Module 2 - Section 2

Question 1

What graphs are best for smaller data sets of numerical variables?

Answer 1

Stem plots and dot plots

Question 2

What graphs are best for large data sets of quantitative data?

Answer 2

histograms

Question 3

appearance of a dot plot?

Answer 3

y-axis: frequency
x-axis: name of variable and the values that the data will fall between
. .
. . . . . . .
. . . . . . . . .
values
-dot above where that data point is
-more dots above a point to indicate a frequency more than one
-(i don’t know look at notes if you are confused)

Question 4

stem

Answer 4

the leading digits of the number in the data
ex: 75 has leading digit or stem 7
100 could have leading digits 100 or 1 (depending on the data)

Question 5

leaf

Answer 5

the last digit of the number in the data

ex: 75 has leaf 5

Question 6

a key is required for …

Answer 6

a stemplot

Question 7

bins

Answer 7

equal-width interval for multiple different numbers of data that are close in values
ex: 70-79 is one bin if 7 is the stem 0-9 are the leaves

Question 8

appearance of stemplot

Answer 8

stem | leaves
4       |0
5       |
6       |05588
7       |00000455
8       |5
9       |05

Price of Walking shoes
8|5 represents $85

Question 9

back-to-back stem plots

Answer 9

-used for the comparison of the distribution of two groups
leaves | stem | leaves
-still require key
-leaves get bigger as you move away from stem! pay attention to left side group

Question 10

left inclusion

Answer 10

-interval notation as [a,b)
so a on the left is included but not b
-used for histograms along the x-axis to organize bins

Question 11

histogram appearance

Answer 11

• bins on x-axis
• frequency or relative frequency on y-axis
• bars with no spaces between (unless there is an empty bin)

Question 12

For dot plots, stem plots, and histograms, which does/does not retain all data values

Answer 12

dot and stem plots retain all data values but not histograms

Question 13

how can we describe the distribution of a plot?

Answer 13

shapes - modes, symmetry or skewness, deviation or outliers
center
spread

Question 14

mode(s)

Answer 14

number of bumps / humps / peaks

Question 15

uniform

Answer 15

no modes, square / rectangle appearance

Question 16

unimodal

Answer 16

a single peak

Question 17

bimodal

Answer 17

two peaks

ex:heights of adults and children will have two peaks one for adults and one for children

Question 18

multimodal

Answer 18

rarely occurs (except for covid?)
more than two peaks

Question 19

symmetry

Answer 19

when a graph is symmetrical

if you didn’t get this…I am ashamed lol

Question 20

non symmetric graphs are

Answer 20

skewed

Question 21

skewed to the right

Answer 21

positively skewed
peaks quickly and then slowly trickles down to the right
as if the tail end of the peak on the right has been pulled to the right

Question 22

negatively skewed

Answer 22

skewed to the left
the left tail is extended and longer than the right tail ( if peak is essentially symmetric)
……^. .

Question 23

Outlier

Answer 23

a deviation that does not follow the overall pattern of the graph

Question 24

numerical summaries

Answer 24

a few important and meaningful numbers that preserves the relevant features of the data set so that you can draw useful conclusions

Question 25

y

Answer 25

variable of interest | the variable for which we have sample data

Question 26

n

Answer 26

the sample size / number of observations of the variable y

Question 27

y₁

Answer 27

the first sample observation of the variable y

Question 28

yn

Answer 28

the nth sample observation of the variable y

Question 29

center and examples

Answer 29

the value that split the data in half or a typical range of values at the center of the graph median, mean, mode

Question 30

spread and examples

Answer 30

how much do the data values vary around the center? the range of values, concentration, are most values close to or far from the center? range, standard deviation, IQR

Question 31

n Σyᵢ i=1 What is this? describe all elements.

Answer 31

n is the upper boundary i is the lower boundary where the set runs from the ith to the nth piece of data Σ is sigma or summation This describes adding all of the values of y used to find the mean

Question 32

ȳ

Answer 32

``` y bar is the mean mean is n Σyᵢ i=1 -------- n aka the sum of all the values in a data set divided by the number of observations ```

Question 33

M

Answer 33

median the value that divides the ordered sample into two sets for n is odd, it is the middle value for n is even, it is the mean of the two middle values

Question 34

mean vs median

Answer 34

mean is affected by outliers, while the median is resistant to outliers or skewness

Question 35

mode

Answer 35

the value that occurs with the highest frequency in a data set may be more than one mode

Question 36

center values of symmetric, right skewed and left skewed data sets

Answer 36

symmetric: mean=median=mode right skewed: mean>median>mode left skewed: mean

Question 37

range

Answer 37

describes spread the difference between the maximum and minimum values in a data set Range = max - min strongly influenced by outliers

Question 38

larger range means

Answer 38

``` larger variability (usually) however sometimes outliers overestimate this ```

Question 39

deviation

Answer 39

yᵢ - ȳ | The deviation of an observation from the mean

Question 40

positive vs negative deviation

Answer 40

positive means it is above the mean | negative means it is below the mean

Question 41

the set of all deviations

Answer 41

- all add to 0 - describes the variability - can square every deviation before summing them all up to make the deviations more useful as a number for calculations

Question 42

variance

Answer 42

s² = (Σ (yᵢ-ȳ)²) / (n-1) | where Σ has lower boundary i-1 and upper boundary n

Question 43

why is variance problematic?

Answer 43

It is measured in squared units which is not very interpretable on its own

Question 44

standard deviation

Answer 44

s square root of the variance most common measure of variability tells us how closely data is clustered around the mean measured in the same units as the original data

Question 45

when would s=0

Answer 45

when all observations have the same value

Question 46

what happens if s > 0

Answer 46

the standard deviation s increases as observations become more spread out / has greater variability

Question 47

when can/should we use standard deviation? why?

Answer 47

we should only use standard deviation and mean together neither of them are resistant to outliers, thus neither should be used if outliers are present and affecting them to be inaccurate

Question 48

IQR

Answer 48

interquartile range measure of variability resistant to outliers, ∴ goes with median divides the data into 4 equal sections ( quartiles

Question 49

percentile

Answer 49

the pth percentile is the value so that p% of the measurements fall below the pth percentile and (100-p)% are above it

Question 50

what is the median in percentile?

Answer 50

50%

Question 51

can 215 be p?

Answer 51

no, percentiles are always between 0-100

Question 52

Q₁

Answer 52

the lower quartile is the 25th percentile (separates 25% and 75% of measurements) median between measurements that fall below the overall median

Question 53

Q₃

Answer 53

the upper quartile is the 75th percentile ( separates the top 25% from the bottom 75%) median between measurements that fall above the overall median

Question 54

what is between Q₁ and Q₃?

Answer 54

the middle 50% of measurements that fall between Q₁ and Q₃

Question 55

IQR calculation

Answer 55

Q₃-Q₁

Question 56

if IQR is small

Answer 56

data is clustered around the center

Question 57

if IQR is large

Answer 57

data is scattered far from the center

Question 58

how do we choose a numerical summary?

Answer 58

1. draw a graph 2. use mean and standard deviation for reasonably symmetric data 3. use median and IQR for skewed data 4. If there are multiple modes try to understand why and consider splitting data into two groups 5. If using mean and standard deviation with outliers, report them with outliers present and removed

Question 59

five-number-summary

Answer 59

minimum, Q₁, median, Q₃, maximum

Question 60

boxplot

Answer 60

visual representation of data using the 5 number summary shows the center, spread, symmetry/skewness at the same time useful for comparing groups

Question 61

fences

Answer 61

upper fence = Q₃ + (1.5 x IQR) lower fence = Q₁ - (1.5 x IQR) measurements outside the fences are considered outliers

Question 62

whiskers

Answer 62

line drawn at the end of the box plot where the highest or lowest value is that is within the fences (not an outlier)

Question 63

far outliers

Answer 63

outliers that are farther than 3 IQRs from the quartiles

Question 64

appearance of boxplots

Answer 64

x___|-------|̲̅ ̅ ̲̲̲̅̅ ̲̅ ̲̅ ̲̅ ̲̅|̲̅ ̲̅ ̲̲̅̅ ̲̅|--------| | symbols for outliers, whiskers, box for the IQR and a line in the box for the median

Question 65

box plots that are skewed

Answer 65

symmetrical skewed right: median to the left of center and a long right whisker skewed left: median to the right of center and a long left whisker

Question 66

comparative box plots

Answer 66

draw two box plots in one graph to compare the data in two different categories

Question 67

time plot

Answer 67

used when interested in how the data behaves over time