In order to find the range, we must find the difference between the largest number in the data and the smallest number in the data. The easier way to locate the smallest and largest numbers in the data is to put them in order of smallest to largest.

\(\displaystyle \small 4,13,24,25,27,28,53,55,56,57,59,63,72\)

By doing this we can see that 72 is our largest number and 4 is our smallest number. Now we find the difference between these two numbers using subtraction.

\(\displaystyle \small 72-4 = 68\)

In order to find the mode of a set of data, we must find the number that occurs the most often. In this set, \(\displaystyle \small 97\) appears three times, making it the most common number in the data set, so it is the mode.

The median of a set of data is the number that is physically in the middle of that data set when it is displayed in order from smallest to largest. In order to find the median of this data, we must first put it in order of smallest to largest.

\(\displaystyle \small 0,0,1,1,1,1,1,3,3,3,3,3,3,3,4,4,4\)

Next we determine how many students there are by adding together how many students reported having each number of siblings.

\(\displaystyle \small 5+2+3+7 = 17\)

Since seventeen is an odd number, one number will represent the median, and that number will be the 9^th number in the sequence. We know this because the 9^th number has eight on either side of it, putting it exactly in the middle of the data.

In our sequence, the 9^th number is \(\displaystyle \small 3\), making the median of our data \(\displaystyle \small 3\).

The mode is defined as the MOST in appearance. In the pack of rubber bands the color blue would appear the most in the pack.

Therefore, the mode [MOST] is Blue.

A subset of a set \(\displaystyle C\), by definition, is any set that contains no elements not in \(\displaystyle C\). All elements in \(\displaystyle \left \{ 1, 5, 7, 9, 11, 15, 17\right \}\), \(\displaystyle \left \{ 5, 7, 9, 11, 15, 17, 19 \right \}\), and \(\displaystyle \left \{ 19\right \}\) are contained in \(\displaystyle C\) and the sets are subsets; also, \(\displaystyle \varnothing\), the empty set, is considered a subset of every set. \(\displaystyle \left \{ 3, 5, 9, 11, 13, 17, 18\right \}\), however, contains element \(\displaystyle 18 \notin C\), so 

\(\displaystyle \left \{ 3, 5, 9, 11, 13, 17, 18\right \} \nsubseteq C\).

\(\displaystyle C \cup D\) is the union of sets \(\displaystyle C\) and \(\displaystyle D\) - the set of all elements that appear in either  \(\displaystyle C\) or \(\displaystyle D\). These elements are:

\(\displaystyle \left \{ 1, 2,3,4,5, 6, 8, 9, 10, 13, 14,15,17, 18\right \}\)

This is a set of 14 elements. 

A subset of a set \(\displaystyle A\), by definition, is any set that contains no elements not in \(\displaystyle A\).  Each of the following subsets can be seen to have at least one such element, which is underlined here:

\(\displaystyle \left \{ g, \underline{h}, p\right \}\)

\(\displaystyle \left \{ a, \underline{e}, g, j, k \right \}\)

\(\displaystyle \left \{ a, f, j, k, \underline{o}, p, t\right \}\)

\(\displaystyle \left \{ a, d, f, g, j, k, m, p, t, \underline{v}\right \}\)

The remaining set can be seen to have only elements from \(\displaystyle A\):

\(\displaystyle \left \{ f, g, k, t\right \} \subseteq \left \{ a, d, \underline{f}, \underline{g}, j, \underline{k}, m, p, \underline{t}\right \}\)

This is the correct choice.

To find the median the set of numbers must be put in order [least to greatest OR greatest to least].  Once the numbers are in order, then cross out one number from each side of the list until the middle of the ordered numbers is reached.

The number in the middle of the ordered numbers is the median.

Placing the scores in order from least to greatest the list would appear as follows:

70, 75, 80, 90, 100

Cross out one number at a time from each side.

First cross out 70. Next, cross out 100.  Then, cross out 75. Finally, cross out 90.

70, 75, 80, 90, 100

The median is the number left in the middle of the ordered list which is 80.

The mode is the number that is repeated most often. \(\displaystyle \small 39\) is repeated three times, more than any other number in the set. 

The mode of a set of numbers is the number that is repeated most often. In this example, \(\displaystyle 13\) is repeated three times, more than any other number in the set. Therefore, \(\displaystyle 13\) is the mode.