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## Is this data Normally Distributed? Methods for Checking for Normality

many of our calculations and ap

statistics require normally distributed

data so here's a set of data this is the

weights of 50 strawberries and we're

gonna try to figure out if they're

approximately normally distributed and

we'll use a few different methods to do

this now the first thing we need to do

is input this data into our calculator

to do this press the stat button now

press enter on edit these are called

your list and in list 1 right here we're

going to type the weights of all 50

strawberries so each time you type a

weight just press ENTER and then you can

input the next weight

all right we got all the data in so the

first thing we should do is graph it and

look if it looks approximately normal

so to do this press 2nd and y equals

this is our stat plot menu and we're

gonna press ENTER on plot 1 so the first

thing we need to do is turn it on so we

can press ENTER and we're gonna go over

to histogram for type that's this third

option right here so it says what data

do you want to use list 1 that's where

we typed our strawberry weights for

frequency leave it as 1 because we're

gonna use each data value just once and

now I'm gonna push graph and not much

happened I see a tiny square right there

that's because our zoom settings aren't

that great

if you press zoom again and then go down

to option 9 so just zoom and the number

9 here's our histogram now looking at it

I don't see tremendous skew it doesn't

look perfectly normal but approximately

normally distributed so we're gonna

write down the histogram looks roughly

symmetric and unimodel

this is consistent with data that is

approximately normally distributed but

I'm not convinced yet let's run another

check if you press stat and you go over

to calculate choose 1-var stats'

now it says what do you want 1-var

stats' for list 1

you can leave frequency blank and when

you press calculate it's going to return

some statistics for us x-bar tells us

the mean of our 50 strawberry weights is

about 17 point two eight grams also our

standard deviation is approximately

three point seven if the data is

normally distributed the empirical rule

also known as the 68 95 99 point 7 rule

tells us that 68% of our strawberries

should be within one standard deviation

of the mean so let's check that our mean

is seventeen point two eight so if we

add and subtract one standard deviation

we get the interval thirteen point five

eight to 20 point nine eight

so our 68% of our strawberry weights

between these two values here's how we

check if you press stat again go down to

sort a we can use this to sort all of

our strawberry weights so we have to

tell it which list to sort so I'm going

to press second and one to access list

one when I press ENTER it says done so

I'm going to go back to stat and press

edit now all my strawberry weights are

in order so let's count how many are

between thirteen point five eight and

twenty point nine eight so none of these

okay thirteen point seven that's the

first value in excess of thirteen point

five eight so let's see how many are

between this value and twenty point nine

eight

so it turns out 32 strawberries are

between those weights so that's 64

percent that's pretty close to 68

percent so again the data looks roughly

normal you could also add and subtract

two standard deviations from the mean

and see if 95 percent of the

strawberries are within that interval

we're going to use one more method to

check if the data is approximately

normal if you press second and y equals

to get to the stat plot menu again on

plot one go over to the last option this

is a normal probability plot we're gonna

leave all these defaults as they are and

press zoom then the number nine all

right we got this plot as long as the

dots on this plot are roughly in a line

your data is roughly normally

distributed so all three of these checks

together I think it's fair to say the

strawberry weights are approximately

normally distributed

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