How to find median in excel

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You can use the following formulas to find the mean, median, and mode of a dataset in Excel:

=AVERAGE(A1:A10)

=MEDIAN(A1:A10) 

=MODE.MULT(A1:A10) 

It’s worth noting that each of these formulas will simply ignore non-numeric or blank values when calculating these metrics for a range of cells in Excel.

The following examples shows how to use these formulas in practice with the following dataset:

Example: Finding the Mean in Excel

The mean represents the average value in a dataset.

The following screenshot shows how to calculate the mean of a dataset in Excel:

The mean turns out to be 19.11. 

Example: Finding the Median in Excel

The median represents the middle value in a dataset, when all of the values are arranged from smallest to largest.

The following screenshot shows how to calculate the median of a dataset in Excel:

The median turns out to be 20.

Example: Finding the Mode in Excel

The mode represents the value that occurs most often in a dataset. Note that a dataset can have no mode, one mode, or multiple modes.

The following screenshot shows how to calculate the mode(s) of a dataset in Excel:

The modes turn out to be 7 and 25. Each of these values appears twice in the dataset, which is more often than any other value occurs.

Note: If you use the =MODE() function instead, it will only return the first mode. For this dataset, only the value 7 would be returned. For this reason, it’s always a good idea to use the =MODE.MULT() function in case there happens to be more than one mode in the dataset.

Additional Resources

How to Calculate the Interquartile Range (IQR) in Excel
How to Calculate the Midrange in Excel
How to Calculate Standard Deviation in Excel

Excel Median Formula (Table of Contents)

• Median Formula in Excel
• How to Calculate the Median in Excel using Formula?

Median Formula in Excel is one of the prime members of the statistical measure of central tendency (the rest two are mean and mode). It gives a more decent approach to finding out the middle most value for the given data.

If we are having a group of observations arranged in ascending or descending order, then the median of that group will be the middle most value. This means exactly 50% (half of the observations) are above median value, and exactly 50% (or half of the observations) are below the median value.

If the data set is with an odd number of observations, the median will be the middle observation. If the data set is with an even number of observations, the median will be the average of the middle two observations.

In cases where we need to calculate the exact center of the data, e.g. Calculation containing data of salary are the ones where the mean value would not be with that efficiency. The reason behind it is, our mean value might have extremely low or high observations, which may affect the average salary. However, the median is least affected by such extreme observations, due to which we prefer calculating it.

In Microsoft Excel, we can calculate the median using the MEDIAN function. It is an in-built function in excel that works on a range of data and calculates the median for that group.

The Formula for Excel MEDIAN function is as below:

Where, number1, number2 … are the arguments for the function. Excel MEDIAN Formula can take numbers, arrays, named ranges, dates, or cell references as input arguments. This function requires at least one argument to provide an output (i.e. number1 is fixed/required argument, the rest all are optional).

How to Calculate the Median in Excel using Formula?

To calculate the Median in excel using a formula is very simple and easy. Let’s understand how to calculate the Median in excel with some examples.

You can download this Median Formula Excel Template here – Median Formula Excel Template

Example #1 – Group with an Odd Number of Observation

Suppose I have data on vehicle sales in a million from 2010 to 2018 for the USA. (9 observations in total which is an odd number).

In the image below, you can see that the observations are listed in ascending order by year.

Put the following formula in cell B12. i.e.=MEDIAN(B2:B10). See the image below:

What you expect to be an output using this formula?

As you might have rightly guessed, this function allows excel to print the Median value for the given range (B2:B10), which is 202 in this case.

• Press enter once you are done with the formula, and you’ll get the following output:

The year associated with the median value can be considered as Median Year (in this case, 2014). It seems logical, right?

Please note that we have arranged the data Year wise and not the Sales wise. So, don’t get confused if the sales value seems to be not in ascending or descending order.

Now, what if I have an even number of observations?

Example #2 – Group with Even Number of Observation

Suppose I have sales detail for one more the year 2019. That means even the number (10) of observations. Let’s see how the median formula works on such data.

Suppose I have data as below:

In cell D2, input the formula =MEDIAN(B2:B11)

Press enter once done and see the output.

When you are having an even number of observations, the Median value is an average of two middlemost values.

Conditional Median Formula

While working on the AVERAGE function in Excel, you might have seen some customized formulas like AVERAGEIF & AVERAGEIFS, which are allowing you to customize the AVERAGE function based on condition/conditions. That means giving an average of a group following specific criteria. Unfortunately, for MEDIAN, there is no such customized formula available ready-made in Excel. However, you can use your own logic and create one of such conditional formulas for the calculation of the Median of a group of observations.

Following is the formula which can be used:

Example #3 – Excel Median If Formula

Suppose you have data of cars type and their costs in Lakhs as below:

You wanted a median cost for Car Type Sedan in your data; what can you do?

For that, put the Car Type values in one separate column, say column D.

Use the conditional formula below:

=MEDIAN(IF($A$2:$A$13 = $D$2, $B$2:$B$13))

See the image below:

Hit Ctrl + Shift + Enter at the same time after you have completed the formula.

Because you are working on a range of cells (i.e. Array), the dollar sign ($) makes the cell ranges absolute and is helpful when you have the same range of data for different other categories.

Moreover, as you can see through the formula, you are working on a range of cells which is array now, to make the array formula work, you need to hit Ctrl + Shift + Enter.

What this formula has done is, it has selected all the Sedan’s and their costs in lakhs, arranged those in ascending order (which is by default) and then selected the median from the available set of value.

Do the same procedure for other cells in column D (cell D3, D4, D5, D6).

You also can add multiple conditions in this formula and make it work like AVERAGEIFS.

That’s it from this article. Let’s wrap up with some things to remember.

Things to Remember About Median Formula in Excel

• When the group of observations has an odd number of values, the MEDIAN formula considers the middle most value as a median. If the group of observations has an even number of values, the MEDIAN formula considers an average of two middlemost values as a median.
• Your group of observation should be sorted in ascending or descending order before you start using this formula.
• If any cell has zero value, it still is a part of median calculations.
• In most of the cases, the median has preference over the mean. Because it is least affected by extreme low/high observations.
• While calculating empty cells, cells with text or logical values are neglected automatically.
• Excel 2003 and earlier allows 30 arguments per formula for the MEDIAN function. In Excel 2007, 2010, 2013, 2016, this limit has been extended from 30 to 255. It means that you can pass till 255 arguments.
• Logical values of TRUE and FALSE gets counted in the MEDIAN formula. For example, MEDIAN(FALSE, TRUE, 2, 3) will be outputting 1.5 as a median which is nothing but an average of Logical value of TRUE (TRUE =1) and a number 2.

Recommended Articles

This has been a guide to Median Formula in Excel. Here we discuss How to calculate Median in Excel along with practical examples and a downloadable excel template. You can also go through our other suggested articles –

1. Excel Frequency Formula
2. Excel FV Formula
3. Statistics in Excel
4. How to Find Mean in Excel

В этой статье описаны синтаксис формулы и использование функции МЕДИАНА в Microsoft Excel.

Описание

Возвращает медиану заданных чисел. Медиана — это число, которое является серединой множества чисел.

Синтаксис

Аргументы функции МЕДИАНА описаны ниже.

Число1, число2. Аргумент «число1» является обязательным, последующие числа необязательные. От 1 до 255 чисел, для которых требуется определить медиану.

Замечания

Если в наборе имеется ряду чисел, медиана вычисляет среднее значение двух чисел в середине. См. вторую формулу в примере.

Аргументы могут быть либо числами, либо содержащими числа именами, массивами или ссылками.

Учитываются логические значения и текстовые представления чисел, которые непосредственно введены в список аргументов.

Если аргумент, который является массивом или ссылкой, содержит текст, логические значения или пустые ячейки, то такие значения пропускаются; однако ячейки, которые содержат нулевые значения, учитываются.

Аргументы, которые являются значениями ошибки или текстами, не преобразуемыми в числа, приводят в возникновению ошибок.

Примечание: Функция МЕДИАНА измеряет центральную тенденцию, которая является центром множества чисел в статистическом распределении. Существует три наиболее распространенных способа определения центральной тенденции:

Среднее значение — это среднее арифметическое, которое вычисляется путем сложения набора чисел с последующим делением полученной суммы на их количество. Например, средним значением для чисел 2, 3, 3, 5, 7 и 10 будет 5, которое является результатом деления их суммы, равной 30, на их количество, равное 6.

Медиана — это число, которое является серединой множества чисел, то есть половина чисел имеют значения большие, чем медиана, а половина чисел имеют значения меньшие, чем медиана. Например, медианой для чисел 2, 3, 3, 5, 7 и 10 будет 4.

Мода — это число, наиболее часто встречающееся в данном наборе чисел. Например, модой для чисел 2, 3, 3, 5, 7 и 10 будет 3.

При симметричном распределении множества чисел все три значения центральной тенденции будут совпадать. При смещенном распределении множества чисел значения могут быть разными.

Пример

Скопируйте образец данных из следующей таблицы и вставьте их в ячейку A1 нового листа Excel. Чтобы отобразить результаты формул, выделите их и нажмите клавишу F2, а затем — клавишу ВВОД. При необходимости измените ширину столбцов, чтобы видеть все данные.

Источник

Let’s say you want to find out what the midpoint is in a distribution of student grades or a quality control data sample. To calculate the median of a group of numbers, use the MEDIAN function.

The MEDIAN function measures central tendency, which is the location of the center of a group of numbers in a statistical distribution. The three most common measures of central tendency are:

Average which is the arithmetic mean, and is calculated by adding a group of numbers and then dividing by the count of those numbers. For example, the average of 2, 3, 3, 5, 7, and 10 is 30 divided by 6, which is 5.

Median which is the middle number of a group of numbers; that is, half the numbers have values that are greater than the median, and half the numbers have values that are less than the median. For example, the median of 2, 3, 3, 5, 7, and 10 is 4.

Mode which is the most frequently occurring number in a group of numbers. For example, the mode of 2, 3, 3, 5, 7, and 10 is 3.

For a symmetrical distribution of a group of numbers, these three measures of central tendency are all the same. For a skewed distribution of a group of numbers, they can be different.

The screen shots in this article were taken in Excel 2016. If you have a different version your view might be slightly different, but unless otherwise noted, the functionality is the same.

Example

The example may be easier to understand if you copy it to a blank worksheet.

Open a blank workbook or worksheet.

How to copy an example

Select the example below.

Note: Do not select the row or column headers.

Источник

This article describes the formula syntax and usage of the MEDIAN function in Microsoft Excel.

Description

Returns the median of the given numbers. The median is the number in the middle of a set of numbers.

Syntax

The MEDIAN function syntax has the following arguments:

Number1, number2, . Number1 is required, subsequent numbers are optional. 1 to 255 numbers for which you want the median.

If there is an even number of numbers in the set, then MEDIAN calculates the average of the two numbers in the middle. See the second formula in the example.

Arguments can either be numbers or names, arrays, or references that contain numbers.

Logical values and text representations of numbers that you type directly into the list of arguments are counted.

If an array or reference argument contains text, logical values, or empty cells, those values are ignored; however, cells with the value zero are included.

Arguments that are error values or text that cannot be translated into numbers cause errors.

Note: The MEDIAN function measures central tendency, which is the location of the center of a group of numbers in a statistical distribution. The three most common measures of central tendency are:

Average which is the arithmetic mean, and is calculated by adding a group of numbers and then dividing by the count of those numbers. For example, the average of 2, 3, 3, 5, 7, and 10 is 30 divided by 6, which is 5.

Median which is the middle number of a group of numbers; that is, half the numbers have values that are greater than the median, and half the numbers have values that are less than the median. For example, the median of 2, 3, 3, 5, 7, and 10 is 4.

Mode which is the most frequently occurring number in a group of numbers. For example, the mode of 2, 3, 3, 5, 7, and 10 is 3.

For a symmetrical distribution of a group of numbers, these three measures of central tendency are all the same. For a skewed distribution of a group of numbers, they can be different.

Example

Copy the example data in the following table, and paste it in cell A1 of a new Excel worksheet. For formulas to show results, select them, press F2, and then press Enter. If you need to, you can adjust the column widths to see all the data.

Источник

by Svetlana Cheusheva, updated on February 7, 2023

When analyzing numerical data, you may often be looking for some way to get the «typical» value. For this purpose, you can use the so-called measures of central tendency that represent a single value identifying the central position within a data set or, more technically, the middle or center in a statistical distribution. Sometimes, they are also classified as summary statistics.

The three main measures of central tendency are Mean, Median and Mode. They all are valid measures of central location, but each gives a different indication of a typical value, and under different circumstances some measures are more appropriate to use than others.

How to calculate mean in Excel

Arithmetic mean, also referred to as average, is probably the measure you are most familiar with. The mean is calculated by adding up a group of numbers and then dividing the sum by the count of those numbers.

For example, to calculate the mean of numbers <1, 2, 2, 3, 4, 6>, you add them up, and then divide the sum by 6, which yields 3: (1+2+2+3+4+6)/6=3.

In Microsoft Excel, the mean can be calculated by using one of the following functions:

• AVERAGE- returns an average of numbers.
• AVERAGEA — returns an average of cells with any data (numbers, Boolean and text values).
• AVERAGEIF — finds an average of numbers based on a single criterion.
• AVERAGEIFS — finds an average of numbers based on multiple criteria.

For the in-depth tutorials, please follow the above links. To get a conceptual idea of how these functions work, consider the following example.

In a sales report (please see the screenshot below), supposing you want to get the average of values in cells C2:C8. For this, use this simple formula:

To get the average of only «Banana» sales, use an AVERAGEIF formula:

=AVERAGEIF(A2:A8, «Banana», C2:C8)

To calculate the mean based on 2 conditions, say, the average of «Banana» sales with the status «Delivered», use AVERAGEIFS:

=AVERAGEIFS(C2:C8,A2:A8, «Banana», B2:B8, «Delivered»)

You can also enter your conditions in separate cells, and reference those cells in your formulas, like this:

Median is the middle value in a group of numbers, which are arranged in ascending or descending order, i.e. half the numbers are greater than the median and half the numbers are less than the median. For example, the median of the data set <1, 2, 2, 3, 4, 6, 9>is 3.

This works fine when there are an odd number of values in the group. But what if you have an even number of values? In this case, the median is the arithmetic mean (average) of the two middle values. For example, the median of <1, 2, 2, 3, 4, 6>is 2.5. To calculate it, you take the 3rd and 4th values in the data set and average them to get a median of 2.5.

In Microsoft Excel, a median is calculated by using the MEDIAN function. For example, to get the median of all amounts in our sales report, use this formula:

To make the example more illustrative, I’ve sorted the numbers in column C in ascending order (though it is not actually required for the Excel Median formula to work):

In contrast to average, Microsoft Excel does not provide any special function to calculate median with one or more conditions. However, you can «emulate» the functionality of MEDIANIF and MEDIANIFS by using a combination of two or more functions like shown in these examples:

How to calculate mode in Excel

Mode is the most frequently occurring value in the dataset. While the mean and median require some calculations, a mode value can be found simply by counting the number of times each value occurs.

For example, the mode of the set of values <1, 2, 2, 3, 4, 6>is 2. In Microsoft Excel, you can calculate a mode by using the function of the same name, the MODE function. For our sample data set, the formula goes as follows:

=MODE(C2:C8)

In situations when there are two or more modes in your data set, the Excel MODE function will return the lowest mode.

Generally, there is no «best» measure of central tendency. Which measure to use mostly depends on the type of data you are working with as well as your understanding of the «typical value» you are attempting to estimate.

For a symmetrical distribution (in which values occur at regular frequencies), the mean, median and mode are the same. For a skewed distribution (where there are a small number of extremely high or low values), the three measures of central tendency may be different.

Since the mean is greatly affected by skewed data and outliers (non-typical values that are significantly different from the rest of the data), median is the preferred measure of central tendency for an asymmetrical distribution.

For instance, it is generally accepted that the median is better than the mean for calculating a typical salary. Why? The best way to understand this would be from an example. Please have a look at a few sample salaries for common jobs:

• Electrician — $20/hour
• Nurse — $26/hour
• Police officer — $47/hour
• Sales manager — $54/hour
• Manufacturing engineer — $63/hour

Now, let’s calculate the average (mean): add up the above numbers and divide by 5: (20+26+47+54+63)/5=42. So, the average wage is $42/hour. The median wage is $47/hour, and it is the police officer who earns it (1/2 wages are lower, and 1/2 are higher). Well, in this particular case the mean and median give similar numbers.

But let’s see what happens if we extend the list of wages by including a celebrity who earns, say, about $30 million/year, which is roughly $14,500/hour. Now, the average wage becomes $2,451.67/hour, a wage that no one earns! By contrast, the median is not significantly changed by this one outlier, it is $50.50/hour.

Agree, the median gives a better idea of what people typically earn because it is not so strongly affected by abnormal salaries.

This is how you calculate mean, median and mode in Excel. I thank you for reading and hope to see you on our blog next week!

Источник

Summary

The Excel MEDIAN function returns the median (middle number) in the supplied set of data. For example, =MEDIAN(1,2,3,4,5) returns 3.

Purpose

Return value

Arguments

• number1 — A number or cell reference that refers to numeric values.
• number2 — [optional] A number or cell reference that refers to numeric values.

Syntax

Usage notes

The MEDIAN function returns the median (middle number) in a set of data. The calculation performed by MEDIAN varies according to the number of numeric values provided. When the number is odd, MEDIAN returns the middle number in the group. When the number is even, MEDIAN returns the average of the two numbers in the middle.

The MEDIAN function takes multiple arguments in the form number1, number2, number3, etc. Arguments can be a hardcoded constant, a cell reference, or a range, in any combination. MEDIAN ignores empty cells, text values, and the logical values TRUE and FALSE. The MEDIAN function will accept up to 255 separate arguments.

Examples

When the number of values provided is odd, MEDIAN returns the middle number:

When the number of values provided is even, MEDIAN returns the average of the two middle numbers:

In the worksheet shown above, the formulas in H5 and H6 are:

Note that MEDIAN ignores the empty cell in D5:D16 and returns the middle number in the eleven values provided.

Источник