Exam 1 (Modules 1-3)

Question 1

What should be avoided in constructing “good” graphs?

Answer 1

minimize white space, avoid clutter on graph, avoid 3D effects

Question 2

Determine the five-number summary

Answer 2

(put data set in ascending order): minimum, Q1, Median (Q2), Q3, maximum

Question 3

Define “statistics”

Answer 3

Science of collecting, organizing, summarizing, and analyzing information. To describe and understand sources of variation in data.

Question 4

Define “the lurking variable”

Answer 4

“Correlation does not equal causation!”

Question 5

Define “statistic”

Answer 5

numerical summary of a SAMPLE (Roman letters)

Question 6

Define “descriptive statistics”

Answer 6

organizing and summarizing data (numerical summaries, graphs, tables)

Question 7

Define “inferential statistics”

Answer 7

take result from a sample, extend it to the population, and measure the reliability of the result

Question 8

Define “parameter”

Answer 8

numerical summary of a POPULATION (Greek letters)

Question 9

Discrete variable

Answer 9

quantitative variable that has either a finite number of possible values OR a countable number of possible values. *Count to get the value. EX: number of pets, number of college credits, number of seats in an auditorium

Question 10

Continuous variable

Answer 10

quantitative variable that has an infinite number of possible values that are not countable. *Measure to get the value. EX: distance, total rainfall, age, data use on a cell phone per month

Question 11

The Process of Statistics

Answer 11

1) Identify the research objective (what questions need to be answered?). 2) Formulate the research question (with at least 1 variable). 3) Collect the data needed to answer the question(s). 4) Describe the data. 5) Perform inference.

Question 12

Define “statistical thinking”

Answer 12

using statistics to analyze and critique information you come across, in order to be an informed consumer of information

Question 13

Qualitative variable

Answer 13

contains a classification system for its variable values. May be text or numeric. EX: gender, zip code, nationality, phone number, numbers on team shirts

Question 14

Quantitative variable

Answer 14

the variable values are a numerical range that can be added or subtracted to provide meaningful results. Equal interval magnitude scale. Can be discrete OR continuous. EX: height, weight

Question 15

Frequency distribution

Answer 15

lists each category of data and the number of occurrences in each category of data. Frequency column = number of observations.

Question 16

Relative frequency

Answer 16

proportion/percent of observations within a category. RF = frequency / number of observations

Question 17

Pareto chart

Answer 17

bar graph whose bars are drawn in decreasing order of frequency or relative frequency

Question 18

Classes

Answer 18

categories in which data are grouped (i.e., 25-34, 35-44). Class width = difference between consecutive lower class limits.

Question 19

Class width value (CWV)

Answer 19

CWV = (largest data value - smallest data value) / number of classes (between 5-20)

Question 20

Describe what can make a graph misleading or deceptive

Answer 20

scale of the graph, inconsistent scale, misplaced origin (aka not starting at 0), use of 3D effects

Question 21

What makes a “good” graph”?

Answer 21

Not too much white space, avoid “prettifying,” avoid 3D effects

Question 22

3 characteristics of distribution

Answer 22

shape (bell-shaped, skewed), center (average value), spread (how far data goes from average value)

Question 23

Population arithmetic mean

Answer 23

(u - mu; N = size of population). u = (x1 + x2 + … xN) / N

Question 24

Sample arithmetic mean

Answer 24

(x-bar; n = size of sample). x-bar = (x1 + x2 + …xn) / n

Question 25

Median (“typical value”)

Answer 25

(n = number of observations). If n is odd, M = (n + 1) / 2 ||| If n is even, M = [(n/2) + (n/2 + 1)] / 2

Question 26

Resistant

Answer 26

numerical summary of data is resistant if extreme values (very large or very small) relative to the data do not affect its value substantially. EX: median, quartiles, IQR = resistant, mean = NOT resistant

Question 27

Mode

Answer 27

most frequent observation of the variable that occurs in the data set. “No mode,” “bimodal,” or “multimodal” (not usually reported). Only measure of central tendency that can be determined for nominal data (i.e., location of injuries)

Question 28

Define “dispersion”

Answer 28

the degree to which the data are spread out

Question 29

Range

Answer 29

the difference between the largest and the smallest data value. Simplest measure of dispersion. NOT RESISTANT

Question 30

Standard deviation

Answer 30

Typical spread from the mean. The farther the observation is from the mean, the larger the [absolute value of] deviation. xi - u = deviation about the mean for the ith value of a population. xi - x-bar = deviation about the mean for the ith value of a sample.

Question 31

Population standard deviation

Answer 31

(o~) = square root of ((sum xi2) - [(sum xi)2 / N]) / N

Question 32

Sample standard deviation

Answer 32

(s) = square root of ((sum xi2) - [(sum xi)2 / n]) / n-1

Question 33

Variance

Answer 33

SQUARE of the standard deviation (so the answer BEFORE you take the square root for the standard deviation formula)

Question 34

the Empirical Rule

Answer 34

*bell-shaped only. 68% = 1 standard deviation. 95% = 2 standard deviations. 99.7% = 3 standard deviations.

Question 35

Chebyshev’s Inequality

Answer 35

*any shape graph. AT LEAST (1 - 1/k**2) x 100% of the observations lie within k standard deviations, where k > 1.

Question 36

The variance of a population is the arithmetic average of the squared deviations about the population mean. (T/F)

Answer 36

TRUE

Question 37

z-score

Answer 37

represents the distance that a data value is from the mean in terms of the number of standard deviations. Can be positive, negative, or zero. Provides a way to compare apples to oranges.

Question 38

z-score formulas (population & sample)

Answer 38

population: z = (x - u) / o~ ||| sample: z = (x - x-bar) / s

Question 39

five-number summary

Answer 39

minimum, Q1, M (Q2), Q3, maximum

Question 40

find lower and upper fences

Answer 40

lower = Q1 - 1.5(IQR) ||| upper = Q3 + 1.5(IQR)

Question 41

​Which variable has more​ dispersion? Why?

Answer 41

Variable y the interquartile range of variable y is larger than that of variable x.