Answer:
[tex]110 = \text{median}[/tex]
Step-by-step explanation:
We can see that there are:
[tex]\rightarrow \ \ \text{1 "x" on 70} \ \ \ \rightarrow \ \ 70}[/tex]
[tex]\rightarrow \ \ \text{1 "x" on 80} \ \ \ \rightarrow \ \ 80}[/tex]
[tex]\rightarrow \ \ \text{2 "x" on 90} \ \ \ \rightarrow \ \ 90,\ 90}[/tex]
[tex]\rightarrow \ \ \text{3 "x" on 100} \ \ \rightarrow \ \ 100,\ 100, \ 100}[/tex]
[tex]\rightarrow \ \ \text{4 "x" on 110} \ \ \rightarrow \ \ 110,\ 110, \ 110, \ 110}[/tex]
[tex]\rightarrow \ \ \text{4 "x" on 120} \ \ \rightarrow \ \ 120,\ 120, \ 120, \ 120}[/tex]
[tex]\rightarrow \ \ \text{2 "x" on 130} \ \ \rightarrow \ \ 130,\ 130[/tex]
[tex]\rightarrow \ \ \text{1 "x" on 140} \ \ \rightarrow \ \ 140[/tex]
Now, let's put the values in descending form (Greatest --- Smallest). Start from the bottom and go to the top.
[tex]\rightarrow140, 130, 130, 120, 120, 120, 120, 110, 110, 110, 110, 100, 100, 100, 90, 90, 80, 70[/tex]
To find the median of the line plot, we need to check how many numbers are in total. Then, use the correct formula to find out which digit is the median. Lastly, use the "descending" data to find the median.
[tex]\rightarrow 1 + 1 + 2 + 3 + 4 + 4 + 2 + 1[/tex]
[tex]\rightarrow 7 + 11[/tex]
[tex]\rightarrow 18 \ \text{digits}[/tex]
Since 18 is an even number, the correct formula to use is [tex]\frac{n}{2}[/tex], where n is the total digits in the line plot.
[tex]\rightarrow \dfrac{n}{2}[/tex]
[tex]\rightarrow \dfrac{18}{2} = 9^{\text{th}}[/tex]
Now, let's take a look at our "descending" data to see which is the median. Remember, the ninth digit is the median.
[tex]140, 130, 130, 120, 120, 120, 120, 110, \boxed{\bold{110}}, 110, 110, 100, 100, 100, 90, 90, 80, 70\\[/tex]
Thus, 110 is the median.
