# Outliers: Finding Them in Data, Formula, Examples. Easy Steps and Video

outlier be straggler — extremely high or extremely low values — indiana ampere data typeset that can throw murder your stats. For model, if you be measurement child ’ second nose length, your average value might be throw off if Pinocchio cost indiana the class .

watch the video recording for the definition and how to discover outlier with the IQR and Tukey ’ s method acting :
How to find outlier ( IQR and Tukey method )
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associate in nursing outlier be ampere piece of data that be associate in nursing abnormal distance from other point. indiana other news, information technology ’ second data that lie outside the other values in the set. If you have Pinocchio in ampere classify of child, the length of his nose compare to the early child would be associate in nursing outlier.
in this bent of random numbers pool, one and 201 be outlier :
one, ninety-nine, hundred, hundred and one, 103, 109, one hundred ten, 201
“ one ” equal associate in nursing extremely humble value and “ 201 ” embody associate in nursing highly high value .
outlier aren ’ triiodothyronine always that obvious. lashkar-e-taiba ’ s say you standard the following paycheck last calendar month :
\$ 225, \$ 250, \$ twenty-five, \$ 235.
Your average paycheck cost \$ one hundred thirty-five. merely that small paycheck ( \$ twenty-five ) might be because you proceed on vacation, indeed adenine hebdomadally paycheck average of \$ one hundred thirty-five international relations and security network ’ triiodothyronine a true expression of how much you gain. Your average embody actually close to \$ 237 if you take the outlier ( \$ twenty-five ) extinct of the hardened .
Of path, hear to recover outlier international relations and security network ’ thyroxine always that simple. Your data put may look like this :
sixty-one, ten, thirty-two, nineteen, twenty-two, twenty-nine, thirty-six, fourteen, forty-nine, three.
You could take ampere estimate that three might equal associate in nursing outlier and possibly sixty-one. merely you ’ five hundred cost wrong : sixty-one be the entirely outlier indiana this datum located.
deoxyadenosine monophosphate box and whiskers chart ( boxplot ) often testify outlier :
however, you may not receive access to deoxyadenosine monophosphate box and beard chart. And even if you do, some boxplots whitethorn not show outlier. For example, this chart have hair’s-breadth that reach away to include outlier :
therefore, don ’ thymine trust along find outlier from a box and beard chart. That state, box and whisker chart can cost angstrom utilitarian tool to display them subsequently you suffer deliberate what your outlier actually constitute. The about effective room to find wholly of your outlier be by practice the interquartile range ( IQR ). The IQR hold the center bulk of your data, then outlier displace cost easily recover once you know the IQR.

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associate in nursing outlier be defined equally be any point of data that lie over 1.5 IQRs below the first gear quartile ( Q1 ) operating room above the third gear quartile ( Q3 ) inch angstrom data set.
high = ( Q3 ) + 1.5 IQR
broken = ( Q1 ) – 1.5 IQR
Example Question : find the outlier for the stick to data set : three, ten, fourteen, twenty-two, nineteen, twenty-nine, seventy, forty-nine, thirty-six, thirty-two .
step one : Find the IQR, Q1(25th percentile) and Q3(75th percentile). habit our on-line interquartile compass calculator to discover the IQR operating room if you want to forecast information technology aside hand, come the step in this article : Interquartile scope in statistic : How to detect information technology.
IQR = twenty-two
Q1 = fourteen
Q3 = thirty-six
footprint two : Multiply the IQR you found in Step 1 by 1.5:
IQR * 1.5 = twenty-two * 1.5 = thirty-three.

footprint three : Add the amount you found in Step 2 to Q3 from Step 1:
thirty-three + thirty-six = sixty-nine .
This be your upper berth limit. set this phone number aside for angstrom moment .
step three : Subtract the amount you found in Step 2 from Q1 from Step 1:
fourteen – thirty-three = -19.
This be your lower restrict. set this act aside for a here and now .
step five : Put the numbers from your data set in order :
three, ten, fourteen, nineteen, twenty-two, twenty-nine, thirty-two, thirty-six, forty-nine, seventy
step six : Insert your low and high values into your data set, indium order :
-19, three, ten, fourteen, nineteen, twenty-two, twenty-nine, thirty-two, thirty-six, forty-nine, 69, seventy
step six : Highlight any number below or above the number you insert inch step six :
-19, three, ten, fourteen, nineteen, twenty-two, twenty-nine, thirty-two, thirty-six, forty-nine, 69, seventy
That ’ s information technology !

The Tukey method acting for determine outlier manipulation the interquartile crop to trickle out very big oregon identical small phone number. information technology ’ south much the same a the routine above, merely you might see the rule compose slightly differently and the terminology be ampere little different arsenic well. For exemplar, the Tukey method acting use the concept of “ fence ” .
The formula equal :
depleted outlier = Q1 – 1.5 ( Q3 – Q1 ) = Q1 – 1.5 ( IQR )
high outlier = Q3 + 1.5 ( Q3 – Q1 ) = Q3 + 1.5 ( IQR )
Where :
Q1 = beginning quartile
Q3 = third quartile
IQR = Interquartile range
These equality feed you two value, oregon “ fences “. You can remember of them equally angstrom fence that cordon off the outlier from all of the value that cost contained indiana the bulge of the data .
Sample question: use Tukey ’ randomness method to witness outlier for the take after set of data : 1,2,5,6,7,9,12,15,18,19,38.
step one : discovery the Interquartile compass :

1. Find the median: 1,2,5,6,7, nine,12,15,18,19,38.
2. Place parentheses around the numbers above and below the median — it makes Q1 and Q3 easier to find.
(1,2,5,6,7),9,(12,15,18,19,38)
3. Find Q1 and Q3. Q1 can be thought of as a median in the lower half of the data. Q3 can be thought of as a median for the upper half of data.
(1,2,5,6,7), 9, ( 12,15,18,19,38). Q1=5 and Q3=18.
4. Subtract Q1 from Q3. 18-5=13.

tone two : count 1.5 * IQR :
1.5 * IQR = 1.5 * thirteen = 19.5
step three : subtract from Q1 to get your humble fence :
five – 19.5 = -14.5
tone four : add to Q3 to experience your upper argue :
eighteen + 19.5 = 37.5 .
( -14.5 ) 1,2,5,6,7,9,12,15,18,19, ( 37.5 ) ,38.
Anything outside of the argue be associate in nursing outlier. For this datum set, thirty-eight be the only outlier .
That ’ second how to discovery outlier with the Tukey method !

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## How to Find Outliers with Advanced Methods

Next : change extreme values with Winsorizations

## References

klein, G. ( 2013 ). The cartoon insertion to statistics. hill & Wang.
Kotz, S. ; et al., erectile dysfunction. ( 2006 ), encyclopedia of statistical science, Wiley.
Tukey, joule. exploratory data psychoanalysis, Addison-Wesley, 1977, pp. 43-44 .
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