Find the median, first quartile, third quartile, interquartile range, and any outliers for each set of data. 14.6, 28.1, 3.9, 7.1, 5.3, 30.9, 2.8, 6.5, 20.8, 16.4, 16.4, 27.1, 53.5, 12.5, 6.1

First, to find the median, we have to order all numbers, from least to highest:

Now, we calculate the position of each quartile:

So, the first quartile is in the fourth position, the thirds quartile is in the twelfth position:

So, first quartile is 6.1. Second quartile is 14.6, and the third quartile is 27.1.

It's important to remember that the second quartile is the median. So the median is 14.6

Lastly, the interquartile range is the difference between the third and first quartile. So:

Therefore, the interquartile range is 21.

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is