What is iqr in excel

In this guide, I will show you how to calculate the interquartile range (IQR) by using Microsoft Excel. I will also show you how to how to calculate the first and third quartiles for a dataset.

What is the IQR?

The IQR is the difference between the first (25th percentile) and third (75th percentile) quartiles. These are often abbreviated to Q1 and Q3 respectively.

The IQR is used to represent the middle (50%) spread of the data. When a dataset is sorted in order from the smallest to the largest values, it is possible to split the data into four parts (the quartiles).

Consider the simple example below. In it, Q1 is 3.5 (half way between 3 and 4) and Q3 is 8.5 (half way between 8 and 9). Thus, the IQR is 5 (ie 8.5 – 3.5).

There is no direct formula to calculate the IQR in Excel, however, it is relatively straight forward to do. The easiest approach is to firstly calculate the Q1 and Q3 and then use these to determine the IQR.

Below is the steps recommended to calculate the IQR in Excel.

1. To calculate the Q1 in Excel, click on an empty cell and type ‘=QUARTILE(array, 1)‘. Replace the ‘array‘ part with the data of interest. For this, simply click and drag on the cells containing all of the data. The ‘1‘ in the formula signifies Excel to return the Q1 of the data.

2. Next, we need to calculate Q3. To calculate Q3 in Excel, simply find an empty cell and enter the formula ‘=QUARTILE(array, 3)‘. Again, replacing the ‘array‘ part with the cells that contain the data of interest.

3. Finally, to calculate the IQR, simply subtract the Q1 value away from the Q3 value. In the example above, the formula used would be ‘=D3-D2‘.

Combine the approach to form one equation

The approach described above to calculate the IQR is rather long winded. If you are more confident with working with Excel and fomulas, you could combine everything into one simple formula.

For example, the formula below would create the IQR in Excel. Just remember to replace the ‘array‘ components with the desired cells containing the data.

=QUARTILE(array, 3) - QUARTILE(array, 1)

Conclusion

The IQR is a measure of the middle dispersion of a dataset, basically the difference between Q1 and Q3. To calculate the IQR in Microsoft Excel, use the =QUARTILE function to calculate Q1 and Q3, and ultimately find the difference between these two values.

Microsoft Excel version used: 365 ProPlus

The IQR is a measure of the middle dispersion of a dataset, basically the difference between Q1 and Q3. To calculate the IQR in Microsoft Excel, use the =QUARTILE function to calculate Q1 and Q3, and ultimately find the difference between these two values.

How do you find the IQR?

The interquartile range is the difference between the upper quartile and the lower quartile. In example 1, the IQR = Q3 – Q1 = 87 – 52 = 35. The IQR is a very useful measurement. It is useful because it is less influenced by extreme values as it limits the range to the middle 50% of the values.

What is Q1 and Q3 in Excel?

First Quartile, Q1: It is also known as the lower quartile where 25% of the scores fall below it. Median (middle value) or second quartile: It is basically the mid-value in the dataset. Third Quartile, Q3: It is also known as the Upper quartile in which 25% of the data is above it and the rest 75% falls below it.

What does IQR stand for in Excel?

The interquartile range, often denoted IQR, is a way to measure the spread of the middle 50% of a dataset. It is calculated as the difference between the first quartile* (Q1) and the third quartile (Q3) of a dataset.

How do you find Q3?

Q1 is the median (the middle) of the lower half of the data, and Q3 is the median (the middle) of the upper half of the data. (3, 5, 7, 8, 9), | (11, 15, 16, 20, 21).

What is Iqr in math?

The “Interquartile Range” is the difference between smallest value and the largest value of the middle 50% of a set of data.

How do you find range on Excel?

Calculating Range in One Step
Imagine you have data running from cell A2 to cell A20. Type “=MAX(A2:A20)-MIN(A2:A20)” to find the range in a single step. This tells Excel to find the maximum of the data and then subtract the minimum of the data from it.

What is range formula in Excel?

A formula range is usually a reference to a range of cells, within which a formula persists consistently throughout the full range.A formula range, like a cell range, is defined by the reference of the upper left cell of the range and the reference of the lower right cell of the range.

How do you find the mode on Excel?

Use a function to find the mode in Microsoft Excel

1. Step 1: Type your data into one column.
2. Step 2: Click a blank cell anywhere on the worksheet and then type “=MODE.
3. Step 3: Change the range in Step 2 to reflect your actual data.
4. Step 4: Press “Enter.” Excel will return the solution in the cell with the formula.

How do you find Q1 Q2 and Q3?

There are four different formulas to find quartiles:

1. Formula for Lower quartile (Q1) = N + 1 multiplied by (1) divided by (4)
2. Formula for Middle quartile (Q2) = N + 1 multiplied by (2) divided by (4)
3. Formula for Upper quartile (Q3) = N + 1 multiplied by (3) divided by (4)

How do you find Q1 and Q3 with even numbers?

Since there are an even number of data points in the first half of the data set, the middle value is the average of the two middle values; that is, Q1 = (3 + 4)/2 or Q1 = 3.5. Q3 is the middle value in the second half of the data set.

How do you find the interquartile range with an even set of numbers?

How To Find Interquartile Range for an Even Set of Numbers

1. Order the numbers from least to greatest.
2. Make a mark in the center of the data:
3. Place the parentheses around the numbers before and after the median.
4. Find the median.
5. Subtract Q1 from Q3 to find the interquartile range.

Which method can be used to find the interquartile range for a set of data?

To find the interquartile range (IQR), ​first find the median (middle value) of the lower and upper half of the data. These values are quartile 1 (Q1) and quartile 3 (Q3). The IQR is the difference between Q3 and Q1.

What is the value of Q3?

The upper quartile, or third quartile (Q3), is the value under which 75% of data points are found when arranged in increasing order. The median is considered the second quartile (Q2). The interquartile range is the difference between upper and lower quartiles.

What is the quartile 3?

The upper or third quartile, denoted as Q3, is the central point that lies between the median and the highest number of the distribution.

How do you find a range of numbers in Excel?

Enter formula =IF(COUNTIF(A1:E8,”new”),”Yes”,”No“) into the Formula Bar, and then press the Enter key. Notes: 1. In the formula, A1:E8 is the range you want to find certain number or value inside.

How do I use mult mode in Excel?

How to use the MODE. MULT Function in Excel?

1. Select a vertical range of cells.
2. Enter the MODE. MULT function.
3. Confirm with Ctrl + Shift + Enter.
4. In each selected cell, MODE. MULTI will return a mode value if one exists.

How do you find the modal number?

The mode is the number that appears the most.

1. To find the mode, order the numbers lowest to highest and see which number appears the most often.
2. Eg 3, 3, 6, 13, 100 = 3.
3. The mode is 3.

How do I find the 5 most common numbers in Excel?

If you just want to find most common number in a list, you can use a simple formula. Select a blank cell, here is C1, type this formula =MODE(A1:A13), and then press Enter key to get the most common number in the list.

Can Google Sheets calculate IQR?

Find IQR Using Percentile Function in Sheets
Since we can find the Q1 and Q3 using the Percentile function, we can use this function also for finding IQR in Google Sheets. Replace the Quartile formulas in cell C2 and D2 with the following Percentile formulas. You can keep the same formula in cell E2, i.e., =D2-C2 .

What is the 1.5 IQR rule?

A commonly used rule says that a data point is an outlier if it is more than 1.5 ⋅ IQR 1.5cdot text{IQR} 1. 5⋅IQR1, point, 5, dot, start text, I, Q, R, end text above the third quartile or below the first quartile.

Для вычисления квартилей в MS EXCEL существует специальная функция

КВАРТИЛЬ()

. В этой статье дадим определение квартилей и научимся их вычислять для выборки и для непрерывного распределения. Также вычислим интерквартильный интервал.

Квартили

(Quartiles) — значения, которые делят

выборку

(набор значений) на четыре части, содержащие приблизительно равное количество наблюдений (по 25%).

Поясним определение

квартиля

на примере. Пусть имеется

выборка

, состоящая из 50 значений в ячейках

А7:А56

(см.

файл примера

, лист Квартиль-выборка). Для наглядности

отсортируем значения по возрастанию

и построим

гистограмму

.

Чтобы разделить

выборку

на 4 части достаточно 3-х

квартилей

.

Первый

квартиль

(или

нижний квартиль

, Q1) делит

выборку

, на 2 части: примерно 25% значений в

выборке

меньше Q1, остальные 75% — больше. Для вычисления

1-го квартиля

используйте формулу

=КВАРТИЛЬ.ВКЛ(A7:A56;1)

. Для нашей выборки формула вернет значение 224. Значения 224 нет в

выборке

, формула произвела интерполяцию на основе 2-х соседних значений 223 и 227.

Примечание

: Функция

КВАРТИЛЬ.ВКЛ()

появилась в MS EXCEL 2010. В более ранних версиях использовалась аналогичная ей функция

КВАРТИЛЬ()

.

Чтобы убедиться, что примерно 25% значений меньше, чем 224, используем формулу

=СЧЁТЕСЛИ(A7:A56;»<«&224)/СЧЁТ(A7:A56)

. В результате получим, что 26% меньше, чем 1-й

квартиль

.

Чем в

выборке

больше значений и меньше

повторов

, тем точнее деление

выборки квартилями

на четверти.

Примечание

: Первый квартиль — это то же самое, что и 25-я

процентиль

. Подробнее см.

статью про процентили

.

Второй

квартиль

(или

медиана

, Q2) также делит

выборку

, на 2 равные части: половина чисел множества больше, чем

медиана

, а половина чисел меньше, чем

медиана

. Для вычисления 2-го

квартиля

используйте формулу

=КВАРТИЛЬ.ВКЛ(A7:A56;2)

или

=МЕДИАНА(A7:A56)

Третий

квартиль

(или верхний

квартиль

, Q3) делит

выборку

, на 2 части: примерно 75% значений в

выборке

меньше Q3, остальные 25% — больше. Для вычисления 3-го

квартиля

используйте формулу

=КВАРТИЛЬ.ВКЛ(A7:A56;3)

или

=ПРОЦЕНТИЛЬ.ВКЛ(A7:A56;0,75)

Примечание

: Третий

квартиль

— это то же самое, что и 75-я

процентиль

.

Второй аргумент функции

КВАРТИЛЬ.ВКЛ()

может также принимать значения 0 и 4. В первом случае функция вернет

минимальное значение

, во втором –

максимальное

.

Интерквартильный размах

Интерквартильным размахом

или

интерквартильным интервалом

(InterQuartile range, IQR) называется разность между третьим и первым

квартилями

(Q3 — Q1).

Интерквартильный размах

является характеристикой разброса значений в

выборке

.

Примечание

: Характеристикой разброса значений в

выборке

является также

дисперсия и стандартное отклонение

.

Интерквартильный размах

, а также

квартили

используются при построении

Блочной диаграммы

, которая полезна для оценки разброса значений (variation) в небольших

выборках

или для сравнения нескольких

выборок

имеющих сходные распределения.

Подробнее о построении

Блочной диаграммы

см. статью

Блочная диаграмма в MS EXCEL

.

Квартили непрерывного распределения

Если

функция распределения

F

(х)

случайной величины

х

непрерывна, то 1-й

квартиль

является решением уравнения

F(х)

=0,25, второй —

F(х)

=0,5, а третий

F(х)

=0,75.

Примечание

: Подробнее о

Функции распределения

см. статью

Функция распределения и плотность вероятности в MS EXCEL

.

Если известна

функция плотности вероятности

p

(х)

, то 1-й

квартиль

можно найти из уравнения:

Например, решив аналитическим способом это уравнение для

Логнормального распределения

lnN(μ; σ

²

), получим, что

медиана

(2-й

квартиль

) вычисляется по формуле e

^μ

или в MS EXCEL =EXP(μ). При μ=1,

медиана

равна 2,718.

Обратите внимание на точку

Функции распределения

, для которой

F(х)=0,5

(см. картинку выше или

файл примера

, лист Квартиль-распределение)

.

Абсцисса этой точки равна 2,718. Это и есть значение 2-го

квартиля

(

медианы

), что естественно совпадает с ранее вычисленным значением по формуле e

^μ

.

Примечание

: Напомним, что интеграл от

функции плотности вероятности

по всей области задания случайной величины равен единице:

Поэтому, линии

квартилей

(

х=квартиль

) делят площадь под графиком

функции плотности вероятности

на 4 равные части.

Квартили в MS EXCEL

Чтобы вычислить в MS EXCEL

квартили

заданного распределения необходимо использовать соответствующую

обратную функцию распределения

.

При вычислении

квартилей

в MS EXCEL используются

обратные функции распределения

:

НОРМ.СТ.ОБР()

,

ЛОГНОРМ.ОБР()

,

ХИ2.ОБР()

,

ГАММА.ОБР()

и т.д. Подробнее о распределениях, представленных в MS EXCEL, можно прочитать в статье

Распределения случайной величины в MS EXCEL

.

Например, в MS EXCEL 1-й

квартиль

для

логнормального распределения

LnN(1;1) можно вычислить по формуле

=ЛОГНОРМ.ОБР(0,25;1;1)

, а 3-й

квартиль

для

стандартного нормального распределения

по формуле

=НОРМ.СТ.ОБР(0,75)

.

Stats students must know about the term Interquartile Range which helps in recognizing the natural flow that appears in a dataset. In Excel, you will not find any direct way to analyze the IQR, however, you still need an answer to how to calculate IQR in Excel.

What is the IQR?

Before getting started let’s understand what this IQR term means in reality. When you tend to find the difference between the first and third quartiles it usually gives IQR value. moreover, the IQR shows 50% of the data. You can simply sort data in four sections when you need a dataset to be sorted from the smallest to the largest values. Below is a simple example you can consider:

Q1 is 3.5 and Q3 is 8.5

The IQR would be 5:

How to Calculate IQR in Excel with Quartile Function?

With the help of the Quartile function, you can easily find out the Interquartile Range in Excel. Using this function, you need to calculate Q1 and Q3 to find IQR in Excel and for this, you need to follow the steps given steps:

• Choose Cell F6 in the first step.
• Enter the following formula.
• =QUARTILE(C5:C15, 1)

• The range C5:C15 is selected in the QUARTILE function and it returns 1 as quart which simply means 25th percentile. Now, you will get the first quartile from the array.
• Press ENTER key and you will get the value of Quartile(Q1).

• Choose cell F7.
• Enter the following formula.

=QUARTILE(C5:C15, 3)

• In this function, the C5:C15 is selected as an array and it returns 3 as a quart in which 3 shows the 75th percentile. You will get the third quartile in return from the array.
• Press ENTER key and you will get the value of Quartile(Q3).

• Now, you need to find the difference between Quartile Q1 and Quartile Q3. For this, enter the following formula in cell F8:

=F7-F6

• Press ENTER key and you will get the Interquartile Range.

That’s it!

This is how to calculate IQR in Excel with the help of the QUARTILE function.

How to Calculate IQR in Excel with the QUARTILE.INC Function?

In this method, you will find an example in which the dataset has test scores given in cell range B2:B21. You need to find the Interquartile Range in the D3 cell.

Here is the formula given:

=QUARTILE.INC(B2:B21,3)-QUARTILE.INC(B2:B21,1)

Let’s have a bit more understanding of how this formula works:

As already explained that Excel does not have a direct function to calculate the IQR, that’s why some alternatives appear including the use of QUARTILE.INC function. It helps in returning the third quartile and the first quartile in the formula.

When you get the value of the difference between these two, it is called the Interquartile Range value. and the syntax for this function is given below:

Syntax of the QUARTILE.INC Function:

=QUARTILE.INC(array, quart)

array: This argument contains the cell range or numeric values. And this is a compulsory value to be added to the formula.

quart: This is also a required value that gives a value between 0 and 4. It simply indicates the function should return. You will always get a minimum value when 0 is specified. On the other hand, you will get the first quartile when 1 is specified. In case, when 2 is specified, you will get the median value.

Ultimately, you have noticed that the first part of the formula is given the third quartile, whereas we have specified the number 3. When the number 1 is specified, the second part of the formula gives the first quartile. And we have an IQR of 6 that appears by calculating the difference between these two values.

How Do You Interpret the IQR Results?

You can interpret the IQR results in several different ways. You can simply take it as a value that shows the value range in which you can see the most data points. Therefore, you must know that the IQR value will be higher when the dataset has multiple variables.

Things to Consider:

MIN, MEDIAN, and MAX values can be used in the QUARTILE function.

You will face the #NUM! error when the array does not have any value.

Whenever you will have the quart<0 or quart>4, you will face the #NUM! error.

Summary:

In this post, you have learned how to calculate IQR in Excel with the help of multiple approaches. Each method is worth appraising and you can try any of them without risk.

In statistics, the five-number summary is mostly used as it gives a rough idea about the dataset. It is basically a summary of the dataset describing some key features in statistics. The five key features are :

1. Minimum value: It is the minimum value in the data set.
2. First Quartile, Q1: It is also known as the lower quartile where 25% of the scores fall below it.
3. Median (middle value) or second quartile: It is basically the mid-value in the dataset.
4. Third Quartile, Q3: It is also known as the Upper quartile in which 25% of the data is above it and the rest 75% falls below it.
5. Maximum value: It is the maximum value in the dataset.

Using two quartiles of the five-number summary we can easily calculate the IQR abbreviated as Interquartile Range.

In this article, we are going to see how to calculate the Interquartile range in Excel using a sample dataset as an example.

Interquartile Range

In terms of Mathematics, it is basically defined as the difference between the third quartile (75th  percentile) and the first quartile (25th percentile).

Q3-Q1

IQR denotes the middle 50% hence also known as midspread or H-spread in statistics. It can be easily observed using a box plot. 

The vertical lines of the rectangular box plot denote the Interquartile range which lies between Quartile 1 and Quartile 3.

Example: Consider the dataset consisting of the BMI of ten students in a class.

Now, in order to calculate the IQR we need to first calculate the two quartile values Q1 and Q3. The function used is :

QUARTILE(Array,quart)         // Used in Excel 2007 version and lower
or
QUARTILE.INC(Array,quart)    // Used in latest version of Excel

Array : Cell range
quart : The five quart values from 0 to 4

0- Minimum value
1- First Quartile (25 percent)
2- Median Value (50 percentile)
3- Third Quartile (75 percentile)
4- Maximum value

Calculation

Follow the below steps to calculate the same:

Step 1: Insert the dataset.

Step 2: Select any cell where you want to write the formula to calculate the values of Q1, Q3, and IQR.

Step 3: First find the values of Q1 and Q3 using the quart values as 1 and 3 respectively.

The dataset is stored in column “A” of the worksheet and the observations are stored from cell A2 to A11.

So the array will start from A2 and end at A11.

You can also find the remaining three parameters of a five-number summary using the same formula just by changing the quart value. But to find the IQR, we only need the values of Q1 and Q3.

The value of Q3 is stored in cell D4 and that of Q1 in cell D3. The formula will be :

=Cell_no_Q3-Cell_no_Q1

The Interquartile range for the above dataset turns out to be 6.5.