![]() ![]() Values that lie farther than 1.5 times the IQR away from either end of the IQR (Q1 or Q3) are considered outliers, as shown in the figure below:Īnything outside the above range of values is an outlier. The IQR can be used to find outliers (values in the set that lie significantly outside the expected value). IQR = 37.5 - 7.5 = 30 Using the IQR to find outliers Thus, the interquartile range can be calculated as: Averaging the terms in those positions yields Q1 and Q3: Thus, Q1 lies between the 3rd and 4th element in the set, and Q3 lies between the 9th and 10th elements. The decimal values indicate that the quartile lies between the elements closest to the value. Where n is the number of terms in the set. The following formulas can be used to determine the position of the quartiles in the set ![]() It indicates the spread of the middle 50 of the data. The distance between the first and third quartilesthe interquartile range (IQR)is a measure of variability. Given a set of data ordered from smallest to largest, If n (3 / 4) is an integer, then the third quartile is the mean of the numbers at positions n (3 / 4) and n (3 / 4) + 1. It can also be used to find outliers in a set of data. The formula to determine whether or not a population is normally distributed are: Q 1 ( z 1 ) + X Q 3 ( z 3 ) + X Where Q 1 is the first quartile, Q 3 is the third quartile, is the standard. has many outliers) because it excludes extreme values. Use the interquartile range formula with the mean and standard deviation to test whether or not a population has a normal distribution. The IQR is particularly useful when data is contaminated (e.g. In summary, the range went from 43 to 69, an increase of 26 compared to example 1, just because of a single extreme. The interquartile range is 45 - 25.5 19.5. Thus, the IQR is comprised of the middle 50% of the data, and is therefore also referred to as the midspread, or middle 50%. The upper quartile is the mean of the values of data point of rank 6 + 3 9 and the data point of rank 6 + 4 10, which is (43 + 47) ÷ 2 45. It is equal to the difference between the 75th and 25th percentiles, referred to as the third (Q3) and first quartiles (Q1), respectively. In statistics, the interquartile range (IQR) is a measure of how spread out the data is. ![]() Home / probability and statistics / descriptive statistics / interquartile range Interquartile range ![]()
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