Really need help with this

Part A

 3

Work Shown:

Original Set = {2, 8, 2, 1, 0, 0, 3, 5, 1, 8, 6, 5, 5}

Sorted set = {0, 0, 1, 1, 2, 2, 3, 5, 5, 5, 6, 8, 8}

There are 13 items in the sorted set, so the middle value will have 13/2 = 6.5 --> 6 items below it and 6 items above it. This means the median is in slot 6+1 = 7. For the sorted set, the number in slot 7 is the value 3

Part B

 one pair is 4 and 5

Work Shown:

The old median (3) increases to 5 since we're told the median increases by 2. This means that 5 must be in the middle slot. Why? Because we go from 13 items to 15 items (again adding 2 numbers on). The set

{0, 0, 1, 1, 2, 2, 3, 5, 5, 5, 6, 8, 8}

becomes

{0, 0, 1, 1, 2, 2, 3, X, Y, 5, 5, 5, 6, 8, 8}

where 3 <= X <= Y

and X is the value of the new median. We must make X = 5 if we want to have this particular configuration.

The value of Y must be 5 as well

We'd have this new set

{0, 0, 1, 1, 2, 2, 3, 5, 5, 5, 5, 5, 6, 8, 8}

and the median would be 5.

Part C

If you had the set {1,2,3,4} then the values 2 and 3 are tied for the middle-most position. Find the midpoint of these two values

midpoint = (A+B)/2 = (2+3)/2 = 5/2 = 2.5

for this example, the median is 2.5 as its directly in the middle of 2 and 3

Part D

looking back at the original sorted set

{0, 0, 1, 1, 2, 2, 3, 5, 5, 5, 6, 8, 8}

the min and max are 0 and 8 respectively, so the range is

range = max - min

range = 8-0

range = 8

If we add in values that are between 0 and 8, then this will not affect the range. We would need to either add values that are larger than 8, or smaller than 0. Considering the values represent the number of runs, this means a negative number of runs makes no sense. So its only possible to have runs exceed 8.

If we had this set

{0, 0, 1, 1, 2, 2, 3, 5, 5, 5, 6, 8, 8, 22}

Then the range is now max-min = 22-0 = 22

But if we had this set

{0, 0, 1, 1, 2, 2, 3, 5, 5, 5, 6, 8, 8, 8}

then the range is still 8

So again, all you need to do is make sure you add in values that are between 0 and 8.

d

step-by-step explanation:

hello and welcome!

so, when we see the words "proportional" along with a table, we need to know that we're looking numbers that divide by the same thing.

looking at this table, we simply have to do a trial and error, and divide to see which numbers have the same quotient. if you look at choice a & c, they both have equal quotients for three of the numbers, with one exception, so those can't be the answer. looking at b, there is no similarity, so that can't be it. then, we see d; if you divide all the numbers in the table, you'll see that they all divide by two, which is a proportional relationship, and our answer!

also, always remember that the x will always be the number that goes into y, and somewhere behind this table, is a formula. for this specific table, the formula would be:

since our x-value is being divided by two to get the y-value. and if they were to ask for more numbers in the series, this is the formula you would use to find them.