### All ACT Math Resources

## Example Questions

### Example Question #11 : Median

67, 73, 85, 83, 80, 73, 94, 65, 80, 73, 98, 59, 76

The list above shows a ninth grader's grades for the academic year. What is the difference between the median and the mode of these grades?

**Possible Answers:**

**Correct answer:**

To find the median, sort the numbers from smallest to largest:

59, 65, 67, 73, 73, 73, 76, 80, 80, 83, 85, 94, 98

The median is the middle value in a list of numbers, it is the number separating the higher half of a data sample or a list of numbers from the lower half.

The median of the grades is 76.

The mode is the value occurring most often. The most occurring value in the list of numbers given is 73. So, the mode is 73.

### Example Question #81 : Data Analysis

In a row of students, each student receives a number of chocolates equal his or her position in the line, multiplied by . What is the median amount of chocolates received by this group?

**Possible Answers:**

There is no median.

**Correct answer:**

To begin, think through the scenario of your line, it is made up of ten students as thus:

Since there is an even number of students, your median will be the average of the amounts given to students and .

Now, your students received chocolates like this:

Thus, you know that the median must be:

### Example Question #8 : Median

Four items are purchased from an electronics store. The first item costs ** **and each successive item costs twice that of the previous one. What is the median cost of these four items?

**Possible Answers:**

There is no median

**Correct answer:**

To start, you should list out the prices of your items:

Now, recall that the median of a group of numbers is the middle value. For four numbers, there is (strictly speaking) no middle. Therefore, you need to add together the values in the second and third place and find their average. This is:

### Example Question #9 : Median

What is the median of the following list of test scores:

**Possible Answers:**

**Correct answer:**

The median is the number in the middle. So order the numbers and find the one in the middle of that list:

61,72,81,84,98 and clearly 81 is the middle

### Example Question #2791 : Act Math

A group of ten students take a math test and their scores are as follows.

.

Based on this information, what is the median?

**Possible Answers:**

**Correct answer:**

The median is the middle number of a group of data. To find the median it is easiest to put all of the data in increasing order and eliminate the highest and lowest value until you are left with a single number. Since there are an even number of data you normally average the final two values, but since they are the same in this case that value is the answer.

### Example Question #12 : How To Find Median

The following is the list of five point totals for James in his last five basketball games:

.

What is the median points scored over those five games?

**Possible Answers:**

**Correct answer:**

To find the median of an odd number of data points, arrange the numbers in ascending order and choose the number in the middle.

Thus we see the answer is .

### Example Question #71 : Statistics

What is the median of the following list of numbers?

**Possible Answers:**

There is no median.

**Correct answer:**

To find the median of a data set, line up all the numbers and find the number in the middle. If two numbers are in the middle (only true of even-numbered data sets) then take the average of the middle two.

Since our data set has an odd number of numbers, the median is 12.

### Example Question #11 : How To Find Median

Find the median of the following set of numbers.

**Possible Answers:**

**Correct answer:**

To find the median, simply sort the numbers from smallest to largest and then find the number in the middle. Since these are already sorted, the answer is .

### Example Question #11 : How To Find Median

Find the median of the following set of numbers:

**Possible Answers:**

**Correct answer:**

To find the median, simply find the middle number.

Since there are an even number of values, you will have to take and average of the two middle numbers.

Thus,

### Example Question #11 : Median

Find the median of the following set of numbers:

**Possible Answers:**

**Correct answer:**

To find median, simply find the middle number. Since there are two in the middle, find their average. Thus,

Certified Tutor