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.
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
To calculate the five-number summary, follow below steps :
Sort the Data: Arrange the data points 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 \(( \mathrm{Q_3} )\):
Find the five number summary of the following data set
\(3, 7, 8, 4, 2, 9, 8, 6, 9, 4, 9, 3, 1, 4, 2, 9, 8, 6, 6, 9\)
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 \( \color{lightcoral} \text{1}, \text{3.5}, \text{6}, \text{8.5}, \text{9}\)
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.