Finding IQR

[Pages:2]Finding IQR

Sadly, we have 2 ways to compute IQR in STAT 216. We compute it using the text book/Pearson online book way, and we do it the TI-83 or 84 way. They are similar, but a little different. Jeff has told us we will be using the "text book" way. It is shown below, from page 53.

Let me list, in order, some (odd number, n=5) of data: 2 4 6 9 12 To find the median, we cross out each value of data from each end, until we meet in the middle. Since we have an odd number of data we will have only a single middle, the 6, which is our median. To obtain the Q1 value, we find the median of the lower half, INCLUDING the median. So, the median of the front half is from 2 4 6, which gives Q1=4. In a similar way, the median of the last half of data, INCLUDING the median is 6 9 12, making Q3=9. This is how the book does the median for an odd number of data. Now let us do an even number of data, say 2 4 6 9 12 15. Again counting from the ends and working to the middle, we have 2 middle numbers, 6 and 9, so the median is the average of those. So, the median = (6+9)/2 = 7.5 . With an even number of data we have the front half and back half divided up equally. So, the median of the front half, which is 2 4 6 is 4=Q1and the back half, which is 9 12 15 has a median of 12=Q3.

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So, during tests, etc. don't rely on your calculator to find the 5 number summary correctly for you, when you have an odd number of data to find the IQR from. Best to do the Q1 and Q3 of this odd numbered set of data "by hand", so you don't get it wrong. Note that if the number in the data set is even, then the TI and book are in agreement on the Q1 and Q3 computation, therefore in the calculation of IQR. Lastly, it is important to remember that the IQR of any data set, when you report it, is a quantitative value, therefore it is NUMBER WITH UNIT. Don't forget to say the units when reporting the numbers. Also, remember that the IQR (as well as the range) is a SINGLE VALUED STATISTIC. For example, the IQR would not be from "24 inches to 36 inches", or "the IQR is 36 inch ? 24 inch". The IQR is 12 inches in this case--a single value,as opposed to a "from...to..." value.

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