First, we need to find the median for the first data set: 

We must put the numbers in order from least to greatest: 

Since there is an even number of items in the data set, we will take the average of the middle two numbers to find the median. 

The median for this data set is:

Next, we must find the new median for the new data set: 

Again, we must put the numbers in order from least to greatest: 

Since there is an odd number of items, we can choose the middle number to be the median. 

In this case, the middle number is , which means the new median is:

Therefore, we know that the median will decrease by .

First we must put the numbers  in order from least to greatest. 

After the numbers are in order, if it is an odd number of numbers we chose the middle number - that is the median. 

In this case, we have an even number of numbers, so we must take the average of the middle two numbers which is given below: 

So the median is !

When finding the median we must first reorganize the numbers from least to greatest, here is what the numbers are before and after they were organized. 

Given: 

After Organized from least to greatest: 

In order to find the Median for an even number of numbers (we have  numbers in this set) we take the average of the middle two numbers. 

Here we would add  which is , we then divide by two to find the mean which is . 

If we were to change the  to an , this does not impact the middle two numbers, they will remain  and  which means the Median will remain . 

The middle two numbers are still  and . 

The Median will remain unchanged.

In order to answer this question correctly, we need to recall the definition of median:

Median: The median of a data set is the middle value, when the data set is ordered from least to greatest. 

In order to find the median, we need to first organize the data from least to greatest:

Next, we can solve for the median by finding the middlemost number in our data:

The median for this data set is 

In order to answer this question correctly, we need to recall the definition of median:

Median: The median of a data set is the middle value, when the data set is ordered from least to greatest. 

In order to find the median, we need to first organize the data from least to greatest:

Next, we can solve for the median by finding the middlemost number in our data:

The median for this data set is 

In order to answer this question correctly, we need to recall the definition of median:

Median: The median of a data set is the middle value, when the data set is ordered from least to greatest. 

In order to find the median, we need to first organize the data from least to greatest:

Next, we can solve for the median by finding the middlemost number in our data:

The median for this data set is 

In order to answer this question correctly, we need to recall the definition of median:

Median: The median of a data set is the middle value, when the data set is ordered from least to greatest. 

In order to find the median, we need to first organize the data from least to greatest:

Next, we can solve for the median by finding the middlemost number in our data:

The median for this data set is 

The quickest way to solve this problem is by making a chart showing the units purchased and the total cost. Start with the 4-packs of umbrellas:

4-packs      cost        shipping cost              total cost

1                $25               $6                          $31        

2                $50               $9                          $59

3                $75               $12                        $87

4                $100             $15                        $115

5                $125             $21                        $146 (too high)

Having determined that Katie can buy four of the 4-packs of umbrellas, now we see how many of the $7 individual umbrellas she can add to her order.

four 4-packs        indiv.        indiv. $     subtotal     shipping $      total $

$100                      1               $7           $107         $18          $125

$100                      2               $14         $114         $18           $132

$100                      3               $21         $121         $21          $142 (too high)

Therefore, Katie can buy (4) 4-packs and (2) individual umbrellas (18 total umbrellas) for $132.

ALTERNATIVELY, you can begin by determining the highest subtotal she can afford and work backwards from there. $120 is 6 x $20, so the shipping charge would be $6 x 3 = $18, for a total cost of $138. One more dollar on the subtotal would bring it into the next $20 segment, bringing the shipping charge up to $21 (and $142 is greater than $140). Thus, from here you could figure out the maximum number of $25 4-packs and $7 individual umbrellas Katie could buy with $120.

Since $6 is not enough to buy any umbrellas, the total would be

The population of Buchanan City in 1960 is greater than it was in 1940, so its decline between 1940 and 1950 must be less than its growth between 1950 and 1960.

(a) Between 1930 and 1940, the population grew by 

(b) Between 1950 and 1960, the population grew by .

This makes (b) greater