinion about which is the comfiest, most comfortable

C. Noise, peeking, conversation with driver

one observation from each individual or object we have ______ data(e.g. height of each person)

univariate

two observations from each individual or object we have ______ data (e.g. height and weight of each person)

bivariate

more than two observations from each individual or object... ______ data (e.g. height, weight, gender, blood pressure, and cholesterol level of each person)

multivariate

Types of data

_______ or ______ -observations that are numbers

Numerical or quantitative

Types of data

_______ or _______ -non-numerical observations that may be placed in categories

Categorical, qualitative

A numerical data set is

_____ if its set of possible values is a finite set or a countably infinite set (i.e. an infinite sequence with a 1stvalue, 2ndvalue, etc.) (usually associated with counting, e.g. "the number of ...")

discrete

A numerical data set is

_______ if its set of possible values is an infinite set that forms an interval on the number line(usually associated with measuring

continuous

Classify each resulting data set as categorical or numerical. If the data set is numerical, determine whether it is discrete or continuous.

(a)The number of books read by middle-school students during the academic year.

(b)The duty status of crew members aboard a U.S. aircraft carrier.

(c)The length of time (in minutes) it takes to get a haircut.

A. Numerical (discrete)

B. Categorical (off, on, limited)

C. Numerical (continuous)

Classify each resulting data set as categorical or numerical. If the data set is numerical, determine whether it is discrete or continuous.

(d)The number of garage sales advertised in a local newspaper.

(e)The types of candy received from different houses on Halloween.

(f)The weight of steel beams used in construction of a high-rise apartment building.

D. Numerical (discrete)

E. Categorical

F. Numerical (continuous)

Classify each resulting data set as categorical or numerical. If the data set is numerical, determine whether it is discrete or continuous.

(g) The type of hardwood floor purchased by customers at Green Tree Flooring Services.

G. Categorical

When both the person doing the experiment and the person in the experiment does not know what is going on, what is this called?

Double blind experiment

Frequency distribution is just the ______ of data

Number

Proportion is the _____ of items

Fraction

A relative frequency bar chart is the _____- graphed

Percentages

In histograms, do the bars touch?

Yes

In which graph has all data relatively the same height?

Uniform

In which graph does the left side have a lot of more data?

Right skewed

In which graph does the right side have a lot of more data?

Left skewed

In which graph does it have two peaks

Bimodal

In which graph are both sides equal

Symmetric

In which graph there is only one peak

Unimodal

In which graph is there one peak in the middle and equal on both sides

Bell-shaped

Why might the sample mean not be a good measure of center?

It does not account for outliers and or skewed data that pull the mean up or down, the mean is sensitive to outliers and skewed data.

What might be a better measure of center?

Median, when there is a lot of outliers and skewed data

When average > median what shape is the graph going to have?

Right skewed

When average < median what shape is the graph going to have?

Left skewed

When average = median what shape is the graph going to have?

Symmetric

When mean is 200 and median is 197 what is shape?

Symmetric

When mean is 200 and median is 100 what is shape?

Right skewed

When mean is 50 and median is 100 what is shape?

Left skewed

The mean is dragged in the direction of the ____

Tail

For measures of spread, if the answer is _____, then the data is more spread out (has _____ variability)

Large, more

For measures of spread, if the answer is _____, then the data is less spread out (has _____ variability)

small, less

What is Q3

the median of the upper half of the data

What is Q1

the median of the lower half of the data

What is IQR

interquartile range (Q3-Q1)

In Q3, _____% of data is at or below it

75

In Q1, _____% of data is at or below it

25

Q1 is closer to the Median, the distribution is likely to have what shape?

Right skewed

Q3 is closer to the Median, the distribution is likely to have what shape?

Left skewed

Q1 and Q3 are equally close to the Median, the distribution is likely to have what shape?

Symmetrical

Q1=80

Q3=121

Median=100

What is shape?

Symmetric

Q1=100

Q3=210

Median=200

What is shape?

Left skewed

Q1=150

Q3=300

Median=200

What is shape?

Right skewed

The median is considered the _____ percentile

50th

What is known as the place in the top 25%

Q3

What is known as the place in the bottom 25%

Q1

______ = the width of the middle 50%, which makes it less sensitive to outliers

IQR

When Q1 is closer to the median?

Right skewed

When Q3 is closer to the median?

Left skewed

Empirical Rule

Applies only when the shape of the distribution is approximately normal (_______ ______)

Approximately 68% of the observations are within 1 standard deviation of the mean

-Approximately 95% of the observations are within 2 standard deviations of the mean -

-Approximately 99.7% of the observations are within 3 standard deviations of the mean

bell-shaped

The _____ and the standard deviation can be used together to describe the distribution of a data set more precisely.

Mean

Chebyshev's Rule

Applies to _____ data set, regardless of shape (Provided 𝑘 > 1) At least 100 (1 − 1 𝑘2 ) % of the data set is within 𝑘 standard deviations of the mean - i.e. lying in the interval from 𝑥̅− (𝑘 ⋅ 𝑠) to 𝑥̅+ (𝑘 ⋅ 𝑠)

Any

Standard deviation is often thought of as measuring the typical distance that an observation is from the _____

Mean