# SAT II Math I : Data Analysis and Statistics

## Example Questions

### Example Question #6 : Median

Cedric measured the height of his tomato plants, in centimeters, and collected the following data:

What is the median height for his plants?

Explanation:

First, arrange all of the data in numerical order: .

Then locate the middle number by using the formula

, which gives you the location of the median in the ordered data set and where  is the number of terms in the data set.

Here, there are 11 terms.

So,

Therefore, our number is the  one in the list, which is .

### Example Question #41 : Data Analysis And Statistics

If  and , then what could be the median of the whole set if all of them are arranged in increasing order?

Explanation:

Since it's in increasing order, let's have some scenarios. Let's say  are both , then that means  at can be  with  maxing out its value up to  with  maxing its value. That leaves  must be  with  maxing out its value and  being in a range of  with  maxing its value and not violating the set. Now, lets say  are respectively, this leaves  only being  and  being  as well. Let's find the range of . If  were both , that means the median of them is . If  are both , that means the median of them is  is highest median of both  and  is the lowest median of . We need to find a number in the answer choices that fit this description. Answer is

### Example Question #42 : Data Analysis And Statistics

What is the median of the first six cubic numbers?

Explanation:

Cubic numbers are numbers taken to the third power. The first six cubic numbers are:  or

Since, the numbers are inceasing, count the numbers in the set. There are six. Then divide six by two. We do this because we will split the number set in half. Because six does divide evenly into two, this means we can't easily determine the median. Since six divided by two is three, we are going to eliminate three numbers from leftmost in number set toward the right direction and three numbers from rightmost in number set toward the left direction. The last number crossed out in both direction are  and . To find the middle number, just add both numbers and divide by two.

### Example Question #43 : Data Analysis And Statistics

There are three numbers. Say that one of the numbers represented is . Another number is two times square root of . The last number is one less than . If the sum is three, what is the median of the set?

Explanation:

Let's interpret the problem. One number is . Another is two times square root of  or . The last number is one less than  or . The sum is three which means the equation to set up is: . Let's solve for

I want to have the square root on one side and the numbers and variable on the other.

When  I square both sides, we get a quadratic equation. If I were to square the equation before, I still have a radical to get rid of.

Remember when foiling, you multiply the numbers/variables that first appear in each binomial, followed by multiplying the outer most numbers/variables, then multiplying the inner most numbers/variables and finally multiplying the last numbers/variables.

Let's factor out a  to reduce the quadratic.

If I divide both sides by , I get:

Remember, we need to find two terms that are factors of the c term that add up to the b term. We have:

Solve for

We are not done as the problem asks for median of the set. If we plug in , we have:  or . Once we arrange in increasing order, we have . By checking, the sum is  and the middle number is . Let's check when  is . We have:  or . In increasing order we have . The answer may be 4, HOWEVER, it doesn't satisfy the problem as the sum should be  but instead we have . Therefore the correct answer to this problem is

### Example Question #44 : Data Analysis And Statistics

Find the median.

Explanation:

When finding the median, you are looking for the middle number. Always arrange the numbers in ascending order. Since, the numbers are inceasing, count the numbers in the set. There are five. Then divide five by two. We do this because we will split the number set in half. Because five doesn't divide evenly into two, this means we can easily determine the median. Since five divided by two is , we are going to eliminate two numbers from leftmost in number set toward the right direction and two numbers from rightmost in number set toward the left direction. The only number left is  and therefore is the right answer.

### Example Question #45 : Data Analysis And Statistics

What is the median?

Explanation:

When finding the median, you are looking for the middle number. Always arrange the numbers in ascending order. Since, the numbers are not in inceasing order, let's arrange it. It should look like: . Now, let's count the numbers in the set which is seven. Then divide seven by two. We do this because we will split the number set in half. Because seven doesn't divide evenly into two, this means we can easily determine the median. Since seven divided by two is , we are going to eliminate three numbers from leftmost in number set toward the right direction and three numbers from rightmost in number set toward the left direction. The only number left is  and therefore is the right answer.

### Example Question #46 : Data Analysis And Statistics

What is the median?

Explanation:

When finding the median, you are looking for the middle number. Always arrange the numbers in ascending order. Since, the numbers are inceasing, count the numbers in the set. There are six. Then divide six by two. We do this because we will split the number set in half. Because six does divide evenly into two, this means we can't easily determine the median. Since six divided by two is three, we are going to eliminate three numbers from leftmost in number set toward the right direction and three numbers from rightmost in number set toward the left direction. The last number crossed out in both direction are  and . To find the middle number, just add both numbers and divide by two.

### Example Question #47 : Data Analysis And Statistics

What is the median?

Explanation:

When finding the median, you are looking for the middle number. Always arrange the numbers in ascending order. Since, the numbers are not in order, lets arrange them.

The new set is

.

Then, we count the numbers in the set. There are six. Then divide six by two. We do this because we will split the number set in half. Because six does divide evenly into two, this means we can't easily determine the median. Since six divided by two is three, we are going to eliminate three numbers from leftmost in number set toward the right direction and three numbers from rightmost in number set toward the left direction. The last number crossed out in both direction are  and . To find the middle number, just add both numbers and divide by two.

### Example Question #48 : Data Analysis And Statistics

What is the median?

Explanation:

When finding the median, you are looking for the middle number. Always arrange the numbers in ascending order. Since, the numbers are not increasing, let's organize it.

The new set is

.

Remember, for negative numbers, the bigger the negative value, the smaller the number is since it's further away in the number line. Now, let's count the numbers in the set. There are six. Then divide six by two. We do this because we will split the number set in half. Because six does divide evenly into two, this means we can't easily determine the median. Since six divided by two is three, we are going to eliminate three numbers from leftmost in number set toward the right direction and three numbers from rightmost in number set toward the left direction. The last number crossed out in both direction are  and . To find the middle number, just add both numbers and divide by two.

### Example Question #49 : Data Analysis And Statistics

Which of the following statements is/are true for finding a median?

I. Always search for the middle number

II. Always arrange in increasing or decreasing order before searching for the middle number

III. Once arranged, if the set has an even number, just take the two middle numbers and subtract them and divide by two

IV. Once arranged, if the set has an even number, just take the two middle numbers and add them and divide by two

I, II, III

I, II, IV

II, III

II, IV

only

II, IV

Explanation:

Let's look at each statement.

I. Always search for the middle number

This is false, because what happens if the number set is jumbled. To find median, it's important to oragnize in increasing or decreasing order.

II. Always arrange in increasing or decreasing order before searching for the middle number

As explained in statement one explanation, this is true.

III. Once arranged, if the set has an even number, just take the two middle numbers and subtract them and divide by two

This s false, because once there is an even number set, you need to ADD the middle numbers and divide it by two. Essentially, the new value represents the middle of the set.

IV. Once arranged, if the set has an even number, just take the two middle numbers and add them and divide by two

This is true based on statement three explanation.