Lesson 3: Working with Quantitative Data

s

notation for standard deviation of a sample of data

tails

parts of a distribution that typically trail off on either side

distributions can be characterized as having…if they straggle off for some distance or…if they don’t

long tails; short tails

skewed

used to describe an asymmetric data set that has one tail stretching out farther than the other

distributions are skewed…when the longer tail stretches to the left and are skewed…when the longer tail stretches to the right

left; right

box-and-whisker plot / boxplot

display of the five-number summary from a set of data

the five number summary of a data set includes…

minimum value, q1, median, q3, and maximum value

outliers

extreme values that don’t appear to belong with the rest of the data

outliers may be…or…

unusual values that deserve further investigation; mistakes

uniform

used to describe a roughly flat distribution

histogram

graph that uses adjacent bars to show the distribution of a quantitative variable

a histogram shows the…or…of data

frequency; relative frequency

gap

region of a distribution where there are no values

dotplot

graphical display of data created using dots and a number line

a dotplot is typically used for…

relatively small data sets

spread

numerical summary of how tightly the values cluster around the center

measures of spread include…

range, interquartile range, and standard deviation

to find range…

subtract minimum value from maximum value

to find interquartile range (IQR)…

subtract q1 from q3

standard deviation is…

the square root of the variance

Σ

Greek capital letter sigma, meaning “the sum of”

symmetric

used to describe a distribution if the two halves on either side of the center look approximately like mirror images of each other

shape

way that the distribution of a data on a graphical display is patterned

when describing shape, you should look for…

the number of modes, symmetry or skewness, outliers, and gaps

quartiles

values that divide a data set into quarters

the lower quartile (q1) is the value with…

a quarter of the data below or equal to it

the upper quartile (q3) is the value with…

three quarters of the data below or equal to it

the median is sometimes referred to as…

q2

ȳ

read as “y-bar;” symbol for the mean of all the values of the variable y

the y-bar can be used over any variable to indicate…

the mean of all the values of that variable

quantitative data condition

condition which states that the data in a set are values of a quantitative variable whose units are known

before making a stem-and-leaf display, a histogram, or a dotplot you need to…

check the quantitative data condition

the ith percentile is the number that…

falls above i% of the data

center

place in the distribution of a variable that one would point to in an attempt to summarize the entire distribution with a single number

measures of center include the…

mean and median

variance

measure of how far a data set is spread out

variance is mathematically defined as…

the average of the squared differences from the mean

cumulative distribution plot

plot that displays the fraction of a data set that lies at or below any given data value

another name for a cumulative distribution plot is an…

ogive plot

s²

notation for variance for a sample of data

stem-and-leaf display

data display where each value is split into a leaf and stem

if you turn a stem-and-lead display on its side, then it will…

resemble a histogram and provide information about the distribution of the data

mode

hump in the shape of the distribution of a variable

distributions can be…, …, or…

unimodal; bimodal; multimodal

unimodal distributions have…

one mode

bimodal distributions have…

two modes

multimodal distributions have…

more than two modes

distribution

list or graphical display of the data

the distribution shows…

all possible values or intervals of the data and how they occur