The outlier formula designates outliers based on an upper and lower boundary (you can think of these as cutoff points). Any value that is 1.5 x IQR greater than the third quartile is designated as an outlier and any value that is 1.5 x IQR less than the first quartile is also designated as an outlier.
What is the formula for Q1 and Q3?
There are four different ways to calculate quartiles: Lower quartile (Q1) = N 1 multiplied by (1) divided by (4) Middle quartile (Q2) = N 1 multiplied by (2) divided by (4) Upper quartile (Q3) = N 1 multiplied by (3) divided by (4)
What is the formula for IQR?
The formula for the interquartile range is the first quartile less the third quartile: IQR = Q 3 – Q 1.
What is the IQR rule for outliers?
Finding Outliers Using the Interquartile Rule Multiply the interquartile range (IQR) by 1.5 (a constant used to identify outliers), add 1.5 x (IQR) to the third quartile, and consider any value higher as a possible outlier.
For example, if you specify a multiple of 1.5, the outlier boundaries are 1.5 standard deviations above and below the mean or median of the values in the outlier field. To position the boundaries, you can specify any positive multiple of the outlier fields standard deviation: 0.5, 1, 1.5, and so on.
What is an outlier example?
A value that lies outside (is significantly smaller or larger than) most of the other values in a set of data. For instance, both 3 and 85 are outliers in the scores 25, 29, 3, 32, 85, 33, 27 and 28.
Why is an outlier 1.5 IQR?
When scale is set to 1.5, the IQR Method considers any data that deviates by more than 2.7 standard deviations (SD) from the mean , on either side, to be outliers. This decision range is the closest to what the Gaussian Distribution tells us, which is 3 sd.
What Z-score is an outlier?
Any z-score that is greater than 3 or less than -3 is typically regarded as an outlier, which is roughly equivalent to the standard deviation method. Typically, z-score =3 is considered as a cut-off value to set the limit.
How do you find outliers using IQR?
Finding Outliers Using the Interquartile Rule Calculate the interquartile range for the data, multiply it by 1.5 (a factor used to identify outliers), add 1.5 x (IQR) to the third quartile, and any value higher than this is likely an outlier.
How do you find outliers in a normal distribution?
To calculate the outlier fences, do the following:
- Take your IQR and multiply it by 1.5 and 3. We'll use these values to obtain the inner and outer fences.
- Take the Q1 value and take the two values from step one and subtract them to calculate the inner and outer lower fences.
- Calculate the upper fences on the inside and outside.
Bivariate data (data with two variables) outliers can be easily identified using a scatter plot because they will be located far from the majority of the points on the scatter plot.
Using the data points (3, 5, 7, 8, 9), | (11, 15, 16, 20, 21), Q1 is the median (the middle) of the lower half of the data, and Q3 is the median (the middle) of the upper half of the data.
Any data point in a data set that is more than 1.5 IQRs above or below the first quartile (Q 1) or the third quartile (Q 3) is referred to as an outlier. High = (Q 3) 1.5 IQR.
When analyzing a box plot, an outlier is a data point outside the whiskers of the box plot, such as outside 1.5 times the interquartile range (Q1 – 1.5 * IQR or Q3 1.5 * IQR) above the upper quartile and below the lower quartile.
Fences are typically found using the following formulas: Upper fence = Q3 (1.5 * IQR) Lower fence = Q1 – (1.5 * IQR) Fences separate outliers from the majority of data in a set.
To check for outliers in SPSS:
- Analyze > Descriptive Statistics > Explore
- Select variable (items) > move to Dependent box.
- Click Statistics >
- In Output window: Go to Boxplot > Look at circles and *.
- There may be outliers in your dataset if there are circles or an asterisk (*).
The Statistical Way
- Sort the data in the column in ascending order (smallest to largest) in Step 1.
- Step 2: Quartiles There are three quartiles that divide any ordered range of values into four equal groups.
- 3rd Step: Inner and External Fences.
In a sense, this definition leaves it up to the analyst (or a consensus process) to decide what will be considered abnormal. An outlier is an observation that lies an abnormal distance from other values in a random sample from a population.