Chapter #7 - 10/04/24

Question 1

what is an outlier ?

Answer 1

is a data point that is significantly different from the other data points in a dataset. It stands out because it is much higher or lower than the majority of the values.

Question 2

what are the four kids of useful information about a set of qantitative data ?

Answer 2

1) center (typical or average value)
2) unusual values (outliers)
3) variability
4) shape

Question 3

what is a stemplot ?

Answer 3

quick and easy way to order numbers and get picture of shape and outliers

Question 4

what is a histogram ?

Answer 4

better for larger data sets, also provides picture of shape and outliers

Question 5

how big should a good stemplot be? how many stems ?

Answer 5

6-15

Question 6

how do you create a stemplot ?

Answer 6

1) create and define the stems
2) attach the leaves

Question 7

what does “splitting stems” mean ?

Answer 7

reusing digits two times

Question 8

define “shape” in regards to defining a common language about shape ?

Answer 8

Are most values clumped in middle with values tailing off at each end? Are there two distinct groupings? Pictures of data will provide this info

Question 9

define “symmetric” :

Answer 9

if draw line through center, picture on one side would be mirror image of picture on other side

Question 10

define “unimodal” :

Answer 10

single prominent peak

Question 11

define “bimodal” :

Answer 11

two prominent peaks

Question 12

define “skewed to the right” :

Answer 12

higher values more spread out
than lower values

Question 13

define “skewed to the left” :

Answer 13

lower values more spread out and higher ones tend to be clumped

Question 14

define “pressence of outliers” :

Answer 14

refers to the existence of data points in a dataset that are significantly different or distant from the majority of the other observations

Question 15

define the units : with the example 3.4 …. which is the leaf anf which is the stem ?

Answer 15

stem = 3
leaf = 4

Question 16

how to create a histogram ?

Answer 16

1) Divide range of data into intervals
2) Count how many values fall into each interval
3) Draw bar over each interval with height = count (or proportion)

Question 17

what are the 3 nummerical summaries ?

Answer 17

1) center (typical or average value)
2) unusual values (outliers)
3) variability

Question 18

what is “mean” :

Answer 18

The average of a set of numbers

Question 19

what is “median” :

Answer 19

The middle value of a set of numbers when they are arranged in order

Question 20

what is “mode” :

Answer 20

The number that appears most frequently in a set of numbers

Question 21

what term is the best summary we can have in regards to outliers ?

Answer 21

median

Question 22

how to find the mean ?

Answer 22

You find it by adding all the numbers together and then dividing by how many numbers there are

Question 23

how to find the median ?

Answer 23

If there’s an even number of values, the median is the average of the two middle numbers

Question 24

how to find mode :

Answer 24

here can be one mode, more than one mode, or no mode at all if no number repeats

Question 25

what are outliers ?

Answer 25

values far removed from rest of data

Question 26

what is variability ?

Answer 26

how spread out are the values? a score of 80 compared to mean of 76 has different meaning if scores ranged from 72 to 80 versus 32 to 98

Question 27

if a graph is skewed to the right what does that mean for mean and median ?

Answer 27

mean > median

Question 28

if a graph is skewed to the left what does that mean for mean and median ?

Answer 28

mean < median

Question 29

if a graph is symmetric what does that mean for mean and median ?

Answer 29

mean and median are apprximately simmilar

Question 30

If a distribution is skewed to the left,

a) the mean is less than the median
b) the mean and median are equal
c) the mean is greater than the median

Answer 30

a) the mean is less than the median

Question 31

define “lowest” :

Answer 31

minimum

Question 32

define “highest” :

Answer 32

maximum

Question 33

define “median” :

Answer 33

number such that half of the values are at or above it and half are at or below it (middle value or average of two middle numbers in ordered list)

Question 34

define “quartiles” :

Answer 34

medians of the two halves

Question 35

how to create a boxplot ?

Answer 35

1) Draw horizontal (or vertical) line, label it with values from lowest to highest in data
2) Draw rectangle (box) with ends at quartiles
3) Draw line in box at value of median
4) Compute IQR (interquartile range) = distance between quartiles.
5) Compute 1.5(IQR); outlier is any value more than this distance from closest quartile.
6) Draw line (whisker) from each end of box extending to farthest data value that is not an outlier (If no outlier, then to min and max)
7) Draw asterisks to indicate the outliers

Question 36

how to interpret boxplots ?

Answer 36

• divide the data into fourths
• easily identify outliers
• useful for comparing two or more groups