2: Exploratory Data Analysis: Single Variable

Question 1

cases

Answer 1

objects described by a set of data (companies, subjects, customers)

Question 2

label

Answer 2

variable used in some data sets to distinguish different cases

Question 3

variable

Answer 3

characteristic of a case

Question 4

distribution

Answer 4

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

Question 5

distribution of categorical variable

Answer 5

lists the categories and gives either the count or the percent of cases who fall in each category

Question 6

stemplot

Answer 6

steam and leaf plot. gives quick pic of distribution shape while includes actual numerical values in graph. separate each observation into a stem consisting of all but the final (rightmost) digit and a leaf – the final digit. write stems in vert. column with smallest at top and draw vert line at right. write each leaf in the row to the right of them stem, in increasing order out from the stem

Question 7

histogram

Answer 7

breaks range of values of a variable into classes and displays only the count or percent of the observations that fall into each class. classes = equal width.

Question 8

tails

Answer 8

extreme values of a distribution

Question 9

modes

Answer 9

major peaks in a distribution

Question 10

time plot

Answer 10

of a variable plots each observation against the time at which it was measured. time is on horiz.. scale of plot and variable measured is on vert. scale

Question 11

mean vs. median

Answer 11

mean is average value.
(x1 + x2+ x3 + xn / n)

median is middle value.

(1) if number of observations is odd – medium’s LOCATION can be found by counting (n+1)/2 observations up from bottom of the list
(2) if even – median is the mean of the two center observations in the ordered list. location is (n+1)/2 observations up from bottom of the list

Question 12

quartile

Answer 12

upper quartile = median of the upper half of the data. lower quartile = median of lower half of the data

Question 13

pth percentile

Answer 13

the value that has p percent of the observations fall at or below it

Question 14

five number summary

Answer 14

set of observations consists of the smallest observation, the first quartile, the median, the third quartile, the largest observation - from small to big.

Min Q1 M Q3 Max

Question 15

boxplot

Answer 15

graph of five-number summary

Question 16

interquartile range IQR

Answer 16

distance b/w first and third quartiles. IQR = Q3-Q1

Question 17

1.5 X IQR rule for outliers

Answer 17

observation = outlier if it falls MORE than 1.5 X IQR above third quartile or below first quartile

Question 18

standard deviation

Answer 18

measures spread by looking at how far the observations are from their mean.

Question 19

variance

Answer 19

s^2 of a set of observation is the average of the squares of the deviations from their mean. OR, the average of the squared differences from the mean.

(1) Work out the Mean (the simple average of the numbers)
(2) Then for each number: subtract the Mean and square the result (the squared difference).
(3) Then work out the average of those squared differences

Question 20

standard deviation

Answer 20

= square root of the variance

Question 21

degrees of freedom

Answer 21

the number n-1 is called the degrees of freedom of the variance or standard deviation

Question 22

properties of standard deviation

Answer 22

(1) s measures spread about the mean and should be used only when the mean is chosen as the measure of center
(2) s = 0 only when there is no spread. this happens only when all observations have the same value. Otherwise, s > 0. As the observations become more spread out about their mean, s gets larger
(3) s, like the mean, is not resistant. a few outliers can make s very large.

Question 23

Which is better for describing a skewed distribution or a distribution with strong outliers: five number summary, mean, or std deviation?

Answer 23

five number summary

Question 24

linear transformation

Answer 24

changes the original variable x into the new variable xnew given by this equation:

xnew = a + bx

they don’t change the shape of the distribution

Question 25

effects of linear transformation

Answer 25

(1) multiplying each observation by + number b multiplies both measures of center (mean and median) and measures of spread (interquartile range and std dev) by b
(2) adding same number a (pos or neg) to each observation adds a to measures of center and to quartiles and other percentiles – but does NOT change measures of spread

Question 26

density curve

Answer 26

overall pattern of a distribution. has a total area of 1 underneath it.

Question 27

normal distributions

Answer 27

are describes by bell-shaped, symmetric, unimodal density curves. the mean U and std dev completely specify the Normal distrubtion.

Question 28

Mean vs. std dev in normal distribution

Answer 28

mean = center of symmetry

std dev = distance from mean to the change-of-curvature points on either side

Question 29

68-95-99.7 rule

Answer 29

In the normal distribution the mean u and std dev,

Approx 68% of the observations fall within std dev of the mean

Approx 95% of the observations fall within 2 x (std dev) of the mean

Approx 99.7% of the observations fall within 3 x (std dev) of the mean

Question 30

z-score

Answer 30

standardized value: subtract the mean of the distribution and then divide by the std dev

z = x - u / std dev

tells us how many standard devs the original observation falls away from the mean (and in which direction)

Question 31

frequency distribution table

Answer 31

1. frequency (f): number of times we observe an event
2. raw frequency: (f/n): # of times event takes place / total events
3. cumulative freq: running count of the frequencies of a particular value and all preceding values (sum raw freq)
4. cum. relative freq: cumulative freq for a particular value in relation to the total (sum rel freqs)

Question 32

measures of central tendency for cat. variables

Answer 32

median (if cat variables can be ranked)

mode

Question 33

measures of central tendency for quant variables

Answer 33

mean

median if lots of outliers

Question 34

calculate median

Answer 34

1. order data from low to high
2. look at location - (n+1).2
3. if at 5.5, then average 5th and 6th values

Question 35

median provides a ______ reasonable measure of central tendency when distributions are skewed or have outliers

Answer 35

median provides a MORE reasonable measure of central tendency when distributions are skewed or have outliers

Question 36

mean is _____ sensitive to outliers

Answer 36

mean is sensitive to outliers

Question 37

if distribution is exactly symmetric, then mean and median

Answer 37

are the same

Question 38

IQR as a measure of spread is ____ useful to describe skewed distributions

Answer 38

NOT

2 “sides” of a skewed distribution have different spreads

Question 39

standard deviation is _____ a good measure when the distribution is highly skewed

Answer 39

NOT