While the Standard Deviation indicates the spread or cluster of data about the Mean value, Quartiles and Percentiles are used to perform a similar function to estimate the dispersion around the Median value. You can estimate the dispersion around the Median in two ways:
 Mathematically: calculate the InterQuartile Range (see below)
 Graphically (e.g: spatial distribution on a map):
 Locate the Median Center (not very precise)
 Visualize the InterQuartile Area (more precise) (see below)
 Calculate the Index of Dispersion to measure the dispersion you see on the map (see below)
InterQuartile (or Percentile) Range (IQR)
This is a simple and quickly obtained measure of dispersion, but is a much coarser (less precise) one than the standard deviation.
Use Excel, or the method below:
The data must be ranked and divided into four groups called quartiles, each containing 25% of the values. The quartile containing the top 25% values is the upper quartile, while the one with the bottom 25% values is the lower quartile:
The InterQuartile Range IQR = Q3  Q1. A high IQR means the data is very dispersed, while a low IQR means the data is less dispersed.
Note that the listings may be divided into any number of equal parts each containing the same number of percentage of the number of values. In this case the categories are called percentiles. The IQR is then called the InterPercentile Range.
Example: the SAT scores of a group of students are given below, ranked from best to worse:
1800 1790 1770 1750 1720 1700 1700 1650 1600 1540 1320 1200 1200 1180 1100
Q0 (minimum value) = 1100
Q1 (25% of values are below this number) = 1260
Q2 (median value) = 1650
Q3 (25% of values are above this number) = 1735
Q4 (maximum value) = 1800
IQR = Q3  Q1 = 1735  1260 = 475
The IQR can then be compared to another set of students to assess the dispersion of the sample.
Quartiles are frequently represented using boxplot (or "boxandwhiskers") graphs. Follow the steps indicated below to create boxandwhiskers graph on Excel 2007.
Use Excel, or the method below:
The data must be ranked and divided into four groups called quartiles, each containing 25% of the values. The quartile containing the top 25% values is the upper quartile, while the one with the bottom 25% values is the lower quartile:
 Q0 is the minimum value
 Q1 is the value between the lower and 2nd quartile (25% of the values in the sample are below)
 Q2 is the value between the 2nd and 3rd quartile, which is also the Median value (50% of the values in the sample are above/below this value)
 Q3 is the value between the 3rd and 4th quartile (25% of the values in the sample are above)
 Q4 is the maximum value
The InterQuartile Range IQR = Q3  Q1. A high IQR means the data is very dispersed, while a low IQR means the data is less dispersed.
Note that the listings may be divided into any number of equal parts each containing the same number of percentage of the number of values. In this case the categories are called percentiles. The IQR is then called the InterPercentile Range.
Example: the SAT scores of a group of students are given below, ranked from best to worse:
1800 1790 1770 1750 1720 1700 1700 1650 1600 1540 1320 1200 1200 1180 1100
Q0 (minimum value) = 1100
Q1 (25% of values are below this number) = 1260
Q2 (median value) = 1650
Q3 (25% of values are above this number) = 1735
Q4 (maximum value) = 1800
IQR = Q3  Q1 = 1735  1260 = 475
The IQR can then be compared to another set of students to assess the dispersion of the sample.
Quartiles are frequently represented using boxplot (or "boxandwhiskers") graphs. Follow the steps indicated below to create boxandwhiskers graph on Excel 2007.

Steps to create a boxandwhiskers graph on Excel 2007:
 List the values of the sample in column A (they do not have to be ranked in order) (here the same SAT scores as above are used)
 Insert the formula listed in cells B1 thru B5 into cells C1 thru C5 to calculate the values needed for the graph
 Select cells B2 thru B4 (yellow), click "insert" and select "column charts": select the 2nd 2D column chart from the left (=stacked bar graph)
 In the tab "Design", click "switch row/column" to obtain a vertical stacked bar graph
 Boxes: select and delete the key and the horizontal axis of the graph, and select. Point your mouse to the bottom box of the bar graph, right click and select "Format Data Series" (or use the pulldown selection menu on the top left under the "Format" tab): under the "Fill" category, select "No Fill" to make the bottom box "invisible". Select the upper two boxes and do the same thing, but instead of "no fill", choose a common color for both boxes (in this example, yellow). You can also use the "Format Data Series" function to format the border style/color of the boxes
 Bottom whisker: select the "invisible" bottom box (the one with "no fill"), click on the "Layout" tab, then in "error bars" (under "Analysis). At the bottom of the pulldown menu, select "more error bars options": under "display", select "minus" and under "error amount", click on "custom" and "specify value". Do not change the "positive error value" and select cell C1 (blue) for the "negative error value".
 Top whisker: select the top (yellow) box, click on the "Layout" tab, then in "error bars" (under "Analysis). At the bottom of the pulldown menu, select "more error bars options": under "display", select "minus" and under "error amount", click on "custom" and "specify value". Do not change the "negative error value" and select cell C5 (red) for the "positive error value". Done!
InterQuartile Area (Q) and Index of Dispersion (Id)
This graphic method is more precise than the Median Center.
It is a variation of the principle above which can be used to
illustrate the distribution of phenomena spatially (e.g.
clustering/dispersion of rural settlements or of highrises in a CBD).
It serves a similar function to the Nearest Neighbor Analysis
but is quicker and easier to operate, although the results are coarser
(less precise). IMPORTANT: there must be a MINIMUM of 8 observed points
in the sample for this method to work.
Method:
* If there is an odd number of points: the midpoint is at point (n+1)/2 by counting left to right (horizontal) or bottom to top (vertical)
1 = maximum dispersal from the central point
Formula: Id = Q / A (Q = InterQuartile Area, A = total area mapped)
In the example below, with 9 points, if the map is 10 cm x 6 cm, Q = approx. 15 sq cm., and Id = 15/60 = 0.25 (=moderate concentration).
Method:
 Mark the location of the observed points (e.g. highrises in a CBD) onto a base map (see sample below) and define the boundaries as you would for the Nearest Neighbor Analysis.
 Count up and number the total number of points (n) from the left to the right of the diagram.
 The horizontal and vertical midpoints are defined as follows:
* If there is an odd number of points: the midpoint is at point (n+1)/2 by counting left to right (horizontal) or bottom to top (vertical)
 Draw a red line vertically through the horizontal midpoint (ie: counting from the left), and draw a red horizontal line through the vertical midpoint (ie: counting down from the top). Note: these two midpoints are not necessarily the same point on the diagram. You should now have an equal number of points on both side of the horizontal line, and on both side of the vertical line.
 Using the same principle for determining the midpoints, divide the map up into 16th by drawing two more (green) lines vertically and two more (green) lines horizontally. Again, you should have an equal number of points in each vertical section (or quartile), and in each horizontal section (or quartile).
 The InterQuartile Area (Q) is the shaded area of the rectangle formed in the center of the base map. Use a ruler to calculate the size and area of the rectangle Q. A small Q suggests clustering while a large Q suggest dispersal.
 It is possible from this method to derive a simple Index of Dispersion (Id) which relates to the dispersal points in relation to a central point, and is useful to compare the dispersal/clustering of two sets of points.
1 = maximum dispersal from the central point
Formula: Id = Q / A (Q = InterQuartile Area, A = total area mapped)
In the example below, with 9 points, if the map is 10 cm x 6 cm, Q = approx. 15 sq cm., and Id = 15/60 = 0.25 (=moderate concentration).