Calculator for calculating the five number summary of a data series
The five number summary is a way to show the statistical dispersion. This summary consists of the minimum, lower quartile, median, upper quartile, and the maximum. If data are placed in order, then the lower quartile is central to the lower half of the data and the upper quartile is central to the upper half of the data.
To perform the calculation, enter a series of numbers. Then click the 'Calculate' button.
Input format
The data can be entered as a series of numbers, separated by semicolons or spaces. You can enter the data as a list (one value per line). Or from a column from Excel spreadsheet by copy & paste
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How to find the five number summary for
2 5 4 8 3 7 9 3 1 6
Determine the amount of numbers by counting all of the numbers in the data set.
Amount of numbers n=10
Organize the data in increasing order
1 2 3 3 4 5 6 7 8 9
1 2 3 3 4 5 6 7 8 9
Minimum: 1
Maximum: 9
Position of the lower quartile in the data set:
\( \displaystyle \frac{1}{4}\cdot (n+1)=\frac{1}{4}\cdot(10+1)=2.75\)
The lower quartile is located at position 2.75, which is between the 2nd and 3rd numbers in the data set.
1 2 3 3 4 5 6 7 8 9
The Lower quartile = \(\displaystyle \frac{2+3}{2}=\color{blue}{2.5}\)
Position of the median in the data set:
\( \displaystyle \frac{2}{4}\cdot (n+1)=\frac{2}{4}\cdot(10+1)=5.5\)
The median is located at position 5.5, which is between the 5nd and 6nd numbers in the data set.
1 2 3 3 4 5 6 7 8 9
The Lower quartile = \(\displaystyle \frac{4+5}{2}= \color{blue}{4.5}\)
Position of the upper quartile in the data set:
\( \displaystyle \frac{3}{4}\cdot (n+1)=\frac{3}{4}\cdot(10+1)=8.25\)
The upper quartile is located at position 8.25, which is between the 8nd and 9nd numbers in the data set.
1 2 3 3 4 5 6 7 8 9
The upper quartile = \(\displaystyle \frac{7+8}{2}= \color{blue}{7.5}\)
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