Fine the mean of the data set: 9 4 7 3 10 9
a. 6
b. 7
c. 8
d. 9
find the median of the data set: 9 6 7 3 10 9
a. 6
b. 7
c. 8
d.9
find the mode of the data set: 9 6 7 3 10 9
a. 6
b. 7
c. 8
d. 9
find the range of the data set: 7 12 15 4 23 15 25 9
a. 4
b. 9
c. 19
d. 21
what number can be inserted in the set 9 12 17 15 13 so that the median of the numbers in the resulting list is 14?
a. 12
b. 13
c. 14
d. 15

The mean is the average. you add the values together and then divide by total number of values ie.  (9+4+7+3+10+9)/6 = 7

The median the value that is in the middle after you order them.  If there are an even number of values, as in this case, you take the mean of the two middle values.
ie. (3,4,7,9,9,10)  => 7,9 are in the middle.  So we take the mean => (7+9)/2 = 8

The mode is the value that is repeated the most.  In this case, there are two 9's and the other values are listed only once.  So the mode = 9.  If all the numbers were listed only once, there would be no mode.

The range is (the largest value in the list) - (the smallest value in the list).  In this case, 25 is the largest, and 4 is the smallest.  So the range is 25-4 = 19

For you last question, 
1. order the values from smallest to largest => 9, 12, 13, 15, 17 
2. currently, the median is 13.  the question asks, what number  can be inserted to make the median 14.  =>  9, 12, 13, ?, 15, 17 
3. if you take the average of 13 and ?, you should get 14  => (13 + ?)/2 = 14
4. now do the algebra =>
13 + ? = 14 * 2  
13 + ? = 28  
? = 28 -13 
? = 15
So you insert 15 to the list, you'll have the median of the list equal to 14.