Most Prominent Methods of How to Find Outliers in Statistics

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What are outliers in statistics? Examples of
outliers in statistics How to find outliers in
statistics using the Interquartile Range
(IQR)? How to find the outliers in statistics
using the Tukey method? Specifications Conclusion
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A definition of outliers in statistics can be
considered as a section of data, which is used to
represent an extraordinary range from a piot to
another point. Or we can say that it is the data
that remains outside of the other given values
with a set of data. If one had Pinocchio within a
class of teenagers, his noses length would be
considered as an outlier as compared to the other
children.
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In the given set of random values, 5 and 199 are
outliers 5, 94, 95, 96, 99, 104, 105, 199 5 is
studied as an extremely low value whereas 199
is recognized as an extremely high value. But,
outliers are not always taken as these simple
values. Lets assume one accepted the given
paychecks in the last month 220, 245, 20,
230. Your average paycheck is considered as
130. But the smaller paycheck (20) can be
because that person went on holiday that is why
an average weekly paycheck is 130, which is not
an actual representation of their earned. Their
average is more like 232 if one accepts the
outlier (20) from the given set of data. That is
why seeking outliers might not be that simple as
it seems. The given data set might resemble as
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60, 9, 31, 18, 21, 28, 35, 13, 48, 2. One might
guess that 2 is an outlier and possibly 60. But
one predicts it as 60 is the outlier in the set
of data. Whiskers and box chart often represent
outliers
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However, one might not has a passage to the
whiskers and box chart. And if one does, the few
boxplots might not explain outliers. For
instance, the chart has whiskers which stand out
to incorporate outliers as That is why do
not believe in obtaining outliers in
statistics from the whiskers and a box chart. It
said that whiskers and box charts could be a
valuable device to present after one will be
determined what their outliers arethe efficient
method to obtain all outliers with the help of
the interquartile range (IQR). These IQR includes
the average amount of the data therefore,
outliers could quickly be determined once one
understands the IQR.
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An outlier is described as a data point that
ranges above 1.5 IQRs, which is under the first
quartile (Q1) or over the third quartile (Q3)
within a set of data. Low (Q1) 1.5 IQR High
(Q3) 1.5 IQR Sample Problem Find all of
the outliers in statistics of the given data set
10, 20, 30, 40, 50, 60, 70, 80, 90, 100. Step
1 Get the Interquartile Range, Q1(25th
percentile) and Q3(75th percentile). IQR 50 Q1
(25th percentile) 30 Q2 (50th percentile)
55 Q3 (75th percentile) 80 How to calculate IQR
of the above data set value Put all the data
values in order and mark a line between the
values to find Q1(25th percentile) and Q3(75th
percentile). Q1(10,20,30,40,50) Q2
(60,70,80,90,100)Find the median of Q1 and Q2,
which is 30 and 80.Subtract Q1 from Q2. 80-30
50IQR 50.
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Step 2 Multiply the calculated IQR with 1.5 that
has been obtained in Step 1 IQR 1.5 50 1.5
75. Step 3 Add the number of Step 2 to Q3
calculated in Step 1 75 80 155. It is
considered as an upper limit. Keep this number
away for a specific moment. Step 4 Subtract the
number which one has found in Step 2 from Q1 from
Step 1 30 50 -20. It is the lower limit. Put
the number aside for a moment. Step 5 Keep the
values from the data set in order 10, 20, 30,
40, 50, 60, 70, 80, 90, 100. Step 6 Include
these low and high values to the given data set
in order -20, 10, 20, 30, 40, 50, 60, 70, 80,
90, 100, 155. Step 7 Highlight a value above or
below the values that one has put in Step 6 -20,
10, 20, 30, 40, 50, 60, 70, 80,
90, 100, 155. Here is the method for how to find
outliers in statistics, and for this example, it
will be 100.
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The Tukey method to discover the outliers in
statistics applies the Interquartile Range to
separate very small or very large numbers. It is
the equivalent of the above method, but one might
examine the formulas which are composed slightly
different, and the specification is slightly
different. For instance, the Tukey method
utilizes the idea of fences. The specifications
are High outliers Q3 1.5(Q3 Q1) Q3
1.5(IQR) Low outliers Q1 1.5(Q3 Q1) Q1
1.5(IQR) Where Q1  first quartile Q2  middle
quartile Q3  third quartile IQR  Interquartile
range The above equations provide two values. One
can study a fence that can highlight the outliers
from the values included in the amount of the
data. Now, lets check how to find outliers in
statistics.
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Sample Problem Use Tukeys method to get the
value of outliers of the following
data  3,4,6,8,9,11,14,17,20,21,42. Step
1 Calculate the Interquartile range follow the
same procedure shown in the table as mentioned
above, which give the value as Q1 6
Q3 20 IQR 14 Step 2 Measure the
value of 1.5 IQR 1.5 IQR 1.5 14 21 Step
3 Subtract the value of Q1 to obtain the lower
fence 6 21 -15 Step 4 Sum the value to Q3
to obtain the upper fence 20 21 41. Step
5 Add these fences to the given data to get the
value of outliers -15, 3, 4, 6, 8, 9, 11, 14,
17, 20, 21, 41, 42. Anything which is outside the
fences is considered to be the outliers. For the
given data set, 42 is considered as an only
outlier.
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Several students face difficulty regarding how to
find outliers in statistics that is why we have
mentioned two different methods to calculate it.
Besides this, there are other advanced methods
too to get the value of outliers, such as Dixons
Q Test, Generalized ESD, and much more. Use the
above-mentioned IQR and Tukey method to solve the
problems of outliers values.
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