Range+and+Interquartile+Range


 * Range and Interquartile Range:**

Range is the difference between the highest and lowest value in a set of data; this number helps describe how spread out the values of data are. However, range can sometimes be misleading if there is an outlier in the set of data. If a set of data has a high standard deviation, it may mean that the range does not accurately depict the content of the data because of the outliers. In order to more accurately describe a pool of data, mathematicians often utilize interquartile range (which eliminates outliers) instead of range.

To understand interquartile range, we should first explain the world “quartile.” A median is a number value that divides numerically numbered set of data exactly in half. So in this series of numbers: 10, 10, 11, 12, 13, 14, 15, 16, 18, 21, 22 the median is 14. The median is represented by the abbreviation Q2.


 * 10 10 11 12 13 __14__ 15 16 18 21 22 **

If we were to further divide the group of numbers to the left of the median (Q2), the number that would divide the lower half of the data into two halves is known as the lower quartile. (Q1). So in the example below, 11 is the lower quartile (Q1).


 * 10 10 __11__ 12 13 14 15 16 18 21 22 **

By the same token, the upper quartile (Q3) divides the upper set of data into two equal halves. In our example, 18 is the upper quartile (Q3).


 * 10 10 11 12 13 14 15 16 __18__ 21 22 **

These three numbers are quartiles because they divide the set of data into four parts, or quarters.

So, the interquartile range would be the difference between the upper and lower __quartiles__, while range is merely the difference between the highest number and the lowest number in a set of given data.

The difference between upper and lower quartiles (Q3–Q1), which is called the interquartile range, also indicates the dispersion of a data set. The interquartile range spans 50% of a data set, and eliminates the influence of outliers because, in effect, the highest and lowest quarters are removed.

For further explanation on the quartiles and medians of sets, check out this link to the 5-number summary.

*Note: when trying to find range or interquartile range, remember to arrange the set of data in numerical order before finding the median, quartiles, range, and interquartile range.


 * Example Problems:**

Find the lower quartile and upper quartile of the following numbers. 12, 5, 22, 30, 7, 36, 14, 42, 15, 53, 25

a. 14;34 b. 17;43 c. 12;36 d. 12;35 e.14;36

What is the interquartile range of the following numbers. 12, 5, 22, 30, 7, 36, 14, 42, 15, 53, 25, 65

a. 60 b. 26 c. 36 d. 28 e. 65

http://www.statcan.gc.ca/edu/power-pouvoir/ch12/5214890-eng.htm#a2
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