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One can define an upper quartile for a population and a upper quartile for a sample.
Population: Let X be a random variable. The the upper population quartile is the value, x, for which Prob { X <=x } = 0.75. Or, in words, the probability of drawing a value from the population that is less than its upper quartile is 0.75, by definition.
Sample: Let x1,x2, ... xn be a sample drawn independently from the same population. Sort them from smallest to largest to form the so-called order statistics: x(1), x(2), ... x(n). For simplicity let's assume that n=100. Then the smallest three-quarters of the values are x(1), x(2), ... x(75), and we would call x(75) the upper sample quartile. If you had only ten values, say, then you might use some value between x(7) and x(8) as the sample upper quartile. For this and other reasons the sample quartile may only be useful where large samples are involved.
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Formula calculating lower quartile?
lower quartile = 1/4(n+1) upper quartile = 3/4(n+1) where n is the number of the values. Obviously the values have to be ordered from the lower to the higher: the number you'll get is the position in this order. Let's say you get 4 for your lower quartile, it means that the 4th value is your lower quartile.
Why is it impossible for the iqr to be bigger than the range?
By definition, a quarter of the observations are at most as large as the lower quartile. Therefore it is possible to have an observation, X, which is smaller than the lower quartile, L. That is X <= L Again, by definition, a quarter of the observations are at least as large as the lower quartile. Therefore it is possible to have an observation, Y, which is larger than the upper quartile, U. That is U <= Y So X <= L <= U <= Y Therefore U - L <= Y - X That is, the IQR must be less than or equal to the range.
What is data which is more than 1.5 times the inter quartile range away from the quartiles?
These are sometimes considered outliers but there is no formal definition for them.
When should you throw out an outliers?
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.
Who do you work out the upper and lower quartile?
you do work out the upper and lower quartile
Inter quartile range?
the interquartile is just subtracting the high quartile from the low quartile. * * * * * No, it is subtracting the lower quartile from the higher quartile.
Can IQR be negative?
No. The upper quartile, by definition, must be at least as large as the lower quartile.
What is the definition for upper quartile in mathematics?
it is the top 25% of the data
What is the Definition of lower quartile?
in a set as such {2,3,4,5,6,7,8,}, 5 would be the median, 7 would be the upper quartile, and 3 would be the lower quartile. The lower quartile divides the lower half of a set of data into two equal parts
Where online can one find a definition of the word 'quartile'?
The website known as businessdictionary, the website known as thefreedictionary and the merriam-webster website all offer a definition of the word quartile. Which is an equal four way division of an object or time period for example the first quartile of the year is January, February and March.
Formula calculating lower quartile?
lower quartile = 1/4(n+1) upper quartile = 3/4(n+1) where n is the number of the values. Obviously the values have to be ordered from the lower to the higher: the number you'll get is the position in this order. Let's say you get 4 for your lower quartile, it means that the 4th value is your lower quartile.
What is the definition to box and whisker plot?
A data display that organizes data values into four parts using the lower extreme,lower quartile,median,upper quartile,and upper extreme.
Is the median greater than the first quartile?
By definition yes. The median is the number which is exactly in the middle of a set of numbers. The first quartile is the point where 25% of the numbers are to the left, and 75% of the numbers are to the right.
Why is it impossible for the iqr to be bigger than the range?
By definition, a quarter of the observations are at most as large as the lower quartile. Therefore it is possible to have an observation, X, which is smaller than the lower quartile, L. That is X <= L Again, by definition, a quarter of the observations are at least as large as the lower quartile. Therefore it is possible to have an observation, Y, which is larger than the upper quartile, U. That is U <= Y So X <= L <= U <= Y Therefore U - L <= Y - X That is, the IQR must be less than or equal to the range.
How do you find the inter quartile range?
Subtract the lower quartile from the upper quartile.
What is the math term for IQR?
IQR = Inter Quartile RangeIQR = Inter Quartile RangeIQR = Inter Quartile RangeIQR = Inter Quartile Range
How do you finde iqr?
IQR = Inter-Quartile Range = Upper Quartile - Lower Quartile.
