Introduction
In descriptive studies or during the preliminary analysis of a large data collection, a five-number summary is extremely useful. The most extreme values in the data set (the maximum and minimum values), the lower and upper quartiles, and the median make form a summary. Minimum value, lower quartile (Q1), median value (Q2), upper quartile (Q3), maximum value are all shown together and arranged from lowest to highest.
The median identifies the center of a data set; the upper and lower quartiles span the middle half of a data set; and the highest and lowest observations provide additional information about the actual dispersion of the data. These values were chosen to give a summary of a data set because each value describes a specific part of a data set and as a result, the five-number summary is a good spread indicator.
Five different numerical summaries can be compared. Two sets with similar means and standard deviations may have quite different five-number summaries, as we will see. A boxplot, often known as a box and whiskers graph, can be used to quickly compare two five-number summaries. A box and whisker plot is a diagram that represents a five-number summary. When we have multiple data sets to analyze, we create a five-number summary with a corresponding box and whisker plot for each.
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: Related topic here...How to Create a Box-and-Whisker's Plot using RExample: How to find the Five-Number Summary?
Consider the following hypothetical values: [15, 8, 16, 25, 16, 19, 23, 20, 16], determine the five number summary.
Solutions: First, arrange the data set from smallest to largets number, it follows:
The order list:[8, 15, 16, 16, 16, 19, 20, 23, 25], so the minimum value is 8 and the maximum value is 25.
Next step, calculate the median value, from the order list the middle value is 16, thus, 16 is the median.
Third, find the First Quartile (Q1) from the order list, the value is the average between the 2nd and the third order, i.e., (15+16)/2 = 15.5.
Fourth, calculate the 3rd Quartile (Q3) from the upper half of the order list, which is:
(20+23)/2 = 21.5
These gives us all the values for the five-number summary as follows:
min:8, Q1:15.5, Q2:16, Q3:21.5, max:25
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Related topic here...How to Create a Five Number Summary using RReferences:
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Thank you for reading! Any thoughts about five number summary and box plot. I'd love to hear your comment.
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