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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.

Q: Why is it impossible for the iqr to be bigger than the range?

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No, it is not possible.

an outlier can be found with this formula... Q3-Q1= IQR( inner quartile range) IQR*1.5=x x+Q3= anything higher than this # is an outlier Q1-x= anything smaller than this # is an outlier

You arrange the data set in ascending order. You then find the observation such that a quarter of the observations are smaller than it and three quarters are bigger. That value is the lower quartile. Next find the observation such that three quarters of the observations are smaller than it and a quarter are bigger. That value is the upper quartile. Upper quartile minus lower quartile = IQR.

the IQR is the third quartile minus the first quartile.

No. The IQR is found by finding the lower quartile, then the upper quartile. You then minus the lower quartile value from the upper quartile value (hence "interquartile"). This gives you the IQR.

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No, it is not possible.

Because the IQR excludes values which are lower than the lower quartile as well as the values in the upper quartile.

IQR = Inter Quartile RangeIQR = Inter Quartile RangeIQR = Inter Quartile RangeIQR = Inter Quartile Range

IQR = Inter-Quartile Range = Upper Quartile - Lower Quartile.

No, since range is max-min and IQR is Q3-Q1. Q1 must be greater than the max and Q3 must be less than the min.

an outlier can be found with this formula... Q3-Q1= IQR( inner quartile range) IQR*1.5=x x+Q3= anything higher than this # is an outlier Q1-x= anything smaller than this # is an outlier

You arrange the data set in ascending order. You then find the observation such that a quarter of the observations are smaller than it and three quarters are bigger. That value is the lower quartile. Next find the observation such that three quarters of the observations are smaller than it and a quarter are bigger. That value is the upper quartile. Upper quartile minus lower quartile = IQR.

The interquartile range (IQR) is a measure of variability, based on dividing a data set into quartiles. Quartiles divide a rank-ordered data set into four equal parts.

Iqr stands for inter quartile range and it is used to find the middle of the quartiles in a set of data. To find this, you find the lower quartile range and the upper quartile range, and divide them both together.

The IQR gives the range of the middle half of the data and, in that respect, it is a measure of the variability of the data.

the IQR is the third quartile minus the first quartile.

No. The IQR is found by finding the lower quartile, then the upper quartile. You then minus the lower quartile value from the upper quartile value (hence "interquartile"). This gives you the IQR.