chapter 1

A physician survey for a common medication in five different pharmacies and reported the average price as $16. Four of the five stores and had prices $12, $15, $17, and $22. Assuming that the survey is correct, what is the price of the medication at the other store? Hint: Use the formula for the mean and solve for the missing value.

$14

variable

a characteristic of a case

label

a special variable used in some data sets to uniquely identify different cases

boxplots

based on the five-number summary are useful for comparing several distributions. the box spans the quartiles and shows the spread of the central half of the distribution. the median is marked within the box. lines extend from the box to the extremes and show the full spread of the data

side-by-side boxplots

can be used to display box plots for more than one group of the same graph

a variable is a characteristic of a

case

how many

cases does the data set contain?

the five-number summary

consisting of the median, the quartiles, and the smallest and largest individual observations, provides a quick overall description of a distribution. the median describes the center, and the quartiles and extremes show the spread

The distribution of a categorical variable is displayed using _______.

counts or percentages

shape, center, & spread

describe the overall pattern of a distribution

observation

describes the data for a particular case

values

different cases can have different values of the variables

bar graphs & pie graphs

display the distribution of a categorical variable

stemplots & histograms

display the distributions of a quantitative variable

why, what purpose

do the data have? do we hope to answer some specific questions? do we want to draw conclusions about cases other than the ones we actually have data for? are the variables that are recorded suitable for the intended purpose?

The tails of a distribution show the _______.

extreme values

the 1.5 x IQR rule

flags observations more than 1.5 x IQR beyond the quartiles as possible outliers

the first quartile

has 1/4 of the observations below it

the third quartile

has 3/4 of the observations below it

linear transformations

have the form Xnew = a + bX. changes the origin of a doesn't equal zero and changes the size of the unit of measurement if b > 0. do not changes the overall shape of a distribution. multiplies a mature of spread by b and changes a percentile or measure of center m into a + bm

what

how many variables do the data contain? what are the exact definitions of these variables? what are the units of measurement for each quantitative variable?

units of measurement

important part of the description of a quantitative variable, may not always be obvious

resistant measure

is relatively unaffected b y changes in the numerical value of a small proportion of the the total number of observations, not matter how large these changes are. the median and quartiles are resistant, but the mean and standard deviation are not

the standard deviation

is zero when there is no spread and gets larger as the spread increases

distribution of a categorical variable

lists the categories and give other the count of the percent of cases that fall in each category

median

midpoint

outliers

observations that lie outside the overall pattern of a distribution

distribution

of a variable tells us what values it takes and how often it takes these values

Categorical variables are best displayed by ______.

pie charts or bar graphs

categorical variable

places a case into one of several groups or categories

modified boxplot

points identified by the 1.5 x IQR rule are plotted individually

Variables that take numeric values for which arithmetic operations make sense are called _______.

quantitative

Suppose you are interested in comparing the quality of different hospitals based on infections occurred from surgery. What would be the best way to measure such a variable?

rate of infections

qualitative variable

takes numerical values for which arithmetic operations such as adding and averaging make sense

mean

the arithmetic average of the observations

The first day of class the professor collects information on each student to make a data set that will be analyzed throughout the semester. The information asked includes hometown, GPA, number of classes, number of siblings, and favorite subject. What are the cases in this data set?

the college students

proportion

the count divided by the sum of the counts

Researchers are conducting a study on cortisol levels in different socio-economic demographic groups. Which of the following variables is categorical?

the county of residence

interquartile range

the difference between the quartiles. it is the spread of the center half of the data

A description of different houses on the market includes the following three variables. Which of these variables is quantitative?

the monthly gas bill, the square footage of the house, the monthly electric bill

cases

the objects described by a set of data

What are labels used for in data sets?

to identify cases

spreadsheet

useful for doing simple computations

exploratory data analysis

uses graphs and numerical summaries to describe the variables in a data set and the relations among them

predictive analytics

using descriptions to predict something in the future

Variables take on ________.

values

who

what cases do the data describe?

time plot

when observations on a variable are taken over time, graphs time horizontally and the values of the variable vertically, can reveal interesting patterns in a set of data

A particularly common question in the study of wildlife behavior involves observing contests between "residents" of a particular area and "intruders." In each contest, the residents either win or lose the encounter (assuming there are no ties).Observers might record several variables, some of which are listed below. Which of these variables is categorical?

whether the residents win or lose