## Related questions with answers

Identify the five-number summary and determine the interquartile range.

$8,12,32,6,27,19,54$

Solutions

VerifiedA five-number summary of a data set consists of five points :

$\textbf{(1) }$ The lowest value of the data set (i.e., minimum)

$\textbf{(2) }$ $Q_{1}$ (first quartile)

$\textbf{(3) }$ The median

$\textbf{(4) }$ $Q_{3}$ (third quartile)

$\textbf{(5) }$ The highest value of the data set (i.e., maximum)

Hence five-number summary of a number is :

$\text{minimum , }Q_{1}\text{ , median , }Q_{3}\text{ , maximum}$

The minimum is 6.

The first quartile is the median of the data values below the median (or at 25% of the data):

$Q_1=8$

The median is the average of the middle scores:

$M=19$

The third quartile is at 75% of the data:

$Q_3=32$

The maximum is 54.

The IQR is the difference of the third and first quartile:

$IQR=32-8=24$

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