Five number summary calculator :
The five number summary calculator is used to find the five number i.e Minimum number, First quartile \((
\mathrm{Q_1} )\), Median \(( \mathrm{Q_2} )\), Third quartile \(( \mathrm{Q_3} )\), Maximum number and
outlier of the
given data set with detailed solution.
What is five number summary
The five number summary consist of minimum number, first quartile \(( \mathrm{Q_1} )\), median \((
\mathrm{Q_2} )\), third quartile \(( \mathrm{Q_3} )\) and
maximum number
How to calculate five number summary
To calculate the fivenumber summary, follow below steps :
Sort the Data: Arrange the data points in ascending order.
Identify the Minimum and Maximum Values:
 Minimum: The smallest value in the dataset.
 Maximum: The largest value in the dataset.
Calculate the Median \(( \mathrm{Q_2} )\):
 If the number of data points is odd, the median is the middle value.
 If the number of data points is even, the median is the average of the two middle values.
Determine the First Quartile \(( \mathrm{Q_1} )\):
 \(( \mathrm{Q_1} )\) is the median of the lower half of the data ( dont include the overall median if
the number of data
points is odd).
Determine the Third Quartile \(( \mathrm{Q_3} )\):
 \(( \mathrm{Q_3} )\) is the median of the upper half of the data ( dont include the overall median if
the number of data
points is odd).
Example:
Find the five number summary of the following data set
\(3, 7, 8, 4, 2, 9, 8, 6, 9, 4, 9, 3, 1, 4, 2, 9, 8, 6, 6, 9\)
Solution:
First we arrange the data in ascending order
\(1, 2, 2, 3, 3, 4, 4, 4, 6, 6, 6, 7, 8, 8, 8, 9, 9, 9, 9, 9\)
Minimum number :
The minimum number is the smallest value in given data.
Therefore, The minimum number is \( \color{lightcoral} \text{1}\)
First quartile :
The first quartile (\(\mathrm{Q_1}\)) is the middle value in the lower half of the data in ascending order
Lower half of the data is \( 1, 2, 2, 3, 3, 4, 4, 4, 6, 6\)
Since there are an even number of observation, the median will be the average of the two middle values i.e
\(\text{3}\) and \(\text{4}\).
\( \begin{align} \mathrm{Q_{1}} &= \mathrm{\frac{ \text{3}+\text{4}}{2}} \\ &=\text{3.5} \end{align} \)
The first quartile is \( \color{lightcoral} \text{3.5}\)
Median :
The median (\(\mathrm{Q_{2}} \)) is the the middle value in ascending order.
Since there are an even number of observation, the median will be the average of the two middle values i.e
\(\text{6}\) and \(\text{6}\).
\( \begin{align} \mathrm{Q_{2}} &= \mathrm{\frac{ \text{6}+\text{6}}{2}} \\ &=\text{6} \end{align} \)
The median is \( \color{lightcoral} \text{6}\)
Third quartile :
The third quartile (\(\mathrm{Q_{3} } \)) is the middle value in the upper half of the data in ascending
order
The upper half of the data is \(6,7,8,8,8,9,9,9,9,9\)
Since there are an even number of observation, the median will be the average of the
two middle values. The two middle values are \(\text{8}\) and \(\text{9}\).
\( \begin{align} \mathrm{Q_{3}} &= \mathrm{\frac{ \text{8}+\text{9}}{2}} \\ &=\text{8.5} \end{align} \)
The third quartile is \(\text{8.5}\)
Maximum number :
The maximum number is the largest value in given data.
The maximum number is \(\text{9}\)
The five number summary is \( \color{lightcoral} \text{1}, \text{3.5}, \text{6}, \text{8.5},
\text{9}\)
References:
Outlier using five number summary calculator
Our five number summary calculator helps you to identify outliers in your data set using the Interquartile
Range (IQR) method. Outliers are data points that are significantly different from the majority of the data.
They can affect the results of statistical analyses and need to be investigated further.
How to determine an outlier
 Sort the data in ascending order.
 Identify the minimum and maximum values.
 Calculate the median (\(\mathrm{Q_{2}} \)).
 Determine the first quartile (\(\mathrm{Q_{1}} \)).
 Determine the third quartile (\(\mathrm{Q_{3}} \)).

Calculate the Interquartile Range (IQR):
 \(\mathrm{ IQR = Q_{3} Q_{1} } \)

Determine the Lower and Upper Boundaries:
 Lower Bound: \(\mathrm{ Q_1 1.5 \times IQR } \)
 Upper Bound: \(\mathrm{ Q_3 +1.5 \times IQR } \)

Identify Outliers:
 Any data points below the lower bound or above the upper bound are considered outliers.
References: