# How to calculate median values

The median is one of the three main measures of central tendency, which is commonly used in statistics for finding the center of a data sample or population, e.g.

for calculating a typical salary, household income, home price, real-estate tax, etc.

In this tutorial, you will learn the general concept of the median, in what way it is different from arithmetic mean, and how to get median in Excel.

## What is median?

In simple terms, the median is the middle value in a group of numbers, separating the higher half of values from the lower half. More technically, it is the center element of the data set arranged in order of magnitude.

In a data set with an odd number of values, the median is the middle element. If there are an even number of values, the median is the average of the middle two.

For example, in the group of values {1, 2, 3, 4, 7} the median is 3. In the dataset {1, 2, 2, 3, 4, 7} the median is 2.5. Compared to the arithmetic mean, the median is less susceptible to outliers (extremely high or low values) and therefore it is the preferred measures of central tendency for an asymmetrical distribution.

A classic example is a median salary, which gives a better idea of how much people typically earn than an average salary because the latter may be skewed by a small number of abnormally high or low salaries.

### Excel MEDIAN function

Microsoft Excel provides a special function to find a median of numeric values. The syntax of the MEDIAN function is as follows:

MEDIAN(number1, [number2], …)

Where Number1, number2, … are numeric values for which you want to calculate the median. These can be numbers, dates, named ranges, arrays, or references to cells containing numbers. Number1 is required, subsequent numbers are optional.

In the recent versions of Excel 2016, 2013, 2010 and 2007, the MEDIAN function accepts up to 255 arguments; in Excel 2003 and earlier you can only supply up to 30 arguments.

### 4 facts you should know about Excel Median

• When the total number of values is odd, the Excel MEDIAN function returns the middle number in the data set. When the total number of values is even, it returns an average of the two middle numbers.
• Cells with zero values (0) are included in calculations.
• Empty cells as well as cells containing text and logical values are ignored.
• The logical values of TRUE and FALSE typed directly in the MEDIAN function's arguments are counted. For example, the formula MEDIAN(FALSE, TRUE,2,3,4) returns 2, which is the median of the numbers {0, 1, 2, 3, 4}.

## Mean, Median, Mode, Range Calculator

• home / math / mean, median, mode, range calculator
• Please provide numbers separated by comma to calculate.

RelatedStatistics Calculator | Standard Deviation Calculator | Sample Size Calculator

### Mean

The word mean, which is a homonym for multiple other words in the English language, is similarly ambiguous even in the area of mathematics. Depending on the context, whether mathematical or statistical, what is meant by the “mean” changes.

In its simplest mathematical definition regarding data sets, the mean used is the arithmetic mean, also referred to as mathematical expectation, or average. In this form, the mean refers to an intermediate value between a discrete set of numbers, namely, the sum of all values in the data set, divided by the total number of values.

The equation for calculating an arithmetic mean is virtually identical to that for calculating the statistical concepts of population and sample mean, with slight variations in the variables used: The mean is often denoted as , pronounced “x bar,” and even in other uses when the variable is not x, the bar notation is a common indicator of some form of mean.

In the specific case of the population mean, rather than using the variable , the Greek symbol mu, or μ, is used. Similarly, or rather confusingly, the sample mean in statistics is often indicated with a capital .

Given the data set 10, 2, 38, 23, 38, 23, 21, applying the summation above yields:

 10 + 2 + 38 + 23 + 38 + 23 + 21 7
=   = 22.143

As previously mentioned, this is one of the simplest definitions of the mean, and some others include the weighted arithmetic mean (which only differs in that certain values in the data set contribute more value than others), and geometric mean.

Proper understanding of given situations and contexts can often provide a person with the tools necessary to determine what statistically relevant method to use.

In general, mean, median, mode and range should ideally all be computed and analyzed for a given sample or data set since they elucidate different aspects of the given data, and if considered alone, can lead to misrepresentations of the data, as will be demonstrated in the following sections.

### Median

The statistical concept of the median is a value that divides a data sample, population, or probability distribution into two halves. Finding the median essentially involves finding the value in a data sample that has a physical location between the rest of the numbers.

Note that when calculating the median of a finite list of numbers, the order of the data samples is important. Conventionally, the values are listed in ascending order, but there is no real reason that listing the values in descending order would provide different results.

In the case where the total number of values in a data sample is odd, the median is simply the number in the middle of the list of all values. When the data sample contains an even number of values, the median is the mean of the two middle values.

While this can be confusing, simply remember that even though the median sometimes involves the computation of a mean, when this case arises, it will involve only the two middle values, while a mean involves all the values in the data sample.

In the odd cases where there are only two data samples or there is an even number of samples where all the values are the same, the mean and median will be the same. Given the same data set as before, the median would be acquired in the following manner:

1. 2,10,21,23,23,38,38
2. After listing the data in ascending order, and determining that there are an odd number of values, it is clear that 23 is the median given this case. If there were another value added to the data set:
3. 2,10,21,23,23,38,38,1027892

Since there are an even number of values, the median will be the average of the two middle numbers, in this case 23 and 23, the mean of which is 23.

Note that in this particular data set, the addition of an outlier (a value well outside the expected range of values), the value 1,027,892, has no real effect on the data set. If however the mean is computed for this data set, the result is 128,505.875.

This value is clearly not a good representation of the seven other values in the data set that are far smaller and closer in value than the average and the outlier. This is the main advantage of using the median in describing statistical data when compared to the mean.

While both, as well as other statistical values, should be calculated when describing data, if only one can be used, the median can provide a better estimate of a typical value in a given data set when there are extremely large variations between values.

### Mode

In statistics, the mode is the value in a data set that has the highest number of recurrences. It is possible for a data set to be multimodal, meaning that it has more than one mode. For example:

2,10,21,23,23,38,38

Both 23 and 38 appear twice each, making them both a mode for the data set above.

## What You Need to Do in Order to Calculate the Mean, Median, or Mode Sam Edwards / Getty Images

Students often find that it is easy to confuse the mean, median, and mode. While all are measures of central tendency, there are important differences in what each one means and how they are calculated. Explore some useful tips to help you distinguish between the mean, median, and mode and learn how to calculate each measure correctly.

In order to understand the differences between the mean, median, and mode, start by defining the terms.

• The mean is the arithmetic average of a set of given numbers.
• The median is the middle score in a set of given numbers.
• The mode is the most frequently occurring score in a set of given numbers.

The mean, or average, is calculated by adding up the scores and dividing the total by the number of scores. Consider the following number set: 3, 4, 6, 6, 8, 9, 11. The mean is calculated in the following manner:

• 3 + 4 + 6 + 6 + 8 + 9 + 11 = 47
• 47 / 7 = 6.7
• The mean (average) of the number set is 6.7.

The median is the middle score of a distribution. To calculate the median

• Arrange your numbers in numerical order.
• Count how many numbers you have.
• If you have an odd number, divide by 2 and round up to get the position of the median number.
• If you have an even number, divide by 2. Go to the number in that position and average it with the number in the next higher position to get the median.

Consider this set of numbers: 5, 7, 9, 9, 11. Since you have an odd number of scores, the median would be 9. You have five numbers, so you divide 5 by 2 to get 2.5, and round up to 3. The number in the third position is the median.

What happens when you have an even number of scores so there is no single middle score? Consider this set of numbers: 1, 2, 2, 4, 5, 7. Since there is an even number of scores, you need to take the average of the middle two scores, calculating their mean.

Remember, the mean is calculated by adding the scores together and then dividing by the number of scores you added. In this case, the mean would be 2 + 4 (add the two middle numbers), which equals 6. Then, you take 6 and divide it by 2 (the total number of scores you added together), which equals 3. So, for this example, the median is 3.

Since the mode is the most frequently occurring score in a distribution, simply select the most common score as your mode. Consider the following number distribution of 2, 3, 6, 3, 7, 5, 1, 2, 3, 9.

The mode of these numbers would be 3 since three is the most frequently occurring number.

In cases where you have a very large number of scores, creating a frequency distribution can be helpful in determining the mode.

In some number sets, there may actually be two modes. This is known as bi-modal distribution and it occurs when there are two numbers that are tied in frequency. For example, consider the following set of numbers: 13, 17, 20, 20, 21, 23, 23, 26, 29, 30. In this set, both 20 and 23 occur twice.

If no number in a set occurs more than once, then there is no mode for that set of data.

How do you determine whether to use the mean, median or mode? Each measure of central tendency has its own strengths and weaknesses, so the one you choose to use may depend largely on the unique situation and how you are trying to express your data.

• The mean utilizes all numbers in a set to express the measure of central tendency; however, outliers can distort the overall measure. For example, a couple of extremely high scores can skew the mean so that the average score appears much higher than most of the scores actually are.
• The median gets rid of disproportionately high or low scores, but it may not adequately represent the full set of numbers.
• The mode may be less influenced by outliers and is good at representing what is “typical” for a given group of numbers, but may be less useful in cases where no number occurs more than once.

Imagine a situation where a real estate agent wants a measure of the central tendency of homes she has sold in the last year. She makes a list of all of the totals:

• \$75,000
• \$75,000
• \$150,000
• \$155,000
• \$165,000
• \$203,000
• \$750,000
• \$755,000

The mean for this group is \$291,000, the median is \$160,000 and the mode is \$75,000.

Which would you say is the best measure of central tendency of the set of sales numbers? If she wants the highest number, the mean is clearly the best option even though the total is skewed by the two very high numbers.

The mode, however, would not be a good choice because it is disproportionately low and not a good representation of her sales for the year. The median, on the other hand, seems to be a fairly good indicator of the “typical” sales prices of her real estate listings.

## Statistics Calculator: Median

Use this calculator to compute the median from a set of numerical values.

This calculator computes the median from a data set:

To calculate the median from a set of values, enter the observed values in the box above. Values must be numeric and may be separated by commas, spaces or new-line. You may also copy and paste data into the text box.

You do not need to specify whether the data is from a population or a sample, unless you will later examine the variance or the standard deviation. Press the “Submit Data” button to perform the computation.

To clear the calculator and enter a new data set, press “Reset”.

### What is the median

The median is a measure of central tendency. It represents the value for which 50% of observations a lower and 50% are higher. Put simply, it is the value at the center of the sorted observations.

### Median formulas

This calculator uses two different formulas for calculating the median, depending on whether the number of observations is odd, or it is even:

When the number of observations is odd the formula is:

When the number of observations is even the formula is: where n is the number of observations.

## How to Calculate Median Change

The “median” value of a series of numbers refers to the middle number when all the data is ordered sequentially. Median calculations are less affected by outliers than the normal average calculation.

Outliers are extreme measurements that greatly deviate from all the other numbers, so in cases where one or more outliers would skew a standard average, median values can be used, since they resist outlier-incurred bias.

As more data is added, the median might change, but it will typically not change as dramatically as an average.

Order your series of numbers from smallest to largest. As an example, say you had the numbers 5, 8, 1, 3, 155, 7, 7, 6, 7, 8. You would arrange them as 1, 3, 5, 6, 6, 7, 7, 7, 8, 155.

Look for the middle number. If there are two middle numbers, as is the case with an even number of data points, you would take the average of the two middle numbers. In the example, the middle numbers are 6 and 7. Since the average of two numbers is the sum divided by 2, you achieve a median value of 6.5.

Note that the average of the entire data set would be 20.5, so you can see the difference taking the median can make. The 155 figure is an outlier, not at all consistent with the rest of the numbers. So a median provides a better measure than an average in this case.

Keep adding numbers, in sequence, as you acquire them. To continue the example, suppose you measured five new data points as 1, 8, 7, 9, 205. You would simply add them to your list, so that it reads 1, 1, 3, 5, 6, 6, 7, 7, 7, 7, 8, 8, 9, 155, 205.

## Median – Analysing data – Edexcel – GCSE Maths Revision – Edexcel – BBC Bitesize

The median average is the middle number in a set of data, when the data has been written in ascending size order.

If there is an even number of items of data, there will be two numbers in the middle. The median is the number that is half way between these two numbers.

To find the median, put all numbers into ascending order and work into the middle by crossing off numbers at each end.

If there are a lot of items of data, add 1 to the number of items of data and then divide by 2 to find which item of data will be the median. This works when it is an odd number but when it is an even number you will get a decimal answer such as 7.5. The median will be halfway between the 7th and 8th items.

### Example

7 babies weigh the following amounts:

2.5 kg, 3.1 kg, 3.4 kg, 3.5 kg, 3.5 kg, 4 kg, 4.1 kg

Find the median weight of the babies.

The numbers are already in order. Find the median amount by finding the middle number.

Cross off the first and last item of data (the items in bold):

2.5 kg, 3.1 kg, 3.4 kg, 3.5 kg, 3.5 kg, 4 kg, 4.1 kg

Repeat until you reach the middle:

3.1 kg, 3.4 kg, 3.5 kg, 3.5 kg, 4 kg

3.4 kg, 3.5 kg, 3.5 kg

3.5 kg

The median weight of these babies is 3.5 kg.

Another method is to find which item of data is the median.

There are 7 numbers, so adding 1 to 7 then dividing by 2 gives: , so the median value is the 4th number in the list:

2.5 kg, 3.1 kg, 3.4 kg, 3.5 kg, 3.5 kg, 4 kg, 4.1 kg

The median weight of these babies is 3.5 kg.

Notice that this is the median value as, in ascending order, there are 3 values before it and 3 values after that central value.

## Mean, Median, Mode Calculator

Get a Widget for this Calculator

Calculate mean, median, mode along with the minimum, maximum, range, count, and sum for a set of data.

Enter values separated by commas or spaces. You can also copy and paste lines of data from spreadsheets or text documents See all allowable formats in the table below.

### What are Mean Median and Mode?

Mean, median and mode are all measures of central tendency in statistics. In different ways they each tell us what value in a data set is typical or representative of the data set.

The mean is the same as the average value of a data set and is found using a calculation. Add up all of the numbers and divide by the number of numbers in the data set.

The median is the central number of a data set. Arrange data points from smallest to largest and locate the central number. This is the median. If there are 2 numbers in the middle, the median is the average of those 2 numbers.

The mode is the number in a data set that occurs most frequently. Count how many times each number occurs in the data set. The mode is the number with the highest tally. It's ok if there is more than one mode. And if all numbers occur the same number of times there is no mode.

### How to Find the Mean

1. Add up all data values to get the sum
2. Count the number of values in your data set
3. Divide the sum by the count

The mean is the same as the average value in a data set.

### Mean Formula

The mean x̄ of a data set is the sum of all the data divided by the count n.

[ ext{mean} = overline{x} = dfrac{sum_{i=1}^{n}x_i}{n} ]

### How to Find the Median

The median ( widetilde{x} ) is the data value separating the upper half of a data set from the lower half.

• Arrange data values from lowest to highest value
• The median is the data value in the middle of the set
• If there are 2 data values in the middle the median is the mean of those 2 values.

### Median Example

For the data set 1, 1, 2, 5, 6, 6, 9 the median is 5.

For the data set 1, 1, 2, 6, 6, 9 the median is 4. Take the mean of 2 and 6 or, (2+6)/2 = 4.

### Median Formula

Ordering a data set x1 ≤ x2 ≤ x3 ≤ … ≤ xn from lowest to highest value, the median ( widetilde{x} ) is the data point separating the upper half of the data values from the lower half.

If the size of the data set n is odd the median is the value at position p where

[ p = dfrac{n + 1}{2} ] [ widetilde{x} = x_p ]

If n is even the median is the average of the values at positions p and p + 1 where

[ p = dfrac{n}{2} ] [ widetilde{x} = dfrac{x_{p} + x_{p+1}}{2} ]

### How to Find the Mode

Mode is the value or values in the data set that occur most frequently.

For the data set 1, 1, 2, 5, 6, 6, 9 the mode is 1 and also 6.

### Related Statistics and Data Analysis Calculators

42, 54, 65, 47, 59, 40, 53 42, 54, 65, 47, 59, 40, 53, or

42, 54, 65, 47, 59, 40, 53

42, 54, 65, 47, 59, 40, 53 42 54 65 47 59 40 53 or

42 54 65 47 59 40 53

42, 54, 65, 47, 59, 40, 53 42 54   65,,, 47,,59,

40 53

42, 54, 65, 47, 59, 40, 53

## Median Definition

The median is the middle number in a sorted, ascending or descending, list of numbers and can be more descriptive of that data set than the average.

• The median is the middle number in a sorted, ascending or descending, list of numbers and can be more descriptive of that data set than the average.
• The median is sometimes used as opposed to the mean when there are outliers in the sequence that might skew the average of the values.
• If there is an odd amount of numbers, the median value is the number that is in the middle, with the same amount of numbers below and above.
• If there is an even amount of numbers in the list, the middle pair must be determined, added together, and divided by two to find the median value.

Median is the middle number in a sorted list of numbers. To determine the median value in a sequence of numbers, the numbers must first be sorted, or arranged, in value order from lowest to highest or highest to lowest. The median can be used to determine an approximate average, or mean, but is not to be confused with the actual mean.

• If there is an odd amount of numbers, the median value is the number that is in the middle, with the same amount of numbers below and above.
• If there is an even amount of numbers in the list, the middle pair must be determined, added together, and divided by two to find the median value.

The median is sometimes used as opposed to the mean when there are outliers in the sequence that might skew the average of the values. The median of a sequence can be less affected by outliers than the mean.

To find the median value in a list with an odd amount of numbers, one would find the number that is in the middle with an equal amount of numbers on either side of the median. To find the median, first arrange the numbers in order, usually from lowest to highest.

For example, in a data set of {3, 13, 2, 34, 11, 26, 47}, the sorted order becomes {2, 3, 11, 13, 26, 34, 47}. The median is the number in the middle {2, 3, 11, 13, 26, 34, 47}, which in this instance is 13 since there are three numbers on either side.

To find the median value in a list with an even amount of numbers, one must determine the middle pair, add them, and divide by two. Again, arrange the numbers in order from lowest to highest.

For example, in a data set of {3, 13, 2, 34, 11, 17, 27, 47}, the sorted order becomes {2, 3, 11, 13, 17, 27, 34, 47}. The median is the average of the two numbers in the middle {2, 3, 11, 13, 17,2634, 47}, which in this case is fifteen {(13 + 17) ÷ 2 = 15}.

## Statistics: Power from Data! Calculating the median

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If observations of a variable are ordered by value, the median value corresponds to the middle observation in that ordered list. The median value corresponds to a cumulative percentage of 50% (i.e., 50% of the values are below the median and 50% of the values are above the median). The position of the median is

{(n + 1) ÷ 2}th value, where n is the number of values in a set of data.

In order to calculate the median, the data must first be ranked (sorted in ascending order). The median is the number in the middle.

Median = the middle value of a set of ordered data.

The median is usually calculated for numeric variables, but may also be calculated for categorical variables that are sequenced, such as the categories in a satisfaction survey: excellent, good, satisfactory and poor. These qualitative categories can be ranked in order, and thus, are considered ordinal.

### Raw data

In raw data, the median is the point at which exactly half of the data are above and half below. These halves meet at the median position.

If the number of observations is odd, the median fits perfectly and the depth of the median position will be a whole number. If the number of observations is even, the depth of the median position will include a decimal.

You need to find the midpoint between the numbers on either side of the median position.

### Example 1 – Raw data (discrete variables)

Imagine that a top running athlete in a typical 200-metre training session runs in the following times:

26.1, 25.6, 25.7, 25.2 et 25.0 seconds.

How would you calculate his median time?

First, the values are put in ascending order: 25.0, 25.2, 25.6, 25.7, 26.1. Then, using the following formula, figure out which value is the middle value. Remember that n represents the number of values in the data set.

• Median = {(n + 1) ÷ 2}th value = (5 + 1) ÷ 2
• = 3

The third value in the data set will be the median. Since 25.6 is the third value, 25.6 seconds would be the median time.

= 25.6 secondes

### Example 2 – Raw data (discrete variables)

Now, if the runner sprints the sixth 200-metre race in 24.7 seconds, what is the median value now?

Again, you first put the data in ascending order: 24.7, 25.0, 25.2, 25.6, 25.7, 26.1. Then, you use the same formula to calculate the median time.

1. Median = {(n + 1) ÷ 2}th value = (6 + 1) ÷ 2 = 7 ÷ 2
2. = 3,5

Since there is an even number of observations in this data set, there is no longer a distinct middle value. The median is the 3.5th value in the data set meaning that it lies between the third and fourth values. Thus, the median is calculated by averaging the two middle values of 25.2 and 25.6. Use the formula below to get the average value.

Average = (value below median + value above median) ÷ 2 = (third value + fourth value) ÷ 2 = (25.2 + 25.6) ÷ 2 = 50.8 ÷ 2

= 25.4

The value 25.4 falls directly between the third and fourth values in this data set, so 25.4 seconds would be the median time.

### Ungrouped frequency distribution

In order to find the median using cumulative frequencies (or the number of observations that lie above or below a particular value in a data set), you must calculate the first value with a cumulative frequency greater than or equal to the median. If the median's value is exactly 0.5 more than the cumulative frequency of the previous value, then the median is the midpoint between the two values.

### Example 3 – Ungrouped frequency table (discrete variables)

• Imagine that your school baseball team scores the following number of home runs in 10 games:
• 4, 5, 8, 5, 7, 8, 9, 8, 8, 7
• If you were to place the total home runs in a frequency table, what would the median be?
• First, put the scores in ascending order:
• 4, 5, 5, 7, 7, 8, 8, 8, 8, 9

Then, make a table with two columns. Label the first column “Number of home runs” and then list the possible number of home runs the team could get. You can start from 0 and list up until the number 10, but since the team never scored less than 4 home runs, you may wish to start listing at the number 4.

Label the second column “Frequency.” In this column, record the number of times 4 home runs were scored, 5 home runs were scored and so on. In this case, there was only one time that 4 home runs were scored, but two times that 5 home runs were scored. If you add all of the numbers in the Frequency column, they should equal 10 (for the 10 games played).

Table 1.  Number of home runs in 10 baseball games

4

5

6

7

8

9

 1 2 2 4 1
1. To find the median, again use the same formula:
2. Median = {(n + 1) ÷ 2}th value = (10 + 1) ÷ 2 = 11 ÷ 2 = 5.5
3. = the median is the 5.5th value in the data set

To get the median, add up the numbers in the Frequency column until you get to 5 (and since the total number of games is 10, the remaining numbers in that column should also equal 5).

You will reach 5 after adding all of the frequencies up to and including those for the 7 home runs. The next set of five will begin with the frequencies for 8 home runs. The median (the 5.5th value) lies between the fifth value and the sixth value.

Thus, the median lies between 7 home runs and 8 home runs.

If you calculate the average of these values (using the same formula used in Example 2), the result is 7.5.

• Average = (middle value before + middle value after) ÷ 2 = (fifth value + sixth value) ÷ 2 = (7 + 8) ÷ 2 = 15 ÷ 2
• = 7.5

Technically, the median should be a possible variable. In the above example, the variables are discrete and always whole numbers. Therefore, 7.5 is not a possible variable—no one can hit 7 and a half home runs. Thus, this number only makes sense statistically. Some mathematicians may argue that 8 is a more appropriate median.

### Grouped frequency distribution

Sometimes it does not make sense to list each individual variable when a frequency distribution table would be long and cumbersome to work with.

In order to simplify this, divide the range of data into intervals and then list the intervals in a frequency distribution table, including a column for the cumulative percentage.

The calculation to find the median is a little longer because the data have been grouped into intervals and, therefore, all of the original information has been lost. Some textbooks simply take the midpoint of the interval as the median. However, that method is an over-simplification of the true value. Use the following calculations to find the median for a grouped frequency distribution.

1. Figure out which interval contains the median by using the (n + 1) ÷ 2

## How to Find the Median Value

It's the middle of a sorted list of numbers.

The Median is the “middle” of a sorted list of numbers.

To find the Median, place the numbers in value order and find the middle.

• Put them in order:
• 3, 5, 12
• The middle is 5, so the median is 5.
1. 3, 13, 7, 5, 21, 23, 39, 23, 40, 23, 14, 12, 56, 23, 29
2. When we put those numbers in order we have:
3. 3, 5, 7, 12, 13, 14, 21, 23, 23, 23, 23, 29, 39, 40, 56
4. There are fifteen numbers.

Our middle is the eighth number:

5. 3, 5, 7, 12, 13, 14, 21, 23, 23, 23, 23, 29, 39, 40, 56
6. The median value of this set of numbers is 23.
7. (It doesn't matter that some numbers are the same in the list.

)

### Two Numbers in the Middle

BUT, with an even amount of numbers things are slightly different.

In that case we find the middle pair of numbers, and then find the value that is half way between them. This is easily done by adding them together and dividing by two.

• 3, 13, 7, 5, 21, 23, 23, 40, 23, 14, 12, 56, 23, 29
• When we put those numbers in order we have:
• 3, 5, 7, 12, 13, 14, 21, 23, 23, 23, 23, 29, 40, 56
• There are now fourteen numbers and so we don't have just one middle number, we have a pair of middle numbers:
• 3, 5, 7, 12, 13, 14, 21, 23, 23, 23, 23, 29, 40, 56
• In this example the middle numbers are 21 and 23.
• To find the value halfway between them, add them together and divide by 2:
• 21 + 23 = 44 then 44 ÷ 2 = 22
• So the Median in this example is 22.

(Note that 22 was not in the list of numbers … but that is OK because half the numbers in the list are less, and half the numbers are greater.)

### Where is the Middle?

A quick way to find the middle: count how many numbers, add 1 then divide by 2

45 plus 1 is 46, then divide by 2 and we get 23

So the median is the 23rd number in the sorted list.

66 plus 1 is 67, then divide by 2 and we get 33.5

33 and a half? That means that the 33rd and 34th numbers in the sorted list are the two middle numbers.

So to find the median: add the 33rd and 34th numbers together and divide by 2.