Question

What are the minimum, first quartile, median, third quartile, and maximum of the data set? 2, 13, 17, 14, 9, 3, 16, 12

Answer 1

So before anything, rearrange the data so that it's in ascending order: {2,3,9,12,13,14,16,17}

Next, the minimum and maximum are as they seem: the smallest and largest numbers in the data. Looking at our data, 2 is our minimum and 17 is our maximum.

Next, to find the median, find the number that is in the middle of the data set. If there isn't one number in the middle, find the average of the two middle numbers to get your median:

$\{2,3,9,\overbrace{\boxed{12,13,}}^{\textsf{middle numbers}}14,16,17\}\\\\\frac{12+13}{2}\\\\\frac{25}{2}\\\\12.5$

The median is 12.5.

Next, to find the first quartile, or the lower quartile, find the "median" of the numbers to the left of the median.

$\overbrace{\{2,\boxed{3,9,}12,}^{\textsf{left of median}}13,14,16,17\}\\\\\frac{3+9}{2}\\\\\frac{12}{2}\\\\6$

The first quartile is 6.

Next, to find the third quartile, or the upper quartile, find the "median" of the numbers to the right of the median.

$\{2,3,9,12,\overbrace{13,\boxed{14,16,}17\}}^{\textsf{right of median}}\\\\\frac{14+16}{2}\\\\\frac{30}{2}\\\\15$

The third quartile is 15.