Question

I am working on finding the IQR of a certain set of values. I have 1,000 different values in the data set.
I've calculated the mean - 674, median - 680 and mode - 632. The variance is 10,878, STD - 104 and IQR: Q1 - 595 and Q3 - 595. IQR = 156.


When evaluating what the IQR is telling me.... how do I compare this to the median of the data set? Are the values in the data set more spread out or more concentrated around the median? How do I explain this?

Answer 1

Median = 680 implies: 680 is the middle most item in the data. 50% of data values lie below 580. 50% of data values lie above 580.

First Quartile = Q1 implies that 25% of data values lie below Q1 and 75% of data values lie above Q1.

Third Quartile = Q3 implies that 75% of data values lie below Q3 and 25% of data values lie above Q3.

Interquartile Range = IQR = 156 is the range of the middle 50% of the data set.

Thus, Interquartile range is another measure of Dispersion like Standard Deviation. But, since IQR, like range, depends only on two values, it is not powerful as Standard Deviation which depends on all values of the data set.

Since IQR is not affected by extreme values and standard deviation is affected by extreme values, in data sets with outliers. IQR is better than standard deviation.