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Statistics Formula (Table of Contents)

What is the Statistics Formula?The term “Statistics” refers to the branch of mathematics that deals with the analysis of numbers and data. Statistics formula refers to the collection of measures of dispersion or central tendency that helps in understanding and interpreting a certain set of data.

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Formulas

Mean x̄ = Σxi / N

[ Nth / 2 term + ( N / 2 + 1)th term ] / 2 ; when N is even

Mode = The value in the data set that occurs most frequently

Variance = Σ(xi – x̄)2 / N

Where

xi: ith Term in The Data Set

N: Number of Variables in The Data Set

Example of Statistics Formula (With Excel Template)

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

Statistics Formula – Example #1Let us take the example of a data set with an odd number of variables to illustrate the statistics formula: 21, 27, 34, 39, 22, 45, 19, 27, 29, 43, 36, 24, 27, 31, 25, 45, 21, 38, 30. The number of variables, N = 19. Calculate the mean, median, mode and variance of the above data set.

Solution:

Mean is calculated using the formula given below

Mean x̄ = Σxi / N

Mean = (21 + 27 + 34 + 39 + 22 + 45 + 19 + 27 + 29 + 43 + 36 + 24 + 27 + 31 + 25 + 45 + 21 + 38 + 30) / 19

Mean = 30.7

Median is calculated using the formula given below

(N+1)th / 2 term

Median = (19 + 1)/2 = 10th term

Median = 10th term, 19, 21, 21, 22, 24, 25, 27, 27, 27, 29, 30, 31, 34, 36, 38, 39, 43, 45, 45

Median = 29

Mode is calculated using the formula given below

Mode = The value in the data set that occurs most frequently

Mode = 19, 21, 21, 22, 24, 25, 27, 27, 27, 29, 30, 31, 34, 36, 38, 39, 43, 45, 45

Mode = 27

Variance is calculated using the formula given below

Variance = Σ(xi – x̄)2 / N

Variance = {(21 – 30.7)2 + (27 – 30.7)2 + (34 – 30.7)2 + (39 – 30.7)2 + (22 – 30.7)2 + (45 – 30.7)2 + (19 – 30.7)2 + (27 – 30.7)2 + (29 – 30.7)2 + (43 – 30.7)2 + (36 – 30.7)2 + (24 – 30.7)2 + (27 – 30.7)2 + (31 – 30.7)2 + (25 – 30.7)2 + (45 – 30.7)2 + (21 – 30.7)2 + (38 – 30.7)2 + (30 – 30.7)2} / 19

Variance = 65.5

Therefore, the mean, median, mode and variance of the given data set are 30.7, 29, 27 and 65.5, respectively.

Statistics Formula – Example #2Now, let us take the example of a data set with even number of variables and calculate the statistics formula: 82, 76, 62, 78, 83, 89, 61, 76, 72, 71, 91, 76, 62, 69, 77, 76, 85, 89, 71, 63, 68, 82. The number of variables, N = 22. Calculates the mean, median, mode and variance of the above data set.

Solution:

Mean is calculated using the formula given below

Mean x̄ = Σxi / N

Mean = (82 + 76 + 62 + 78 + 83 + 89 + 61 + 76 + 72 + 71 + 91 + 76 + 62 + 69 + 77 + 76 + 85 + 89 + 71 + 63 + 68 + 82) / 22

Mean = 75.4

Median is calculated using the formula given below

Median = [ Nth / 2 term + ( N / 2 + 1)th term ] / 2

Median = (76 + 76) / 2

Median = 76

Mode is calculated using the formula given below

Mode = The value in the data set that occurs most frequently

Mode = The Data Set is 76, which occurs the most (4 times) frequently in this data set.

Mode = 76

Variance is calculated using the formula given below

Variance = Σ(xi – x̄)2 / N

Variance = {(82 – 75.4)2 + (76 – 75.4)2 + (62 – 75.4)2 + (78 – 75.4)2 + (83 – 75.4)2 + (89 – 75.4)2 + (61 – 75.4)2 + (76 – 75.4)2 + (72 – 75.4)2 + (71 – 75.4)2 + (91 – 75.4)2 + (76 – 75.4)2 + (62 – 75.4)2 + (69 – 75.4)2 + (77 – 75.4)2 + (76 – 75.4)2 + (85 – 75.4)2 + (89 – 75.4)2 + (71 – 75.4)2 + (63 – 75.4)2 + (68 – 75.4)2 + (82 – 75.4)2} / 22

Variance = 78.5

Therefore, the mean, median, mode and variance of the given data set are 75.4, 76, 76 and 78.5, respectively.

ExplanationThe formula for Statistics can be calculated by using the following steps:

Mean: It is the average of all the numbers available in the data set.

Median: If arranged in ascending or descending order, it is exactly the midpoint of the data set. For instance, if there are 100 numbers in a data set, then 50th and 51st terms are the median numbers.

Mode: It is that number in a data set that appears the maximum number of times.

Variance: It measures how dispersed are the numbers in a data set, i.e. how far spread out are each number from the mean of the data set.

Relevance and Use of Statistics FormulaFrom the vantage point of a statistician, it is very important to understand the statistics formula concept as it helps organise and analyse large volumes of data. These statistical techniques are also used in various decision-making tools, especially drawing conclusions from data collected through surveys.

Statistics Formula CalculatorYou can use the Statistics Formula Calculator

xi N Statistics Formula Statistics Formula = Σxi / N Σ

0

/

0

= 0

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

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## Calculator (Examples With Excel Template)

Normalization Formula (Table of Contents)

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What is Normalization Formula?In statistics, there are many tools to analyze the data in detail and one of the most commonly used formula or method is the Normalization method. Normalization and standardization have been used interchangeably but they have usually different interpretations and different meanings altogether. Normalization in layman terms means normalizing of the data. Normalization refers to a scaling of the data in numeric variables in the range of 0 to 1.

The formula for Normalization is

X new = (X – X min) / (X max – X min)

Where

X: It is a set of the observed values present in X.

X min: It is the minimum values in X

X max: It is the maximum values in X

Examples of Normalization Formula (With Excel Template)

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

Normalization Formula – Example #1Maximum Value in the data set is calculated as

So 75 is the maximum value in the given data set.

Minimum Value in the data set is calculated as

20 is the minimum value in the given data set.

Normalization is calculated using the formula given below

X new = (X – X min) / (X max – X min)

Similarly, we calculated the normalization for all data value.

Normalization Formula – Example #2Calculate Normalization for the following data set.

Maximum Value in the data set is calculated as

So 164 is the maximum value in the given data set.

Minimum Value in the data set is calculated as

101 is the minimum value in the given data set.

Normalization is calculated using the formula given below

X new = (X – X min) / (X max – X min)

Similarly, we calculated the normalization for all data value.

Normalization Formula – Example #3Calculate Normalization for the following data set.

Maximum Value in the data set is calculated as

So 197 is the maximum value in the given data set.

Minimum Value in the data set is calculated as

121 is the minimum value in the given data set.

Normalization is calculated using the formula given below

X new = (X – X min) / (X max – X min)

Similarly, we calculated the normalization for all data value.

ExplanationThe normalization formula can be explained in the following below steps: –

Step 1: From the data the user needs to find the Maximum and the minimum value in order to determine the outliners of the data set.

Step 2: Then the user needs to find the difference between the maximum and the minimum value in the data set.

Step 3: Value – Min needs to be determined against each and every data point in the set.

Step 4: After determining all the values in the data set the value needs to be put in the formula i.e. X new = (X – X min) / (X max – X min)

Relevance and Uses of Normalization Formula

Normalization is widely used in data mining techniques and data processing techniques. It is usually known as featured scaling under which you try to bring data in a normalized or a standardized form to do analysis on it and draw various interpretations.

This formula is also used in prediction modeling and forecasting which makes the model more relevant and user-friendly.

This formula and technique is also used in the marking scheme of various entrance examinations where in order to ensure that the candidate is neither benefited nor deprived by the level of difficulty in the examination, as a result, the candidate who has attempted simple or easier questions can get more marks in the test in comparison with the candidates who attempt difficult questions in the thought of getting more marks.

Normalization also has its own limitations in the sense if the data set has more outliers then normalization of the data set becomes are tedious and a difficult task to be done to the data.

Normalization Formula CalculatorYou can use the following Normalization Calculator

X Xminimum Xmaximum Xnew Xnew = X − Xminimum = Xmaximum-Xminimum

0

−

0

= 0

0

–

0

Recommended Articles

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

## Top Examples With Excel Template

Definition of Quick Ratio

The term “Quick Ratio” refers to the liquidity ratio that assesses the ability of a company to cover its short-term liabilities by utilizing all those assets that can be easily converted into cash. The name “quick ratio” comes from the underlying idea that the ratio considers only those assets that can be quickly liquidated. The ratio is also known as the name acid test ratio.

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If a company’s quick ratio is greater than 1, it means that it has more than enough liquid assets that can be used to repay the current liabilities immediately. On the other hand, if it is less than 1, it indicates that the company’s liquidity is inadequate to pay off its current liabilities in case it is required to pay immediately.

Formula:

The formula for Quick Ratio can be derived by dividing the sum of cash, marketable securities, accounts receivables, and other current assets (other than inventories and prepaid expenses) by the total current liabilities. Mathematically, it is represented as,

Quick Ratio = (Cash + Marketable Securities + Accounts Receivable + Other Current Assets) / Total Current Liabilities

One can also derive the formula for Quick Ratio by subtracting inventories and prepaid expenses from the total current assets and then dividing the resulting figure by the total current liabilities. Mathematically, this is represented as:

Quick Ratio = (Total Current Assets – Inventories – Prepaid Expenses) / Total Current Liabilities.

Examples of Quick Ratio (With Excel Template)Let’s take an example to understand the calculation of the Quick Ratio formula in a better manner.

You can download this Quick Ratio Excel Template here – Quick Ratio Excel Template

Example – #1Let us take the example of a company that has applied for a bank loan in order to remodel its storefront. The company has provided the following balance sheet information to the bank:

Based on the given information, Calculate the quick ratio of the company.

Solution:

Of the above-mentioned current assets, only cash, marketable securities, and accounts receivable can be considered quick assets.

Calculate Quick Ratio using the formula given below:

QR = ($15,000 + $20,000 + $10,000) / $35,000

QR = 1.29

Therefore, the quick ratio for the company stood at 1.29, which indicates a fairly comfortable liquidity position.

Example – #2Let us take the latest annual report of Apple Inc. to explain the quick ratio calculation. As per the annual report for the year ended on Sep 29, 2023, the following information is available:

Based on the given information, Calculate the quick ratio for Apple Inc. for the year ending Sep 29, 2023.

Solution:

Out of the above-mentioned current assets, only cash and cash equivalents, marketable securities, net accounts receivable, vendor non-trade receivables, and other current assets can be considered quick assets.

Quick Ratio = (Cash and Cash Equivalents + Marketable Securities + Accounts Receivable + Net Accounts Receivable + Vendor Non-Trade Receivables + Other Current Assets) / Total Current Liabilities

QR = ($25,913 Mn + $40,388 Mn + $23,186 Mn + $25,809 Mn + $12,087 Mn) / $116,866 Mn

QR = 1.09

Therefore, the QR for Apple Inc. for the year ending Sep 29, 2023, stood at 1.09, indicating a moderate liquidity position.

Source:d18rn0p25nwr6d.cloudfront.net

Advantages

It assesses the ability to repay current liabilities based on the assets a company can quickly convert to cash. As such, it is a relatively more conservative liquidity ratio.

Its calculation omits inventories because converting inventories into cash could take too long. Elimination of inventories from its calculation helps management and other stakeholders to have a precise idea about the liquidity position of the concerned company.

This ratio is one of the easiest ratios to understand, and as such, it can be very helpful for people who do not have a deep understanding of accounting and finance.

It doesn’t provide any information about the timing of cash flows which can be a defining factor in the assessment of the liquidity position of a company.

Some of the assumptions of the QR are not realistic. For instance, it assumes that accounts receivable is readily available for collection, which is not always true.

It does not consider the situation that may arise in times of crisis. During the crisis, even the most easily saleable securities may find it difficult to trade in the market.

ConclusionSo, it can be seen that the quick ratio is a moderate conservative liquidity measure which is more conservative than the current ratio but less conservative than the cash ratio. This ratio helps the creditors in the assessment of the liquidity position of a company more accurately.

Recommended Articles## How Does It Work With Example And Application?

What is a Balloon Payment?

Balloon payment, as the term suggests, refers to a lump sum payment made by the borrower to the lender towards the loan or mortgage, usually higher than the monthly installments made towards the loan. A balloon payment is produced mainly at regular intervals or even at the end of the loan tenure.

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Key Takeaways for Balloon PaymentBalloon payments and mortgages have a commercial flair to them. Since it involves more significant loan amounts and larger payments, it’s not uncommon for retail consumers to prefer to stay away from it.

There is no question here to check whether balloon payments are good or bad, as it depends on the borrower and his financial obligations/requirements.

How does it work?The borrower takes a short-term loan, but monthly payments to be made towards the loan are calculated as if the loan is to be repaid in a longer timeframe, say 10, 20, or even 30 years timeframe. Here if you notice, the amount to be repaid by the borrower for the loan taken for the short term may not cover the whole loan repayment, and thus the concept of balloon payment comes into the picture.

Here, the borrower takes a loan from the lender at a mutually agreed timeframe and interest rate. Once the loan transaction has taken place, parties agree on when to schedule the balloon payments and accordingly arrive at a monthly payment to be made by the borrower regularly.

It is not uncommon for the borrower to make balloon payments towards the loan at the end of loan tenure to repay the whole balance principal amount.

Example of Balloon PaymentLet’s say Mr. Peter has taken a $500,000 loan for a tenure of 5 years at an interest rate of 4%.

Based on the above example, Peter will have to make a balloon payment of $356,780 at the end of the 5th year.

Based on mutual discussion amongst the parties, the reader may note that they may agree to a balloon payment at the beginning of the loan tenure or anytime during the loan tenure. In such a scenario, the interest charge may change accordingly.

Let’s take another scenario of the balloon payment, wherein Mr. Peter takes the loan with the same conditions. Still, the parties agree to charge only interest for the loan tenure period, with the principal repaid at the end of the loan tenure.

In such a case, Mr. Peter will pay approximately $900 monthly for five years, which will be adjusted towards interest. In such a situation, Mr. Peter can use the $500,000 immediately for his financial needs for small payments towards the interest component. This helps him in finance management.

Balloon Payments and MortgagesA balloon payment mortgage is nothing but a loan taken, and the repayment is structured so that it already considers the balloon payments to be made by the borrower at the end of the loan tenure.

Application of Balloon PaymentsApplication of balloon payments is mainly found by organizations which may be small business owners, home buyers, businesses planning an expansion, and companies being in or entering into the development phase of the growth cycle.

Usually, these are the businesses or categories which require an initial more enormous cash outflow, with revenue-yielding activities taking up starting a couple of years.

It will be good to understand that having balloon payments structured in loan help these businesses meet the initial cash crunch and act as a great financial tool.

Advantages of Balloon Payments

Lower monthly payments are to be made, as the calculation for monthly payments is made on a more extended tenure basis.

Saved from the burden of high-interest rates, the person will not have to bear interest if he has to take a loan for a longer duration.

Beneficial for people who have bulk payments coming into the business

Helpful for people who need short-term financing

A person may be able to fetch larger loans in comparison to the usual loan

Useful for people who anticipate getting bulk income at particular or specified times

A default will be very detrimental, as the borrower will have to make the balloon payment in any way.

High risk as the repayment to be made towards balloon payment is huge

Refinancing is possible but will entail higher interest rates

The borrower may overestimate his repaying capacity

In case the borrower plans to sell off a particular asset to make the balloon payment, a change in a market scenario can have a significant impact on the prices of the asset

Improper planning is a significant hindrance to balloon payment structures

ConclusionIn a few words, balloon payment means a loan that involves monthly payments of a smaller amount towards interest and principal (mostly good) and a lump sum payment at the end of loan tenure towards the principal. This large payment made at the end of loan tenure is nothing but a balloon payment, a name given because of the nature of the transaction.

Due to its nature, it’s easier to understand why such a transaction is usually seen in commercial transactions rather than consumer ones.

Recommended Articles## Powerpoint Digital Marketing Strategy Planning Template

PowerPoint digital marketing strategy planning template Create a detailed digital marketing strategy structured using our RACE planning system to present to senior management or clients How will this template help me and my business?

If you’re working on your first digital strategy or integrated multichannel marketing review, it can be difficult to know if you’re using the best structure or using the right tools to assess your capabilities and strategic options. You need a strategy summary document that clearly lays out what you need to achieve and how you’re going to achieve it. That’s why we’ve created this strategy planning template – one of our most popular resources – split into two useful documents.

In your download, you get:

1.) Guidance and examples document – this document provides an overview on creating your strategy, with a range of completed examples to give you an idea of how to complete certain templates.

2.) Blank template for you to complete – the accompanying resource in this download is a blank presentation deck that you can use to create your own digital marketing strategy presentation, using your company’s analysis, KPIs, channels etc.

Whether you need to create a brand new strategy or review specific digital marketing techniques such as content, search or social media strategy for an upcoming project, this template will help you summarize your strategy. Digital veterans can place their initiatives into this template to present them to others, whereas members who need more guidance can follow the instructions in the notes section of each slide to complete their strategy.

Who is it for?This slide deck is for anyone who is charged with developing an integrated digital marketing strategy and achieving buy-in to the plan from colleagues or clients, including:

Digital marketing managers and marketing managers

CMOs and marketing directors

Account managers and consultants working at agencies to develop strategies for their clients

Our members who are consultants or work for agencies can use it to present their analysis and recommended strategies to their clients. Others, who work for brands, can use it to explain and justify strategies to their colleagues in the business.

You can use the analysis in the comprehensive blank templates to review every digital marketing tactic to assess your own capabilities and define your future roadmap. Guidance and examples are provided so you can see completed versions of the templates.

The examples cover business-to-consumer (B2C) and business-to-business (B2B) examples, plus our library also contains examples from specific sectors such as consumer brands, financial services, healthcare/pharma, retail e-commerce and travel.

How is the template structured?We have structured this template around the 25 elements of the Smart Insights RACE marketing planning system so that you can clearly define a comprehensive digital strategy that fits into each step of the framework:

Plan: Ensuring you’re able to plan for success by knowing how well you’re performing, what your internal capabilities are, and how you stack up against competitors.

Reach: Your strategy needs to show how you will invest to reach new customers through search marketing, owned, earned and paid media.

Act: Once you’ve attracted visitors to your website, you need to persuade them to act by improving customer journeys and optimizing your content and landing pages.

Convert: Depending on your type of business, conversion may happen online or offline. This part of the strategy covers lead nurturing, personalization and multichannel selling activities to make this happen.

Each element of RACE is broken down into five tasks with summary tables so you can present recommendations for all aspects of your digital marketing.

The template is presented as two files:

One ‘README’ guidance and examples document that instructs you through creating your strategy and provides you with completed examples.

One ‘BLANK’ file for you to use when creating your own strategy document.

The notes tab of each slide contains explanations, summaries, and instructions based on marketing tasks from our Microsoft Word-based Digital marketing plan workbook to help you through every element of your strategy.

Latest updatesWe’ve improved the guidance and examples document so it contains more useful information about how to create a strategy using RACE, with updated completed examples to help you complete the templates. We’ve also added a new visual scorecard option that is better for presenting and added 6 pillars for assessing digital marketing capabilities for smaller businesses.

The blank template doc has been re-designed giving you more space to complete the templates and contains new useful models (including our new customer journey mapping template) and links to other supporting resources. We have cross-referenced where there is a completed example in the READ ME guide to help you complete the blank template.

Resource Details

Author: Dr. Dave Chaffey

Editor: Amelia Mayes

Format: PowerPoint files

About the authorDr. Dave Chaffey

Dave is co-founder of Smart Insights and creator of the Smart Insights RACE planning framework. For his full profile, or to connect on LinkedIn or other social networks, see the About Dave Chaffey profile page on Smart Insights. Dave is author of 5 bestselling books on digital marketing including Digital Marketing Excellence and Digital Marketing: Strategy, Implementation and Practice. In 2004 he was recognized by the Chartered Institute of Marketing as one of 50 marketing ‘gurus’ worldwide who have helped shape the future of marketing.

## The Ppc Roi Calculator: How To Forecast And Optimize Your Ppc Roi

We created a PPC ROI Calculator over at chúng tôi to help you in a couple ways:

If you haven’t started PPC yet, you can forecast your ROI.

If you’re already running PPC, you can play with the metrics and see how you might increase ROI.

You can increase ROI by improving its component metrics.

The components of PPC ROI are:

Conversion Rate (CR)

Average Sale

Want to change your ROI? Return on investment increases when more money comes in, decreases when money goes out. So…

If average sale increases, so does ROI. If it decreases, ROI decreases. We want average sale to increase.

If conversion rate increases, it takes less ad spend to get a sale, so ROI goes up. We want conversion rate to increase.

In order to do this, you need a few pieces of information… or you can guess at them.

Monthly ad spend: your client may provide this, or you can recommend one. We prefer clients with a minimum of $5k monthly spend. But some go into the hundreds of thousands of dollars.

Conversion Rate: your PPC CR will differ from the rest of your site, depending on how well you optimize your account structure and landing pages, but you can start with one that’s based on natural search traffic. If your site is new and has no traffic, PPC will help you find this value. Hopefully, your ecommerce site conversion rate is 1.00% or above, and your lead generation site gets 3.00-5.00% or more. Yeah, the FutureNow guys expect better- good for them and their conversion optimization friends. If you aren’t there yet, use my values. If your CR is lower than what I suggest, your site needs work.

Average Sale: if you don’t have this from your website, base it on offline sales, or a realistic purchase. (Are customers likely to buy just one? What’s the price? Use that.)

Enter these into the PPC ROI Calculator and hit “calculate”, and stare in amazement at the results. You’re welcome.

How to Optimize PPC ROI With The PPC ROI Calculator

Once you’ve taken a look at your real metrics, you can play with the values to see how you might realistically increase ROI. Here’s how you could tactically optimize the components of ROI to achieve that goal.

Can you get any benchmarks or look at other businesses doing ppc in the same vertical to find out if your CPC is higher than average? Or, again, try KeywordSpy and SpyFu.

Are you allocating as much of your budget as possible to the keywords that are both low CPC and high ROI? If not, move them into their own campaigns so that you can. Read more about PPC budget optimization here.

Head back to the PPC ROI Calculator and see what decreasing CPC 10% or 20% would do for your ROI.

Average Sale (Value/Conversion)

If you often sell multiple products per conversion, can you incentivize to increase cart size? Upsell and cross-sell your heart out.

Use the PPC ROI Calculator to see what increasing your average sale by 10% or 20% would do to your ROI.

Conversion Rate (CR)

Go back to the PPC ROI Calculator and see what an acceptable minimum CR would do to your ROI. Or if you’re already there, raise your CR by 20% and look at what that does for your ROI.

Work with web designers to improve conversion rate. Integrate conversion optimization into redesign strategy.

After trying out improvements in ROI component metrics in the PPC ROI Calculator and thinking about what you realistically can improve in your PPC accounts and websites, take action. Improve those metrics!

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