Chapter 2 Statistics

Front 1

stem and leaf plot

Back 1

Put stems on left side and leaves on right in ascending order

Be sure to put a null if a stem doesn't have the value

Front 2

back-to-back stem and leaf

Back 2

for two sets of data

stem goes in middle and put leaves on either side

Front 3

skewed left (negatively skewed)

Back 3

mean is less than median

the mean is being made less because of too many lower values

most of the higher frequencies appear on the right, however

Front 4

skewed right (positively skewed)

Back 4

mean is more than the median

most of the higher frequencies appear on the left, however

Front 5

frequency table

Back 5

a set of data against their associated frequencies

Front 6

frequency distribution

Back 6

shows all of the variables and their associated outcomes (frequencies)

Front 7

probability distribution

Back 7

the frequency divided by the total number of outcomes

relative frequency

Front 8

cumulative frequency

Back 8

add up each frequency along the way (down the column)

the total should be the total of all the data

Front 9

cumulative relative frequency

Back 9

the cumulative frequency over the total amount of outcomes

the end result should be 1

Front 10

bar chart (qual)

Back 10

used for qualitative data with their associated frequencies (much like a frequency table)

x= outcomes

y= frequency

bars do not touch

Front 11

pareto chart (qual)

Back 11

much like a bar chart, but you order it in descending order (highest to lowest frequencies)

Front 12

pie chart (qual)

Back 12

each piece corresponds to a relative frequency of each outcome

to find percent: frequency/total

to find degree: percent*360

Front 13

pictogram (qual)

Back 13

each picture corresponds to a fixed value (frequency of outcomes)

Front 14

contingency table (qual)

Back 14

a frequency table of two-way data

has one variable (color) with two separate frequencies (male and female preference)

Front 15

tree diagram (qual)

Back 15

represents the relationship between multi-stage outcomes

Front 16

how to make the best graph

Back 16

1. include title

2. label each axis

3. use proper scaling

Front 17

histogram (qual and quant)

Back 17

much like a bar graph, except the bars touch

shows the frequency/probability distribution

width of bars: class width

height of bars: frequency

Front 18

parts of a histogram

Back 18

1. tolerance & number of classes

2. class width

3. class width

4. class boundaries

5. class marks (midpoints)

Front 19

how to calculate tolerance

Back 19

the level of decimal precision in the measure data

19.53 = 0.01

120 = 1

Front 20

how to determine class width

Back 20

divide range by class and round up based on tolerance

or

look at the distance between each LCL and UCL and add one tolerance

Front 21

how to determine class limits (LCL and UCL)

Back 21

start by calculating all the LCL

1. the first LCL is the min

2. add a class width to each previous LCL to obtain the rest

now calculate the UCL

1. subtract one tolerance to the 2nd LCL

2. add a class width to each previous UCL to obtain the rest

Front 22

how to determine class marks

Back 22

add each LCL and UCL and divide by 2

Front 23

how to determine class boundaries

Back 23

subtract 1/2 tolerance to each LCL

add 1/2 tolerance to each UCL

Front 24

how to create histogram

Back 24

mark each end of the bars using the class bounds

mark the midpoint for each corresponding bar

make sure they all touch (only time they don't is if theres a freq of 0)

plot against their frequency (or cumulative if asked)

Front 25

ogive graph (quant)

Back 25

plots the cumulative frequencies of the variables

a line graph

Front 26

how to construct an ogive graph

Back 26

start with 0, and use the class boundaries (UCB) corresponding to a said frequency

then take the cumulative frequency of the net UCB, and so on

the last data point should be the total of all the outcomes

Front 27

box plot (quant)

Back 27

uses the five-number summary

{min, Q1, median, Q3, max}

Front 28

constructing a box plot

Back 28

1. Put the data in ascending order

2. Find the minimum and maximum

3. Compute the median

4. Compute Q1 and Q3

5. Construct the plot using the information found in the previous steps

Front 29

outliers

Back 29

if not bell-shaped, an outlier is found by:

[(Q1 – 1.5*IQR),(Q3 + 1.5*IQR)]

Front 30

interquartile range

Back 30

found by subtracting Q3 to Q1

Front 31

scatter plot

Back 31

represents 2 variable data (bivariate) using a rectangular coordinate plane (x,y)

lets us see how one variable relates to another

line of best fit is often fashioned into the data