5-Number+Summary+and+Box+Plots

5-Number Summary and Box Plots Back to Statistics Summary

=__5-Number Summary__ =

**__INTRODUCTION __** Using a 5-Number Summary is a helpful way to analyze data, especially when there is a large data set. Instead of using just mean, median, and mode to describe the data set, the 5-Number Summary spans the set of data using 5 different numbers: minimum value, lower quartile (Q1), median value (Q2), upper quartile (Q3), maximum value (in order of least to greatest). Each value specifies a different section or piece of the data, allowing it to be divided into four sections, each containing 25% of the data set given. **__THE NUMBERS __** *The set of data **//must//** be organized from least to greatest for the 5-Number Summary to be effective* <span style="font-family: Tahoma, Geneva, sans-serif;">

<span style="font-family: Tahoma, Geneva, sans-serif;"> <span style="font-family: Tahoma,Geneva,sans-serif;"><span style="font-family: Tahoma, Geneva, sans-serif;"><span style="font-family: Tahoma,Geneva,sans-serif;"><span style="font-family: Tahoma, Geneva, sans-serif;"> <span style="font-family: Tahoma, Geneva, sans-serif;"><span style="font-size: 115%; font-family: Tahoma, Geneva, sans-serif;">**__EXAMPLE__** <span style="color: rgb(98,20,210);"><span style="font-size: 115%; font-family: Tahoma, Geneva, sans-serif;"> **Set {1, 2, 4, 4, 4, 5, 8, 9, 11, 13, 13} Minimum Value = 1 Median = 5 Finding the Median first is helpful because it divides the data set in two halves: The lower half contains {1, 2, 4, 4, 4} (use this set to find Q1) The upper half contains {8, 9, 11, 13, 13} (use this set to find Q3) Q1 = 4 Q3 = 11 Maximum Value = 13**

<span style="font-size: 115%; font-family: Tahoma, Geneva, sans-serif;"> =<span style="font-size: 115%; font-family: Tahoma, Geneva, sans-serif;">__**Box Plots**__ =

<span style="color: #6214d2; font-family: Tahoma, Geneva, sans-serif;"> Box Plots are used to form a visual summary of the 5-Number Summary Key points about the box plot: - The box contains 50% of the data set - Upper Hinge (of the box): shows 75th percentile of the data set (Q3) - Lower Hinge (of the box): shows 25th percentile of the data set (Q1) - Upper Hinge - Lower Hinge =  <span style="font-family: Tahoma, Geneva, sans-serif;"> Inter-Quartile Range <span style="font-family: Tahoma, Geneva, sans-serif;"> - Minimum value - maximum value = the range -  Line between the two boxes of the large box: median (Q2) *if the line is not equidistant from the Q1 and Q3 hinges, the data is skewed. To grasp the meaning of "skewed" check out histograms  * - The box's whiskers represent the minimum and maximum values - The points outside the whiskers are suspected outliers Using the data from the 5-Number Summary above, we will construct a box plot. Median = 5 Q1 = 4 Q3 = 11 Maximum Value = 13**
 * Minimum Value = 1

Comparing box plots is also a useful way to visualize two sets of data.

What can we learn from this graph of box plots? - The top box plot has a larger data set than the bottom box plot. - Although the medians are generally close, the middle 50% of data for each box plot differs greatly.

For help with using a graphing calculator to visualize box plots, use this site: http://wind.cc.whecn.edu/~pwildman/statnew/new_page_14.htm