In these lessons, we will learn how to calculate the median of a given set of data. We will also learn how to solve some mean, median, mode SAT questions.

**Related Pages**

Median From Frequency Table

Mean

Mode

Central Tendency

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The following diagrams show how to obtain the median from a given set of data. Scroll down the page for examples and solutions.

Given a set of observations, the **median** is the middle value
among the observations. To find the median, you must first arrange the observations in an
ascending (or descending) order.

There are 2 possible cases to consider in finding the median.

**Case 1.** When the number of observations is odd,
the median is the middle value.

**Example:**

Find the median of the following set of points in a game:

15, 14, 10, 8, 12, 8, 16

**Solution:**

First arrange the point values in an ascending order (or descending order).

8, 8, 10, 12, 14, 15, 16

The number of point values is 7, an odd number. Hence, the median is the value in the middle position.

Median = 12

**Case 2.** When the number of observations is even,
the median is the average of the two middle values.

**Example:**

Find the median of the following set of points:

15, 14, 10, 8, 12, 8, 16, 13

**Solution:**

First arrange the point values in an ascending order (or descending order).

8, 8, 10, 12, 13, 14, 15, 16

The number of point values is 8, an even number. Hence the median is the average (mean) of the 2 middle values.

Given a partial data set, you may need to determine the possible values of the median of a set of numbers.

**Example:**

x is the median for 4, 3, 8, x and 7. Find the possible values for x.

**Solution:**

Arrange the numbers in ascending order with x in the middle.

3, 4, x, 7, 8

This tells us that the possible values of x are 4, 5, 6 and 7.

The following videos will show you how to find the median.

In this lesson you learn how to find the median from a set of numbers using the median position formula (n+1)/2.

**Example:**

Find the mean, median and mode of the following set of data:

23, 29, 20, 32, 23, 21, 33, 25

**Mean, Median, Mode Song**

A song to help you remember how to calculate mean, median and mode.

In the SAT, mean, median and mode questions may be given in the following manner.

**SAT Mean, Median, and Mode Math Question**

This video will show you how to answer SAT mean, median, and mode math questions.

In a set of nine distinct numbers which of the following cannot affect the median

a) squaring

b) increasing every other number by 5

c) increasing the smallest number only

d) increasing the largest number only

e) decreasing the largest number only

In a certain Chemistry class, the median score on a test was 84. Which of the following must be true?

I. The highest score in the class is at least one point higher than the lowest score.

II. If there was a score of 83 in the class, there was also a score of 85.

III. The mode of the test scores was 84.

If w, x and y represent 3 positive numbers where x = y + 5 and y = w + 20, what is the result
when the average of the three numbers is subtracted from the median?

a) -5

b) 0

c) 4

d) 5

e) 15

**SAT Math - Averages, Median, List of Real Numbers**

The least and greatest numbers in a list of 7 real numbers are 2 and 20, respectively. The median
of the list is 6, and the number 3 occurs most often in the list. Which of the following could be
the average (arithmetic mean) of the numbers in the list?

I. 1

II. 8, 5

III. 10

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