**What Is Covariance Function In Excel?**

The

COVARor theCovariance function in Excelcalculates the relationship between two given datasets whether they vary together directly or inversely. Users can use the function to evaluate the relationship between two groups of values, such as analyzing whether, investing more in marketing results in improved sales. If the variables vary directly, it is a positive covariance, and if the variables vary inversely or in the opposite direction, it is a negative covariance.

*The Covariance in Excel is replaced by COVARIANCE.P and COVARIANCE.S in Excel 2010. Thus, COVAR() is now available as a Compatibility function for backward compatibility.*

For example, we must determine the covariance of two datasets given in the table below.

Select cell **B13**, enter the formula **=COVAR(A2:A11,B2:B11), **and enter the “**Enter**” key.

The result is ‘**15.3’**, as shown above.

[**Output Observation:** Mathematically, the **COVAR()** calculates the aggregate of the products of the deviations for every data point pair in the two given datasets and then averages the resulting sum value.

As the **COVAR()** output is positive, it indicates a positive correlation between the two sets of values. For example, if the first dataset’s values increase, the second also follows the same trend.]

##### Table of contents

###### Key Takeaways

- The
**COVAR**function helps assess the correlation between two sets of values. For example, we can analyze the relationship between the revenue changes of two companies. - The supplied arguments can be number arrays, named ranges, or cell range references to numbers.
- The function ignores the text, logical values, and blank cells in the two supplied arrays or cell ranges. However, it counts cells containing zero.
- Newer
**Statistical**functions with improved accuracies, such as**COVARIANCE.P**and**COVARIANCE.S**, replaced the**COVAR**function in Excel 2010.

**COVAR() Excel Formula**

The syntax of the **COVAR Excel formula **is,

The arguments of the **COVAR Excel formula **are,

*array1***:**The first set of integers or variables or cell range. It is a mandatory argument.*array2***:**The second set of integers or variables or cell range. It is a mandatory argument.

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**How To Calculate Covariance in Function?**

We can use the **COVAR Excel Function to calculate covariance **in 2 ways, namely,

**Access from the Excel ribbon.****Enter in the worksheet manually.**

**Method #1 – Access from the Excel ribbon**

Choose an empty cell for output – select the “**Formulas**” tab – click the “**More Functions**” option drop-down – click the “**Compatibility**” option right arrow – select the “**COVAR**” function, as shown below.

The “**Function Arguments**” window appears. Enter the arguments in the “**Array1**”, and the “**Array2**” fields – click “**OK**”, as shown below.

#### Method #2 – Enter in the worksheet manually

- Select an empty cell for the output.
- Type
**=COVAR(**in the cell. [Alternatively, type**=C**or**=COV**and double-click the**COVAR**function from the Excel suggestions.] - Enter the arguments as cell values or cell references and close the brackets.
- Press
**Enter**to execute and get the required covariance value.

Let us take a basic example to understand its calculations.

We will calculate the covariance of the two given arrays, which will help determine whether spending on marketing improves the company’s sales figures **using** **Covariance in Excel**.

The table below shows a small venture’s monthly marketing costs and sales data.

The steps to calculate Covariance in Excel using COVAR() are,

**Select the target cell****B15**, and enter the formulai.e., the first variable range.*=COVAR(B2:B13,***Enter the second variable cell range as****C2:C13,**and close the brackets. The complete formula is**=COVAR(B2:B13,C2:C13).****Press the “****Enter**” key. The result is ‘18385.41667’, as shown below.

[Alternatively, select the target cell B15 and go to **Formulas** – **More Functions** – **Compatibility** – **COVAR** to apply the function in the chosen cell.

The above step will open the **Function Arguments **window.

Next, enter the given cell ranges in the respective fields in the **Function Arguments** window.

Finally, click **OK** to close the window, and we will see the **COVAR() **output in the target cell B15.]

[**Output Observation:** In the above example, the **COVAR() **accepts the two given array ranges as its arguments, B2:B13 and C2:C13. It then determines the average of the products of deviations for every data value pair in the two arrays and returns the covariance as **18385.41667**.

And since the **COVAR()** output is positive, it indicates a positive correlation between marketing costs and sales figures. Therefore, it implies that spending more on marketing improves the company’s sales.]

**Examples**

We will see some advanced scenarios using the **Covariance in Excel examples**.

**Example #1**

We will calculate the covariance between the two sets of given data using the **Covariance function.**

The below table shows the 10-day daily returns data of two stocks in a portfolio.

The procedure to calculate the** c**ovariance using the** COVAR()** is,

Select the target cell **B13**, enter the formula ** =COVAR(B2:B11,C2:C11), **and press

**Enter**.

The result is ‘**-0.59’, **as shown above.

[**Output Observation:** The result shows a negative correlation between the two stock sets. Thus, suggesting that if one stock shows a positive daily returns trend, the other will have a negative trend.]

**Example #2**

Mathematically, the below equation represents **Covariance in Excel**.

The terms **x̄** and ȳ denote the ** array1**, and

**mean values. And**

*array2***is the given sample’s size.**

We shall see how the above equation works and gives the same result as the **Covariance function** in the following example to determine the covariance of the two given arrays.

The first table contains the two given datasets, **Group 1** and **Group 2**, containing numbers.

Assume the first array is **x** and the second one is **y**. And the sample size **n** is **10** (The number of data points in each dataset).

The steps to calculate the covariance using **COVAR()** using AVERAGE Function are,

**Step 1: **Select cell **D4**, enter the formula ** =AVERAGE(A3:A12) **to get the first array’s mean value, and press

**Enter**. The result is ‘

**53.4’**, as shown below.

**Step 2: **Select cell **E4**, enter the formula ** =AVERAGE(B3:B12) **to get the second array’s mean value, and press

**Enter**. The result is ‘

**10’**, as shown below.

**Step 3: **Select cell **G4**, enter the formula** =A3-$D$4** to determine the deviation of the first data point in

**Group 1**from its mean, and press

**Enter**. The result is

**‘-9.5’,**as shown below.

Next, drag the formula from cell **G4 **to** G13** using the fill handle to iterate the process for all the data points in **Group 1**. The output is shown below.

**Step 4: **Select cell **H4**, enter the formula ** =B3-$E$4 **to determine the deviation of the first data point in

**Group 2**from its mean, and press

**Enter**. The result is

**’91.8’,**as shown below.

Next, drag the formula from cell **H4 **to** H13** using the fill handle to iterate the process for all the data points in **Group 2**. The output is shown below.

**Step 5: **Select cell **I4**, enter the formula ** =G4*H4 **to find the product of deviation of the first data point pair in the two given datasets, and press

**Enter**.

Next, drag the formula from cell **I4 **to** I13** using the fill handle to iterate the process of all the data point pairs in the two groups. The output is shown below.

**Step 6: **Select the target cell **K3**, enter the formula ** =SUM(I4:I13)/D7 **representing the mathematical expression of Covariance, and press

**Enter**. The result is ‘

**25**’, as shown below in cell

**K3**.

First, the cell K3 formula determines the aggregate of the products of the deviations we found in cells I4:I13. It then finds the average of the resulting sum value, with the sample size** n** being **10**.

**Step 7: **Select the target cell **L3**, enter the formula ** =COVAR(A3:A12,B3:B12) **to find the covariance of the two given datasets, and press

**Enter**. The result is ‘

**25**’, as shown below in cell

**L3**.

[**Output Observation:** The above example shows the covariance value obtained by solving the mathematical expression in cell **K3** and applying the **COVAR() **in cell** L3** is the same.]

**Example #3**

In the following example, we will compare the **Covariance** **in Excel**, i.e., **COVAR()**, and the latest **Statistical** functions that replaced it to determine the covariance of the two firms’ revenues.

While one new function is the **COVARIANCE.P()**, which gives the Population Covariance, the other is **COVARIANCE.S(),** returns the **Sample** **Covariance in Excel**.

The first table shows the yearly revenue data of **Firm A** and **Firm B**.

The steps to calculate the covariance and compare the results with **COVAR()**, **COVARIANCE.P()**, and **COVARIANCE.S()** are,

** Step 1: **Select cell

**E3**, enter the

**COVAR()**formula

**, and press**

*=COVAR(B3:B9,C3:C9)***Enter**.

**Step 2: **Select cell **F3**, enter the **COVARIANCE.P() **formula** =COVARIANCE.P(B3:B9,C3:C9)**, and press

**Enter**.

**Step 3: **Select cell **G3**, enter the **COVARIANCE.S() **formula ** =COVARIANCE.S(B3:B9,C3:C9)**, and press

**Enter**.

The results are shown above in cells **E3, F3, **and** G3.**

[Output Observation: All three functions accept the cell range references to the two given datasets. While the **COVAR()** and **COVARIANCE.P()** return the result **3.918367347**, the **COVARIANCE.S()** returns the **Sample Covariance in Excel** as **4.571428571**.

The difference in the function outputs is because the mathematical formula for **COVAR()** and **COVARIANCE.P()** is the same. However, in the case of the **COVARIANCE.S()**, the denominator term in the corresponding mathematical expression is **n-1** instead of **n**, where **n** is the sample size.

In the above example, the determined covariance is positive, which indicates a positive correlation between the two firms’ revenues.]

### Important Things To Note

- The
**COVAR()**returns the**#N/A**error if the two supplied arrays are of different sizes. - If we provide empty datasets or datasets with no numbers as the arguments, the
**COVAR**function output will be the**#DIV/0!**error. - We must ensure the two given arrays contain numbers. They should not be empty, and the standard deviation of their data points should not be zero.

**Frequently Asked Questions**

**1. How does the function Covariance in Excel, COVAR, work when the input arrays also contain text values along with numbers?**

The **COVAR** works in the following way when the input arrays contain text values with numbers.

Let us see the steps with an example.

The below table shows two datasets containing numbers and text values.

The procedure to find the covariance using the **COVAR()** is,

Select the target cell B9, enter the formula ** =COVAR(A2:A7,B2:B7), **and press

**Enter**.

The result is ‘

**0.888889**’, as shown below.

[

**Output Observation:**The

**COVAR()**accepts the references to the two given data ranges and returns their covariance as

**0.888889**. The function ignores the text values and counts only the numbers to calculate the required covariance.]

**2. How to apply the Covariance in Excel VBA?**

We can apply the **Covariance **and** Excel VBA** by applying the following method:

But if we require to use the latest Covariance functions, apply the below methods in Excel VBA.

The two arguments in the above methods are the same as those explained in the **COVAR() Excel Formula** section.

**3. Why is the COVAR function not working in Excel?**

The **COVAR **function may not work for the following reasons:

One of the supplied arrays does not contain any numbers.

One of the supplied arrays is empty.

The selected datasets or cell ranges are of different sizes.

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