# SAT II Math I : Data Analysis and Statistics

## Example Questions

### Example Question #24 : Median

If the median of the set is , which of the following is a possibility for the values of  and ?

Explanation:

The set is already in increasing order. We have six numbers in the set and we need to ensure the set will have a median of . When there is an even number in the set, we need to take the two middle numbers by adding them then dividing by two. The two middle numbers represent  and .  Let's set up an equation.

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The numerator represents the two middle numbers being added and divided by the denominator. If we multiply both sides by  we get the sum of the variables to be . So we need to find the sum of  and  to be . The only choices are  and . However,  doesn't work because  is bigger than both  and  and thus changing the median.  is good because both of the values are les than  but greater than

### Example Question #25 : Median

If the median of the set is , which of the following is a possibility for the values of  and ?

Explanation:

The set is already in increasing order. We have six numbers in the set and we need to ensure the set will have a median of . When there is an even number in the set, we need to take the two middle numbers by adding them then dividing by two. The two middle numbers represent  and .  Let's set up an equation.

.

The numerator represents the two middle numbers being added and divided by the denominator. If we multiply both sides by , and subtract  on both sides, we get  to be . Finally, to find , we need a number that is greater than or equal to  and less than or equal to . Answer  satisfies all conditions.

### Example Question #26 : Median

If we want the median to be , what number can be put into the set to make this true?

Explanation:

The set is already in increasing order. We have five numbers in the set, however, we need to add another number to ensure the set will have a median of . This will make the set have six numbers. When there is an even number in the set, we need to take the two middle numbers by adding them then dividing by two. Let's say this number is . Let's setup an equation.

.

The numerator represents the two middle numbers being added and divided by the denominator. If we multiply both sides by  and subtract  on both sides,  is . Make sure this answer doesn't violate the set.  is less than  but greater than , so therefore  is the correct answer.

### Example Question #27 : Median

Find the median of the set:

Explanation:

The median is the middle number of the set, when it is listed in order from smallest to largest or vice versa. In this case we have an even amount of numbers in the set meaning there are two "middle numbers". But for this set, both of those middle numbers are 89, meaning we don't need to take an average.

This gives us the final answer of 89 for the median.

### Example Question #28 : Median

Find the median of the set:

Explanation:

The median is the middle number of the set, when it is listed in order from smallest to largest or vice versa. In this case we have an even amount of numbers in the set meaning there are two "middle numbers"- 23 and 25. In order to find the median we take the average of 23 and 25:

### Example Question #31 : Median

Find the median of the set:

Explanation:

The median is the middle number of the set, when it is listed in order from smallest to largest or vice versa. In this case we have an even amount of numbers in the set meaning there are two "middle numbers"- 22 and 23. In order to find the median we take the average of 22 and 23:

### Example Question #32 : Median

Find the median of the set:

Explanation:

The median is the middle number of the set, when it is listed in order from smallest to largest or vice versa. In this case we have an even amount of numbers in the set meaning there are two "middle numbers"- 11 and 12. In order to find the median we take the average of 11 and 12:

### Example Question #231 : Data Properties

Find the median of the set:

Explanation:

The median is the middle number of the set, when it is listed in order from smallest to largest or vice versa. In this case we have an even amount of numbers in the set meaning there are two "middle numbers"- 8 and 13. In order to find the median we take the average of 8 and 13:

### Example Question #232 : Data Properties

Find the median of the set:

Explanation:

The median is the middle number of the set, when it is listed in order from smallest to largest or vice versa. In this case we have an even amount of numbers in the set meaning there are two "middle numbers"- 24 and 26. In order to find the median we take the average of 24 and 26:

### Example Question #233 : Data Properties

Find the median of the set: