No, interquartile range cannot be for any data. The lower quartile for data must be used below the lower quartile.
In statistics, a quartile is a type of quantile that divides a data set into four equal parts, each containing 25% of the data. For example, if you have a set of test scores, the first quartile represents the score below which 25% of the scores fall. Understanding quartiles helps in analyzing the distribution and spread of data.
If the result is 1.5 x Inter Quartile Range (or more) above the Upper Quartile or 1.5 x Inter Quartile Range (or more) below the Lower Quartile.
In a dataset, the interquartile range (IQR), which is the range between the first quartile (Q1) and the third quartile (Q3), contains 50% of the data. This means that 25% of the data lies below Q1, 50% lies between Q1 and Q3, and another 25% lies above Q3. Therefore, the percentage of data that lies between Q1 and Q3 is 50%.
Since the set of data is arranged in numerical order, first we need to find the median (also called the second quartile), which separates the data into two equal groups, in our case there are 6 numbers in each group.54 65 66 68 73 75 | 75 78 82 82 87 97The first quartile (also called the lower quartile) is the middle value of numbers that are below the median, in our case is 67.54 65 66 | 68 73 75 | 75 78 82 82 87 97The third quartile (also called the upper quartile) is the middle value of numbers that are above the median, in our case is 82.54 65 66 | 68 73 75 | 75 78 82 | 82 87 97The interquartile range is the difference between the first and third quartiles, which is 15, (82 - 67).
Outliers are typically found in the first and fourth quartiles, outside the interquartile range (IQR). Specifically, any data point that falls below Q1 - 1.5 × IQR or above Q3 + 1.5 × IQR is considered an outlier. Therefore, outliers can exist in both the lower and upper extremes of the data distribution.
By definition a quarter of the observations are below the lower quartile and a quarter are above the upper quartile. In all, therefore, half the observations lie outside the interquartile range. Many of these will be more than the inter-quartile range (IQR) away from the median (or mean) and they cannot all be outliers. So you take a larger multiple (1.5 times) of the interquartile range as the boudary for outliers.
Consider the data: 1, 2, 2, 3, 4, 4, 5, 7, 11, 13 , 19 (arranged in ascending order) Minimum: 1 Maximum: 19 Range = Maximum - Minimum = 19 - 1 = 18 Median = 4 (the middle value) 1st Quartile/Lower Quartile = 2 (the middle/median of the data below the median which is 4) 3rd Quartile/Upper Quartile = 11 (the middle/median of the data above the median which is 4) InterQuartile Range (IQR) = 3rd Quartile - 1st Quartile = 11 - 2 = 9
One definition of outlier is any data point more than 1.5 interquartile ranges (IQRs) below the first quartile or above the third quartile. Note: The IQR definition given here is widely used but is not the last word in determining whether a given number is an outlier. IQR = 10.5 â?? 3.5 = 7, so 1.5. IQR = 10.5.
If the result is 1.5 x Inter Quartile Range (or more) above the Upper Quartile or 1.5 x Inter Quartile Range (or more) below the Lower Quartile.
The upper quartile is the 75% point of the variable. That is, it is the point with 75% of the observations below it and 25% of the observations above it. The upper quartile is the upper 25% of the data.
First quartile is the value below which 25 % (one-fourth) of the cases fall.
A quartile divides a distribution into four equal parts, each containing 25% of the data. The first quartile (Q1) represents the value below which 25% of the data fall, the second quartile (Q2) is the median, and the third quartile (Q3) is the value below which 75% of the data fall.
The upper quartile is the 75% point of the variable. That is, it is the point with 75% of the observations below it and 25% of the observations above it.
Since the set of data is arranged in numerical order, first we need to find the median (also called the second quartile), which separates the data into two equal groups, in our case there are 6 numbers in each group.54 65 66 68 73 75 | 75 78 82 82 87 97The first quartile (also called the lower quartile) is the middle value of numbers that are below the median, in our case is 67.54 65 66 | 68 73 75 | 75 78 82 82 87 97The third quartile (also called the upper quartile) is the middle value of numbers that are above the median, in our case is 82.54 65 66 | 68 73 75 | 75 78 82 | 82 87 97The interquartile range is the difference between the first and third quartiles, which is 15, (82 - 67).
A quartile deviation from some specified value, is the value or values such that a quarter of the observed values fall between these values and the specified value. Usually, but not always, the specified value is the median - the value such that have the observed values are below (and above) it. In that case, one quartile values will have a quarter of the values below it and the other will have a quarter of the values above it. The quartile deviations will be the differences between median and the two quartiles just calculated.
A range of data is split into 4 parts.0-25%25-50%50-75%75%-100%being above the 25% quartile means that 25% of all tested or categorized subjects are below the person in question.
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