Find Median in this data set
12 65 3 8 23 64 19 53 0 24 57 15 39. with explanation pls!

23

Step-by-step explanation:

12, 65, 3, 8, 23, 64, 19, 53, 0, 24, 57, 15, 39

First put in order.

0, 3, 8, 12, 15, 19, 23, 24, 39, 53, 57, 64, 65

Eliminate each number alternating from beginning and end like so.

3, 8, 12, 15, 19, 23, 24, 39, 53, 57, 64

Keep doing until you get to the middle.

8, 12, 15, 19, 23, 24, 39, 53, 57

12, 15, 19, 23, 24, 39, 53

15, 19, 23, 24, 39

19, 23, 24

23

Since 23 is the last remaining number, that is the median.

let's add {f(x)=x+1}f(x)=x+1 and {g(x)=2x}g(x)=2x together to make a new function.

f(x)+g(x) =(x+1)+(2x)=x+1+2x=3x+1

let's call this new function hh. so we have:

{h(x)}={f(x)}+{g(x)}{=3x+1}h(x)=f(x)+g(x)=3x+1

we can also evaluate combined functions for particular inputs. let's evaluate function hh above for x=2x=2. below are two ways of doing this.

method 1: substitute x=2x=2 into the combined function hh.

h(x)

h(2)

​    

=3x+1

=3(2)+1

=7

​ since h(x)=f(x)+g(x)h(x)=f(x)+g(x), we can also find h(2)h(2) by finding f(2) +g(2)f(2)+g(2).

first, let's find f(2)f(2):

f(x)

f(2)

​    

=x+1

=2+1

=3

​  

now, let's find g(2)g(2):

g(x)

g(2)

​    

=2x

=2⋅2

=4

​  

so f(2)+g(2)=3+4=\greend7f(2)+g(2)=3+4=7.

notice that substituting x =2x=2 directly into function hh and finding f(2) + g(2)f(2)+g(2) gave us the same answer!