Answer:
a. 3
b. [5,6]
c.[tex]Median=\frac{n}{2}[/tex]
d.Game theory to predict future outcomes based on past results.
Step-by-step explanation:
a. Median is defined as the middlemost data point in a data set of data points arranged in a ranking order.
-Arranging our data points in Ranking order:
0,0,1,1,2,2,3,5,5,5,6,8,8
-Our set has 13 entries. The 7th term is the median Value.
#Hence, the median value of our data set is 3
b. Increasing the median value by 2. And let x and y be the two new scores
-From a above, median is 3:
[tex]M_n=M_{old}+2=3+2\\\\=5[/tex]
-The new median value is 5. Adding two data points, makes the 8Th term the median value.
-Given that values of 5 was originally the 8th term, For the median value to be 5,both x and y have to have a value of 5, or one must be a 5 and the next a higher value:
-Hence, [5,6], 5,5] are both possible pairs of x and y
c. From the definition of median in a above,
#If the data points are an odd number of entries, then the median value is (n/2)+1, hence a whole number.
[tex]Median=\frac{n}{2}+1[/tex]
#If the data points are an odd number of entries, then the median value is (n/2), hence a decimal number e.g 2.5:
[tex]Median=\frac{n}{2}[/tex]
d. Using game theory, real-world scenarios for such situations asruns in baseball games can be predicted from past outcomes.
-As such, we can predict that the next two games are likely to be in the range of the first 13 scores.
