Outliers are values below Q 1-1.5(Q 3-Q 1) or above Q 3+1.5(Q 3-Q 1) or equivalently, values below Q 1-1.5 IQR or above Q 3+1.5 IQR. A very popular method is based on the following: There are several methods for determining outliers in a sample. When there are outliers in a sample, the median and interquartile range are used to summarize a typical value and the variability in the sample, respectively. When there are no outliers in a sample, the mean and standard deviation are used to summarize a typical value and the variability in the sample, respectively. The same approach is used in the upper half to determine the third quartile ((77+81)/2=79). There are 4 values in the lower half, the first quartile is the mean of the 2 middle values in the lower half ((64+64)/2=64). When the sample size is 9, the median is the middle number 72. The quartiles are determined in the same way looking at the lower and upper halves, respectively. The median and quartiles are indicated below.įigure 10 - Interquartile Range with Odd Sample Size When the sample size is odd, the median and quartiles are determined in the same way. Suppose in the previous example, the lowest value (62) were excluded, and the sample size was n=9. There are 5 values below the median (lower half), the middle value is 64 which is the first quartile. There are 5 values above the median (upper half), the middle value is 77 which is the third quartile. The interquartile range is 77 – 64 = 13 the interquartile range is the range of the middle 50% of the data. The interquartile range is defined as follows:įor the sample (n=10) the median diastolic blood pressure is 71 (50% of the values are above 71, and 50% are below). The quartiles can be determined in the same way we determined the median, except we consider each half of the data set separately.įigure 9 - Interquartile Range with Even Sample Size When a data set has outliers, variability is often summarized by a statistic called the interquartile range, which is the difference between the first and third quartiles. The first quartile, denoted Q 1, is the value in the data set that holds 25% of the values below it. The third quartile, denoted Q 3, is the value in the data set that holds 25% of the values above it. The quartiles can be determined following the same approach that we used to determine the median, but we now consider each half of the data set separately. If you want to know more about statistics, methodology, or research bias, make sure to check out some of our other articles with explanations and examples.When a data set has outliers or extreme values, we summarize a typical value using the median as opposed to the mean. NoteTo get a clear idea of your data’s variability, the range is best used in combination with other measures of variability like interquartile range and standard deviation. It can’t tell you about the shape of the frequency distribution of values on its own. Although we have a large range, most values are actually clustered around a clear middle.īecause only two numbers are used, the range is easily influenced by outliers. In the example above, the range indicates much more variability in the data than there actually is. With an outlier, our range is now 42 years. Using the same calculation, we get a very different result this time: Range example with an outlierOne value in your data set is replaced with an outlier. One extreme value in the data will give you a completely different range. When paired with measures of central tendency, the range can tell you about the span of the distribution.īut the range can be misleading when you have outliers in your data set. The range generally gives you a good indicator of variability when you have a distribution without extreme values. Then subtract the lowest from the highest value.ĭiscover proofreading & editing How useful is the range? Participantįirst, order the values from low to high to identify the lowest value ( L) and the highest value ( H). Range exampleYour data set is the ages of 8 participants. This process is the same regardless of whether your values are positive or negative, or whole numbers or fractions. Subtract the lowest value from the highest value.Order all values in your data set from low to high.The range is the easiest measure of variability to calculate. You can calculate the range by hand or with the help of our range calculator below. Frequently asked questions about the range.
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