Q&A for How to Calculate Outliers

The range can never truly be negative. If your interquartile range is negative, you subtracted the upper quartile from the lower quartile. To correct this, either subtract the lower quartile from the upper quartile, or multiply your current answer by -1.

Find the median of the data (if it is a singular number, do not include this in either side) and separate into two groups. Then, find the median of each group. The first median is quartile 1 (Q1) and the second is quartile three(Q3). Use the general formula (Q3 - Q1) to find the interquartile range.

1.5 is always used to multiply the IQR to find the fences. This is because the definition of an outlier is any data point more than 1.5 IQRs below the first quartile or above the third quartile. And 3 is just 1.5 doubled.

All measures of central tendency are influenced by outliers, but median is affected the least. For example, if the median is 5 and the number above it is 6, it doesn't matter if you have another number that is 7 or if that number is 300. Because median is mostly about how many numbers are on each side, an outlier wouldn't affect it any more then any other number.

In stats, you use 1.5.

It's okay to have your lower outlier as a negative, just calculate it the same way.

Probably not. Let's say your data set is 4000 systolic blood pressure measurements. In most studies, just to prevent the problem with human measurement errors, the blood pressure will be reported as the mean of two samples. This reduces human error greatly. Some systolic pressures are going to be way more than 200mmHg, while others are way lower than 100mmHg. Trust your summary statistics and then do some graphics.

An outlying value is a value X such that either is, X>upper quartile+1.5x (upper quartile-lower quartile), Xupper quartile+3.0x (upper quartile-lower quartile) or X.

With large amounts of data, it is possible to have multiple outliers, but it can be quite difficult to identify them as they are more likely to fall at the center of the quartiles.

Yes, it can (depending on how small the sample size is). If the sample size is 4+, then yes.

Yes, you can achieve this by using the Descriptive Statistics option under Data Analysis in Excel 2016.

To find the UQ and LQ (sometimes refereed to as Q1 and Q3), you must first find the median. The median is basically the middle [median-middle]. For example, in the sequence "1 2 3 5 6 8 9 13 15," 6 is in the middle. You can cut it into sections to begin the process, like [1 2 3 5] {6} [8 9 13 15]. The six is not counted in the process. For the first section, [1 2 3 5], would would add 2 and 3 and then divide the answer by 2, giving you 2.5. In the sequence [8 9 13 15], you would do the same with 9 and 13, giving you 11. Therefore, Q1:2.5 and Q3:11.

When your data set has outliers (extreme values), you summarize the data using the median instead of the mean because it isn't susceptible to extreme values. The mean and standard deviation are the preferred statistics when your data is normal.

The easiest way is to run summary statistics using statistical software. The mean and standard deviation is preferred for data, but if you need to know about outliers, it's best to do summary stats using software.

You would do it the same way that you would if you had only integers. Just make sure that you do the decimal multiplication correctly.

Then your already know them. If a number in your data does not fit between the lower fences, it is a minor outlier, if it does not fit between the upper fences, it is a major outlier.

When finding outliers, multiply the IQR by 1.5. Then subtract that value from your Q1 and add it to your Q3. Any number higher than your Q3 or lower than your Q1 is considered an outlier.

Look for the data values that are more than 3 standard deviations away from the mean in either direction.