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A8. Boxplot

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hi we are now on the second graphical

analysis tool

and this time we will have box plot

box plot is also known as box plot and whiskers

whiskers

box plot is defined as a graphical

method of displaying variation

in a set of data in most cases

a histogram analysis provides a

sufficient display

but a box and whisker plot can provide

additional detail

while allowing multiple sets of data to

be displayed in the same graph

like histogram this falls under the data

distribution tools

but unlike histogram box plot can give

us an idea of central tendency

and dispersion better if you want to compare

compare

data sets and their measures of central tendency

tendency

and this per shot at the same time you

can actually use

box plot this is my personal favorite

because i have done so many things using

box plot and i have established a system

using a box plot that i can share with

you on the next section

now let's study the anatomy of a box

plot a box plot

technically divides the data set into four

four

partitions this partitions is called a quartile

quartile

just like how a year is being divided

into four

which we call a quarter now for every quartile

quartile

there is 25 percent of data set within it

now if we will divide a part into four

we will have a four

quartile meaning four 25 percent of

partition each the first partition is called

called

the first quartile wherein 25

of the data is located the second is the

second quartile

for the second quartile it would be 25

and another 25 which is 50 of the data

within it it is also known as the median

one of the central tendency measure

next is the third quartile third

quartile so we have to add another 25

percent from our second quartile so this is

75 of the data within it

and the last will be the fourth quartile

which is the 100

partition which means 100 of the data is

within this number

now we we can actually detect outlier

denoted by an asterisk symbol whenever

you are using

the box plot if the tails of what we

call the whiskers

this one and this one cannot contain

the data value the very high or very low

data value

then boxplot will tag it as an outlier

or an unusual observation if you can

still remember our study about central

tendency measures

mean is susceptible to outliers that is why

why

we are using median when we are using

box plot as our graphical analysis tool

in box plot central tendency is based on

the median

and dispersion is based on what we call

the inter-quartile range or

iqr iqr is the difference of the third quartile

quartile

and the first quartile practically speaking

speaking

if we have a greater amount of iqr

we have a greater picture of the box

and we have and if we have the greater

picture of the box or greater span of

the box

there is a higher amount of variation present

present

now if we want to check on the smaller

amount of variation

we're looking for smaller size of boxes

smaller the size of the box the smaller

the amount of the variation

so let's put it into practice we have to

go to minitab again

but before that let's go to our

worksheet and

copy energy okay so from worksheet we

have to copy here

the same dataset that we use in our

histogram case study

so this is again energy cost now we want

to check the distribution of the energy cost

cost

and uh using box plot

we have to click graph and then

find box plot here it is click box plot

now we have again simple y here one

column with one data so we will be using

this one

upper left we have to double click

and what is the variable data

energy cost double left click after that

we have to click ok

drag your worksheet down a little and

then adjust so you can see

now we have a box plot of distribution

of the energy cost

you can see here on the left side or the y-axis

y-axis

it's the value or data values of your

energy cost

so you don't have anything on your

x-axis because it's energy cos

as a function of the particular x-axis

but for now

it's black now how to read this you can

actually get the values of the quartiles

and everything that you want to know

about the box plot by putting your

mouse cursor on top of your box plot

so it revealed that first quartile is

197.5 percent

second quarter armenian is 320 third

quartile is 447.5

the iqr is 250 the whiskers

spans from 7 to 7 to 676

and the data values that we have is

25 data points now how to

interpret it only says that there is 25

of data that is equal to or less than 197

197

percent and the remaining 75 percent

is more than that value for median

it only says that there are 50 percent

of data above

and below that number because it's the midpoint

midpoint

now talking about the third quartile 447.5

447.5

there is 75 percent of data below that number

number

and the remaining 25 on top of that number

number

that is how we use the data and the

quartile values

as we use box plot in order for us to analyze

analyze

our data set and our data set has no

missing values nor it has no outlier

because we don't see any asterisk on the

chart that has been

created here say we have

a target value let's say our target value

value

is 300 now

let's put a reference line so

we have to right click here and then

click edit graph okay so this

graph will will appear then you have to

right click and then add

now we will be adding a reference line

why because we want to check whether

where are we as against our target so a

reference line could help us

visualize that so we want to

put a value of a reference line at y

value so

let's click 300 as mentioned

and then click ok and there will

appear a 300 here now click ok

for you to apply that now if we have a

target of 300 how can we answer the

question of how much of the data points

is already meeting

the 300 target so because this is cause

we want

lower the better again we have to

put our cursor on the box plot so we can

see the value of the median

so the closest value is the median okay

so you will be using the closest

value of the quartile in interpreting

for this case closer to 300 is

the median which is 320 using an

estimation based on the visual

output or the graphical output of our

box plot

we can say that almost 50 percent of the data

data

is actually meeting the target of 300

based on the median

so that is how we can use box plot to

interpret the results

of our data as we visualize them moving

forward you can use box plot

to check the distribution of your data

set as against your target

to check your process capability on how capable

capable

are you in meeting the target so you

will so you will have an idea or understanding

understanding

of how much is the problem that you are facing

facing

based on historical data now let's take

another example

this time we will use the same data set

from instagram

the fertilizer problem but now using

box plot so now let's go to our

i have to create a new worksheet i have

to close this one

and then paste it

now we will have to create a box plot

for this case study

we have to go to graph and then

box plot earlier we use

simple y because we have one column of

data but

we now have three columns of data so we

have to choose

the lower left which corresponds to

multiple y

then i have to click okay now i have to

repeat the same process

highlight c1 drag down and then select

make sure that all of the data variables

are here

if it's already there you have to click ok

for you to generate the chart and then

you have your chart already

now let's move this and interpret

so as you can see this is now a

representation of

the previous data set that we have

regarding fertilizer

you can see here on the y-axis we have

the data

which is the plant height in centimeters

for the three conditions that we have

we have none grow fast and super bland

now as mentioned using a box plot

central tendency is given on using the

median so median remember median is the line

line

inside the box so these are the median

okay for this person it is

the height of the box so this

height this height of the boxes

now if you are asked to check which has the

the

highest amount of central tendency

and because this is to put context this

plant height so we want higher the

better so zero

to higher value so we're asking for

a central tendency measure or median

which is closer to

the upper part of this chart which is 40

on this particular axis

now which has the highest amount of

median among the three

okay so we have grow fast so we can check

check

for none the median is 18. for rufus the

median is 25.5

and for super plant the median is 21.

therefore the highest median

is yes grow fast

okay so that's for measure of sensual tendency

tendency

how about four measures of this person

we have to check on which has the smallest

smallest

box so which has a smallest box

using visual judgment we have

grow fast again we can check using what

yes iqr so iqr

for none it's eight for growfus

it's 6.25 and for

super plant it's eight therefore the smallest

smallest

amount of variation can be found in

grow fast because it has the smallest iqr

iqr

and visually speaking it has the smallest

smallest

size of the box okay so therefore

you can use box plot if you want to

compare categories of data

it should be continuous data your y is

continuous data because these are your x's

x's

plant height in terms of

condition of whether there is fertilizer

or no fertilizer so again y

is continuous and x is categorical

so if you have that kind of data set

therefore you can use this

for your data analysis or your root

cause analysis

moving forward you will be using box

plot as you prove

your root cause analysis in your case study

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A8. Boxplot