The interquartile range, or IQR, is the range of a collection of data in the middle half. The interquartile range is a measure of variation that is calculated using the upper and lower quartiles. The upper quartile (UQ) or Q3 is the median of the upper half of a set of data. The lower quartile (LQ) or Q1 is the median of the lower half of a set of data. A set of data is divided in half by its median. The quartiles are the values in a piece of data that divide it into four equal portions. The following are some examples of common relative dispersion methods: This metric compares values without the use of units.
When comparing the distribution of two or more data sets, relative measures of dispersion are used. Mean and mean deviation:- The mean is the arithmetic mean of the absolute deviations of the observations from a measure of central tendency, and the mean deviation is the arithmetic mean of the absolute deviations of the data from a measure of central tendency (also called mean absolute deviation).Standard deviation:- the square root of the variance is known as standard deviation.Variance: – The variance is calculated by subtracting the mean from each data point in the set, then squaring and adding each square, and lastly dividing them by the total number of values in the data set.The range of observation is the term used to describe the outcome. Range:- The difference between the highest and lowest observation could also be characterized as the range.Some of the types of absolute measures of dispersion are:. It includes terms such as range, standard deviation, and quartile deviation, among others. The absolute dispersion approach expresses changes as the average of observed deviations, such as standard or means deviations. Generally, there are two methods by which we can measure the dispersion of the data i.e.Īn absolute measure of dispersion consists of the same unit as the original data set is used in an absolute measure of dispersion. In simple words, it indicates whether the variable is squeezed or distributed. to determine how homogeneous or heterogeneous the data is. Measures of dispersion are used in statistics to interpret data variability, i.e. In other words, dispersion aids in the comprehension of data distribution. The extent to which numerical data is likely to vary around an average value is referred to as statistical dispersion. The state of being distributed or spread is known as dispersion. The difference here is that the range of a collection of data is calculated by subtracting the sample maximum and minimum values. The difference between the largest value and the smallest values in a set of data is known as the range in statistics. In statistics, the range denotes the dispersion of observations. 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 difference between the highest and lowest observation could also be characterized as the range. 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 Given a set of data ordered from smallest to largest, It can also be used to find outliers in a set of data. has many outliers) because it excludes extreme values. The IQR is particularly useful when data is contaminated (e.g. Thus, the IQR is comprised of the middle 50% of the data, and is therefore also referred to as the midspread, or middle 50%. 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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