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The median formula finds the middle value in a set of data, i.e., the middle number in a set of numbers. It tells us where the center of the data is, which can be helpful in different scenarios like studying temperatures, analyzing student scores, or finding the central age in a population.

The median formula is useful when a dataset is uneven or has extreme numbers (values that are much higher or lower than the others). In such cases, other methods, like the mean, can give a less accurate result as extreme values can influence the center value. However, the median formula is less affected by these outliers and provides a more precise estimate of the middle value.

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We can calculate the median using a simple mathematical formula:

Median = (n + 1) / 2

Where “n” represents the total number of items, i.e., the total number of values present in the dataset.

Note: This formula helps us find the position of the median in the dataset rather than the actual value of the median.

How to Calculate Median in Excel?We can use the built-in function called “MEDIAN” to calculate the median in Excel.

The syntax for the MEDIAN function is as follows:

1. Range of Dataset

Here, we must add the cell range for the data in the function as the first argument.

For example, if our data is present in the cells A2 to A 10, we will write the MEDIAN function as:

=MEDIAN(A2:A10)

2. Array of Data

In this approach, we directly provide all the dataset values to the MEDIAN function in the form of an array. You can use this method when the dataset is small, or else directly selecting the range is an easy option.

For example, if our dataset has the following values: 2,4,6,8,10, our MEDIAN function will be:

=MEDIAN(2,4,6,8,10)

Note: Unlike the mathematical formula for calculating the median, the MEDIAN Excel function gives the actual value of the median rather than the position.

Examples of Median FormulaLet’s take a look at some examples of median formulas. We have provided examples of both the Simple median formula as well as MEDIAN function in Excel.

1. Simple Median Formula

2. MEDIAN Function in Excel

We have included an Excel template with solved examples to help you better understand how to use the median function and formula in Excel.

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

1. Simple Median Formula Examples Example #1: Odd Number of ObservationsCalculate the Median for the dataset: A= 42, 21, 34, 65, 90, 45, 109. As the number of values in the dataset is 7, n will be 7.

To sort the data from the smallest to the highest number, you have 2 options:

Therefore, the median value for the dataset sorted in ascending order (21, 34, 42, 45, 65, 90, 109) is 45.

Example #2: Even Number of ObservationsStep 3: Find the Median

Thus, the median value for the dataset is 36.5.

2. MEDIAN Function in Excel Examples Example #1: Dataset with Odd Number of ValuesA company has the following sales data for the years 2014 to 2023.

Year

2014 2023 2023 2023 2023 2023 2023 2023 2023

Sales

141 177 157 191 211 206 214 202 212

Let us find the median for the above data using the MEDIAN function.

While using the MEDIAN function, there is no need to sort the data in ascending order. The function does this automatically before finding the median.

Step 1: To find the median, add the following formula in the cell B12:

=MEDIAN(B2:B10)

Step 2: Press “Enter”. The MEDIAN function finds and returns the median value.

So, the median for the given sales data is 202.

Example #2: Dataset with an Even Number of ValuesC = 13, 25, 12, 40, 27, 80, 55, 62, 99,73

Step 1: Enter the folding formula in the cell B13:

=MEDIAN(13, 25, 12, 40, 27, 80, 55, 62, 99,73)

Here, the function returns the value of 47.50. It is the average between the two middle values of the dataset (40 and 55).

Therefore, the median for the dataset (13, 25, 12, 40, 27, 80, 55, 62, 99,73) is 47.5.

Things to Keep in MindIf you want to find the number of values in a large dataset containing hundreds or thousands of values, you can use the COUNTA function to find the ‘n’ value.

Example: Let’s say you want to find the median for a dataset present in cells A1 to A1000. To quickly and easily find the value for ‘n’, you can use the formula: =COUNTA(A1:A1000)

While calculating the median, the MEDIAN function will automatically ignore any cell with a non-numeric value, i.e., if the cell has text or is empty.

Example: Suppose we have a dataset in cells A1 to A7, where A3 is empty, and A6 contains the text “eduCBA”, the formula “=MEDIAN(A1:A7)” will only consider the numeric values (1, 2, 4, 5, 7) and ignore the empty cell and text.

The MEDIAN function takes into account logical values (TRUE and FALSE) during the calculation. TRUE is treated as 1, while FALSE is treated as 0.

Example: If you use the MEDIAN function for the dataset: FALSE, 5, TRUE, 2, the median will be 3. It is the average of the two middle values, 5 and TRUE (equivalent to 1). However, if the dataset was FALSE, 5, 2, the median would be 5 (not 3).

Importance and Uses of Median Formula

The Median is the point where 50% of the numbers are above & 50% of the numbers are below. It is a centrality denoting the middle value, which is helpful for a historical dataset or data set over time.

Economists use median values to draw conclusions and frame economic policies. For instance, they can determine the median price of houses in a specific area to see if houses in that area are affordable or expensive.

Median Formula CalculatorUse the following medium calculator for calculating the median.

n Median Formula Median Formula = (n + 1) = 2 (

0

+ 1) = 0 2

Frequently Asked Questions(FAQs)The value of “n” would be 7 because there are 7 values in the dataset.

Answer: In statistics, the mean, median, and mode have a connection known as the empirical relationship. It means that if we know the value of any of the two metrics, we can find the value of the remaining one. We can use the following equation to find this:

Mode = 3 x Median – 2 x Mean

Mode = 6

Answer: We have two formulas for the median, i.e., the odd number of observations and the even number of observations.

If the number of terms(n) is even, then the formula is ½ [(n/2)+((n/2)+1)]

If the number of terms(n) is odd, then the formula is (n+1)/2

Answer: If you want to find the median for a group of data based on a condition, you can use the conditional median formula. For instance, if you want to find the median for all values that are below 100, we can use the conditional median formula. Here we use the IF function combined with the MEDIAN function. The IF function checks if a given condition is true for each value in the dataset. If the condition is true, the MEDIAN function includes that value when determining the median of the dataset.

The syntax is as follows:

MEDIAN (IF(criteria_range = criteria, median_range))

Recommended ArticlesThis article shows how to calculate the median in Excel using the median formula and the median Excel function. We have explained each formula and how to use them and given solved examples with a downloadable Excel template. You can also use the calculator to directly find the median value for a dataset. You may also look at the following articles to learn more,

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## How To Calculate Variance In Excel

So you’ve been asked to calculate variance using Excel, but you aren’t sure what that means or how to do it. Don’t worry, it’s an easy concept and even easier process. You’ll be a variance pro in no time!

What Is Variance?“Variance” is a way to measure the average distance from the mean. The “mean” is the sum of all values in a dataset divided by the number of values. Variance gives us an idea of whether the values in that data set tend, on average, to stick uniformly to the mean or scatter all over the place.

Table of Contents

Mathematically, variance isn’t that complex:

Calculate the mean of a set of values. To calculate the mean, take the sum of all the values divided by the number of values.

Take every value in your set and subtract it from the mean.

Square the resulting values (to cancel out negative numbers).

Add all the squared values together.

Calculate the mean of the squared values to get the variance.

So as you can see, it’s not a hard value to calculate. However, if you have hundreds or thousands of values, it would take forever to do manually. So it’s a good thing that Excel can automate the process!

What Do You Use Variance For?Variance by itself has a number of uses. From a purely statistical perspective, it’s a good shorthand way to express how spread out a set of data is. Investors use variance to estimate the risk of a given investment.

For example, by taking a stock’s value over a period of time and calculating its variance, you’ll get a good idea of its volatility in the past. Under the assumption that the past predicts the future, it would mean that something with low variance is safer and more predictable.

You can also compare the variances of something across different time periods. This can help detect when another hidden factor is influencing something, changing its variance.

Variance is also strongly-related to another statistic known as the standard deviation. Remember that the values used to calculate variance are squared. This means that variance is not expressed in the same unit of the original value. The standard deviation requires taking the square root of variance to return the value to its original unit. So if the data was in kilograms then the standard deviation is as well.

Choosing Between Population and Sample VarianceThere are two subtypes of variance with slightly different formulas in Excel. Which one you should choose depends on your data. If your data includes the entire “population” then you should use population variance. In this case “population” means that you have every value for every member of the target population group.

For example, if you’re looking at the weight of left-handed people, then the population includes every individual on Earth who’s left-handed. If you’ve weighed them all, you’d use population variance.

Of course, in real life we usually settle for a smaller sample from a larger population. In which case you’d use sample variance. Population variance is still practical with smaller populations. For example, a company may have a few hundred or few thousand employees with data on each employee. They represent a “population” in the statistical sense.

Choosing the Right Variance FormulaThere are three sample variance formulas and three population variance formulas in Excel:

VAR, VAR.S and VARA for sample variance.

VARP, VAR.P and VARPA for population variance.

That leaves VAR.S and VAR.P, which are for calculating the variance of a set of numerical values and VARA and VARPA, which include text strings.

VARA and VARPA will convert any text string to the numerical value 0, with the exception of “TRUE” and “FALSE”. These are converted to 1 and 0 respectively.

The biggest difference is that VAR.S and VAR.P skip over any non-numerical values. This excludes those cases from the total number of values, which means the mean value will be different, because you’re dividing by a smaller number of cases to get the mean.

How to Calculate Variance in ExcelAll you need to calculate variance in Excel is a set of values. We’re going to use VAR.S in the example below, but the formula and methods are exactly the same regardless of which variance formula you use:

Assuming you have a range or discrete set of values ready, select the empty cell of your choice.

In the formula field, type =VAR.S(XX:YY) where the X and Y values are replaced by the first and last cell numbers of the range.

Press Enter to complete the calculation.

Alternatively, you can specify specific values, in which case the formula looks like =VAR.S(1,2,3,4). With the numbers replaced with whatever you need to calculate the variance of. You can enter up to 254 values manually like this, but unless you only have a handful of values it’s almost always better to enter your data in a cell range and then use the cell range version of the formula discussed above.

You Can Excel at, Er, ExcelCalculating variance is a useful trick to know for anyone who needs to do some statistical work in Excel. But if any of the Excel terminology we used in this article was confusing, consider checking out Microsoft Excel Basics Tutorial – Learning How to Use Excel.

If, on the other hand, you’re ready for more, check out Add a Linear Regression Trendline to an Excel Scatter Plot so you can visualize variance or any other aspect of your data set in relation to the arithmetic mean.

## How To Calculate Dpmo (Excel Template)

DPMO Formula (Table of Contents) DPMO Formula

DPMO stands for defects per million opportunities. This concept we used to hear in the production and most of the time it is used by manufacturing who involve in the production process. DPMO is one of the useful tools to know the chances for defects during the production process so we can use available resource properly and control the defects happening during the production process. DPMO used to know the number of opportunities to make defects under the production process.

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The formula for DPMO –

DPMO = Total Number of Defects found in Sample / (Sample Size * Number of Defects Opportunities per Unit in the Sample) * 1000000

Examples of DPMO Formula (With Excel Template)

You can download this DPMO Excel Template here – DPMO Excel Template

DPMO Formula – Example #1A form contains 20 fields of information and only 10 forms are check and sampled and 26 defects found in the sample. Calculate the DPMO.

Solution:

DPMO is calculated using the formula given below

DPMO = Total Number of Defects found in Sample / (Sample Size * Number of Defects Opportunities per Unit in the Sample) * 1000000

DPMO = 26 / (10 * 20) * 1000000

DPMO = 130000

Above calculation, we can clearly see that there are chances of 130000 defects per million opportunities.

DPMO Formula – Example #2Voltas Company is in the business of air conditioner so every month they used to manufacture air conditioner as per demand in the market. So they manufacture 50 air conditioners, but they only take out 40 air conditioner for evaluation and they found there is some defect in some of the air conditioner when they pass on this air conditioner to research and development department, in the evaluation they found there are 70 defects. Calculate the DPMO.

Solution:

DPMO is calculated using the formula given below

DPMO = Total Number of Defects found in Sample / (Sample Size * Number of Defects Opportunities per Unit in the Sample) * 1000000

DPMO = 70 / (40 * 50) * 1000000

DPMO = 35000

DPMO Formula – Example #3Company A is in the business of manufacturing and they have their own research and development center for quality evaluation. They manufacture mobile parts and provide parts to many mobile companies. Every week they manufacture 100 and only take out 80 for evaluation purpose and at the time of evaluation, they find 156 defects in products, Calculate DPMO.

Solution:

DPMO is calculated using the formula given below

DPMO = 156 / (80 * 100) * 1000000

DPMO = 19500

DPMO Formula – Example #4Tata Sponge is in the business of iron and provides finished iron to the steel company. And they manufacture 520 iron rods and provide to the research and development department only 500 rods for evaluation and research and development department found that there are 635 defects in the iron rod. Calculate the DPMO.

DPMO is calculated using the formula given below

DPMO = 635 / (500 * 520) * 1000000

DPMO = 2442.308

ExplanationDPMO = Total number of defects found in sample/ Total number of defects opportunity in the sample * 100000

So DPMO Stands for defects per million opportunities. DPMO is one of the quality parameter used by many organizations and manufacturing company for better use of available so they can provide better services. With this parameter, we can find out the chances or opportunity for any defects. So the total number of a sample is taken into consideration in this formula and that figure divided by the total number of defects opportunity in the sample and it is multiplied by 1000000. So with the use of one of the six sigma tool, we can find out the chances of defects in the product and we try to rectify it by using all resources properly.

Relevance and Uses of DPMO FormulaDPMO we used to hear in the economics and operation and it is having relevance in the era of today’s world because it helps you to know the defects per million opportunities. So it helps the many manufacturers and evaluates to know the chances for defects per million. DPMO is one of the six sigma matric which used by many manufacturing and many companies to check the quality. DPMO can be used by any organization to check quality because the quality is a major concern in each and every aspect, so it is very necessary to provide proper and high quality to a customer so that customer has to be loyal towards the product of a company.

For the purpose of quality check, there is a tool called six sigma. In six sigma there is six tool which used by companies for quality check, but here we are talking about the DPMO which one of the most important six sigma tools, In DPMO we can find defects per million opportunities in the production process. Due to DPMO we can identify the defects and take corrective major to avoid this type of defects during the production process.

DPMO Formula CalculatorYou can use the following DPMO Calculator

Total Number of Defects found in Sample Sample Size Number of Defects Opportunities per Unit in the Sample DPMO Formula = DPMO Formula = Total Number of Defects found in Sample X1000000 (Sample Size * Number of Defects Opportunities per Unit in the Sample)

0

X1000000= 0 (

0

*

0

)

Recommended ArticlesThis has been a guide to DPMO formula. Here we discuss how to calculate DPMO along with practical examples. We also provide a DPMO calculator with downloadable excel template. You may also look at the following articles to learn more –

## How To Calculate Irr In Excel

Last Updated on September 2, 2023

IRR or the Internal Rate of Return calculates a series of cash flows. This is assuming there are equal-sized periods of payment.

Today we’ll look at how to calculate IRR and how to interpret the results.

1

How To Calculate IRR

There are three ways to calculate IRR. We recommend using formulas as doing manual calculations can incur human error and be time-consuming.

This is why you are using Excel in the first place so you may as well make use of its functionality!

Using Excel, the formulas you will be using are IRR, XIRR, and MIRR.

In our example, the first column represents Year, the second column represents the Date Of Payment, and the third column represents Payment.

Step

1

IRRStarting with IRR and using our sample table from above, the IRR formula you would use would be “=IRR((C2:C10,.1)*12,” which will give an internal rate of return.

In certain examples where the period of time is not going to be equal, i.e. when you use months in which some have 31 days, whilst others have 30 days or less, the monthly periods are not going to be exactly the same in length.

This means that the IRR is going to return a somewhat incorrect result. Add this over multiple months, i.e. a year and you can expect this to be consistent.

Step

2

XIRRIf we look at Excel’s XIRR function, we will be able to calculate a more accurate rate of return. This is because it will take into consideration a different sized time period.

In order to use this functionality, you will need to apply a cash flow amount and a specific date on which those payments are going to be made. Hence our second column is; Date Of Payment.

So in our example from above, if we wanted to calculate using XIRR we would use “=XIRR(C2:C10,B2:B10,.1)” which would yield an internal rate of return.

Step

3

MIRRFinally, Excel’s IRR function, which stands for modified internal rate of return, will work similarly to the IRR function, although this function will take the cost of borrowing the initial investment funds into consideration.

It will also use the compounded interest which was earned by reinvesting wash cash flow.

What makes the MIRR function so useful is that it has enough flexibility to accommodate separate interest rates, concerning borrowing and investing.

As compound interest is calculated, the internal rate of return is going to be different from those of the original internal rate of return, but also the XIRR function.

Taking into consideration our example and that C14 represents Financing Rate and C15 represents Reinvestment Rate, the formula for MIRR is “=MIRR(C2:C10,C14,C15)*12” for our final internal rate of return.

Which Is Best? What Is The Difference Between IRR And NPV?The one major difference is that NPV is an actual numerical amount, and IRR is simply the interest yield which is calculated as a percentage expected from an investment.

In terms of investors, they will typically go with an IRR that is greater than the cost of the capital investment.

Although this could increase the risk of return on investment greater than a weighted average cost of capital.

Final ThoughtsThose are the three methods for calculating IRR in Excel. Use them all and you will have the best range of results.

## How To Calculate Image Size In Photoshop

Learn how Photoshop calculates the file size of your image, why the image size changes as you change the number of pixels, and how easy it is to figure out the file size on your own!

Written by Steve Patterson.

In the previous lesson in this series on image size, we learned how to resize images for email and for sharing online using the Image Size command in Photoshop. In that lesson, we saw that by changing the number of pixels in the image, the image size in megabytes also changed. More pixels meant a larger file size, and fewer pixels made the file size smaller.

But how does that work? What does the number of pixels in an image have to do with its file size? In this quick lesson, I’ll show you exactly how pixels and file size are related, and how the colors in your image also play an important role. By the end, you’ll know how to easily figure out the size of an image on your own, and you’ll know exactly where that image size number comes from in Photoshop’s Image Size dialog box!

To follow along, you can open any image in Photoshop. I’ll use this photo that I downloaded from Adobe Stock:

The original image. Photo credit: Adobe Stock.

This is lesson 5 in my Resizing Images in Photoshop series.

Let’s get started!

Download this tutorial as a print-ready PDF!

Where to find the current image sizeTo view the current size of your image, go up to the Image menu in the Menu Bar and choose Image Size:

This opens Photoshop’s Image Size dialog box, with a preview window on the left and the image size options along the right. The preview window was added in Photoshop CC:

The Image Size dialog box in Photoshop CC.

The current size, both in pixels (px) and in megabytes (M), is found at the top. The number next to the words Image Size shows the amount of space that the image is taking up in your computer’s memory. And below that, next to the word Dimensions, is the width and height of the image in pixels.

In my case, my image is taking up 42.1M of memory. And it has a width of 4700 px and a height of 3133 px. In a moment, I’ll show exactly how the image size and pixel dimensions are related:

The current image size, both in megabytes and in pixels.

How pixels and color affect the image sizeTo really understand how the number of pixels in an image affects its file size, we also need to know how Photoshop displays the colors in your image. That’s because pixels alone don’t create the file size. Much of the size comes from the way Photoshop displays the color of each pixel.

Most full color images use what’s called RGB color. RGB stands for “Red, Green, and Blue”, which are the three primary colors of light. Every color you see in your image is made by mixing some combination of red, green and blue together.

Photoshop’s color channelsCanceling the Image Size command.

Then I’ll switch over to the Channels panel, which you’ll find next to the Layers panel. And here we see the Red, Green and Blue channels that Photoshop is using. The RGB channel at the top isn’t really a channel. It represents the full color image that we’re seeing on the screen:

All colors in your image are made by mixing red, green and blue.

Learn more about RGB color and color channels in Photoshop

How do color channels affect image size?Each of the three color channels (Red, Green and Blue) takes up exactly 1 byte in memory for each and every pixel in the image. For example, if your image contained 10 pixels, each pixel would need 1 byte for red, 1 byte for green and 1 byte for blue, for a total of 3 bytes.

Of course, most images contain millions of pixels, not just 10. But the amount of memory that each pixel needs doesn’t change. It’s always 3 bytes for every pixel; one for red, one for green and one for blue.

How to calculate the file sizeSo to figure out the file size of an image, all we need to do is take the total number of pixels, multiply it by 3, and we have our answer! Here’s how to do it.

Step 1: Find the total number of pixels in the imageFirst, we need the total number of pixels, and we find that in the Image Size dialog box. I’ll re-open it by going back up to the Image menu and choosing Image Size:

And again, we see in the Dimensions section that my image has a width of 4700 px and a height of 3133 px:

The width and height of the image in pixels.

To find the total number of pixels, multiply the width and height together. In this case, 4700 pixels x 3133 pixels = 14,725,100 pixels. That’s a lot of pixels. But as we learned, the pixel count alone isn’t the whole story.

Step 2: Multiply the total number of pixels by 3Remember that each pixel in the image needs 3 bytes in memory; one for the Red channel, one for the Green channel, and one for the Blue channel. So to find the total file size, in bytes, multiply the total number of pixels by 3. In my case, 14,725,100 pixels x 3 bytes per pixel = 44,175,300 bytes.

Step 3: Convert the image size from bytes to kilobytesWe have our total file size in bytes. But a byte is a very small unit of measurement, so it’s not very practical to refer to the size of an image in bytes. Instead, we usually talk about image size in either kilobytes or, more commonly, in megabytes.

One kilobyte is equal to 1024 bytes. So to convert bytes to kilobytes, divide the total number of bytes by 1024. With my image, 44,175,300 bytes ÷ 1024 = 43,139.94 kilobytes (or KB).

Step 4: Convert the image size from kilobytes to megabytesEven kilobytes is too small of a measurement type to be very practical for most images. So instead, we usually refer to file size in megabytes. One megabyte is equal to 1024 kilobytes. So to find the total image size in megabytes, divide the number of kilobytes (43,139.94) by 1024, which gives us 42.1 megabytes (or MB, although for whatever reason, the Image Size dialog box shortens “MB” to just “M”).

And if we look again at the Image Size dialog box, we see that sure enough, Photoshop is showing me that the size of my image is 42.1M:

Photoshop agrees with our calculations.

How to calculate image size – Quick summaryAnd that’s really all there is to it! To figure out the image size, just follow these simple steps:

4. Divide the number of kilobytes by 1024 to get the image size in megabytes.

And there we have it! In the next lesson, we’ll look at web resolution, the popular belief that you need to lower the resolution of an image before uploading it online, and how easy it is to prove that it’s just not true!

You can jump to any of the other lessons in this Resizing Images in Photoshop chapter. Or visit our Photoshop Basics section for more topics!

## How To Calculate A Square Root By Hand (With Pictures)

This article was co-authored by David Jia . David Jia is an Academic Tutor and the Founder of LA Math Tutoring, a private tutoring company based in Los Angeles, California. With over 10 years of teaching experience, David works with students of all ages and grades in various subjects, as well as college admissions counseling and test preparation for the SAT, ACT, ISEE, and more. After attaining a perfect 800 math score and a 690 English score on the SAT, David was awarded the Dickinson Scholarship from the University of Miami, where he graduated with a Bachelor’s degree in Business Administration. Additionally, David has worked as an instructor for online videos for textbook companies such as Larson Texts, Big Ideas Learning, and Big Ideas Math. This article has been viewed 2,571,505 times.

Article Summary

X

To calculate a square root by hand, first estimate the answer by finding the 2 perfect square roots that the number is between. A perfect square root is any square root that’s a whole number. For example, if you’re trying to find the square root of 7, first you’d need to find the first perfect square below 7, which is 4, and the first perfect square above 7, which is 9. Then, find the square root of each perfect square. The square root of 4 is 2, and the square root of 9 is 3. Therefore, you know that the square root of 7 falls somewhere between 2 and 3. Now, divide your number by one of the perfect square roots you found. For example, you would divide 7 by either 2 or 3. If you were to choose 3, your answer would be 2.33. Next, find the average of that number and the perfect square root. To find the average in this example, add 2.33 and 2, then divide by 2 and get 2.16. Repeat the process using the average you got. First, divide the number you’re trying to find the square root of by the average. Then, find the average of that number and the original average by adding them together and dividing by 2. For example, first you would divide 7, the number you started with, by 2.16, the average you calculated, and get 3.24. Then, you’d add 3.24 to 2.16, the old average, and divide by 2 to find the new average, which is 2.7. Now, multiply your answer by itself to see how close it is to the square root of the number you started with. In this example, 2.7 multiplied by itself is equal to 7.29, which is 0.29 away from 7. To get closer to 7, you would just repeat the process. Keep dividing the number you started with by the average of that number and the perfect square, using that number and the old average to find the new average, and multiplying the new average by itself until it equals your starting number. If you want to learn how to use the long division algorithm to find the square root, keep reading the article!

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