EDUCBA

EDUCBA

MENUMENU
  • Free Tutorials
  • Free Courses
  • Certification Courses
  • 250+ Courses All in One Bundle
  • Login

Standard Error Formula

By Madhuri ThakurMadhuri Thakur

Home » Finance » Blog » Finance Formula » Standard Error Formula

Standard Error Formula.

Standard Error Formula (Table of Contents)

  • Formula
  • Examples
  • Calculator

What is Standard Error Formula?

In statistics, the term “standard error” of a statistic refers to the estimate of the standard deviation of the sample mean from the true population mean. To put it simply, just as standard deviation measures each individual’s dispersion value from the sample mean, the standard error of mean measures the dispersion of all the sample means around the population mean.

Start Your Free Investment Banking Course

Download Corporate Valuation, Investment Banking, Accounting, CFA Calculator & others

The formula for standard error can be derived by dividing the sample standard deviation by the square root of the sample size. Although population standard deviation should be used in the computation, it is seldom available, and as such a sample, the standard deviation is used as a proxy for population standard deviation. Mathematically, it is represented as,

Standard Error = s / √n

Where,

  • s: √Σni(xi-x̄)2 / n-1
  • xi: ith Random Variable
  • x̄: Sample Mean
  • n: Sample Size

Examples of Standard Error Formula (With Excel Template)

Let’s take an example to understand the calculation of Coupon Bond in a better manner.

You can download this Standard Error Formula Excel Template here – Standard Error Formula Excel Template

Standard Error Formula – Example #1

Let us take the example of a survey where 100 respondents were asked to provide their feedback on the recently concluded college fest. They were asked to rate the fest on a scale of 1 to 5, with 5 being the best. Now, a random sampling method was used to build a sample of 5 responses out of the 100 responses. The selected responses are – 3, 2, 5, 3 and 4. Calculate the standard error of the statistic based on the selected responses.

example of a survey

Solution:

Sample Mean ( x̄ ) is calculated using the formula given below

x̄ = Σnixi/n

Standard Error Formula - 1.2

  • Sample Mean ( x̄ ) = (3 + 2 + 5 + 3 + 4) / 5
  • Sample Mean ( x̄ ) = 3.4

Calculated Deviation as

Deviation

Similarly Calculated as below

Standard Error Formula - 1.4

Standard Deviation (s)  is calculated using the formula given below

Popular Course in this category
Sale
Finance for Non Finance Managers Course (7 Courses)7 Online Courses | 25+ Hours | Verifiable Certificate of Completion | Lifetime Access
4.5 (9,197 ratings)
Course Price

View Course

Related Courses
Investment Banking Course (123 Courses, 25+ Projects)Financial Modeling Course (5 Courses, 14 Projects)

s = √Σni(xi-x̄)2 / n-1

Standard Deviation

  • Standard Deviation = √ [{(3 – 3.4)2  + (2 – 3.4)2 + (5 – 3.4)2 + (3 – 3.4)2 + (4 – 3.4)2} / (5 – 1)]
  • Standard Deviation = 1.14

Standard Error is calculated using the formula given below

Standard Error = s / √n 

Standard Error Formula - 1.6

  • Standard Error = 1.14 / √5
  • Standard Error = 0.51

Therefore, the standard error of the sample mean is 0.51.

Standard Error Formula – Example #2

Let us take the example of a survey conducted at an office in New York where around 1,000 employees were asked how much they liked the work that they were doing in their current profile. They were to rate on a scale of 1 to 10, with 10 being the best. Then a sample of 10 responses was selected, and the responses are – 4, 5, 8, 10, 9, 5, 9, 8, 9 and 7. Calculate the standard error of the statistic based on the selected responses.

Example of A Survey

Solution:

Sample Mean ( x̄ ) is calculated using the formula given below

x̄ = Σnixi/n

Sample Mean

  • Sample Mean ( x̄ ) = (4 + 5 + 8 + 10 + 9 + 5 + 9 + 8 + 9 + 7) / 10
  • Sample Mean ( x̄ )= 7.2

Calculated Deviation as

Deviation

Similarly Calculated as below

Standard Error Formula - 2.4

Standard Deviation (s)  is calculated using the formula given below

s = √Σni(xi-x̄)2 / n-1

Standard Deviation

  • Standard Deviation  = √ [{(4 – 7.2)2  + (5 – 7.2)2 + (8 – 7.2)2 + (10 – 7.2)2 + (9 – 7.2)2 + (5 – 7.2)2  + (9 – 7.2)2 + (8 – 7.2)2 + (9 – 7.2)2 + (7 – 7.2)2} / (10 – 1)]
  •   Standard Deviation = 2.44

Standard Error is calculated using the formula given below

Standard Error = s / √n 

Standard Error Formula - 2.6

  • Standard Error = 2.44 / √10
  • Standard Error = 0.77

Therefore, the standard error of the sample mean is 0.77.

Explanation

The formula for standard error can be derived by using the following steps:

Step 1: Firstly, collect the sample variables from the population-based on a certain sampling method. The sample variables are denoted by x such that xi refers to the ith variable of the sample.

Step 2: Next, determine the sample size, which is the total number of variables in the sample.   It is denoted by n.

Step 3: Next, compute the sample mean, which can be derived by dividing the summation of all the variables in the sample (step 1) by the sample size (step 2). It is denoted by, and mathematically it is represented as,

x̄ = Σnixi/n

Step 4: Next, compute the sample standard deviation (s), which involves a complex calculation that uses each sample variable (step 1), sample mean (step 3) and sample size (step 2) as shown below.

s = √Σni(xi-x̄)2 / n-1

Step 5: Finally, the formula for standard error can be derived by dividing the sample standard deviation (step 4) by the square root of the sample size (step 2), as shown below.

Standard Error = s / √n

Relevance and Use of Standard Error Formula

It is very important to understand the concept of standard error as it predominantly used by statisticians as it allows them to measure the precision of their sampling method. Statisticians usually use the sample from a large pool of data as it is difficult to process such a huge data set, and as such, sampling makes the task a lot easier. So, standard error helps estimate how far the sample mean from the true population means.

In the case of finite population standard deviation, an increase in sample size will eventually reduce the standard error of the sample mean to zero as the population’s estimation will improve. Additionally, the sample standard deviation will also become approximately equal to the population standard deviation with the increase in sample size.

In the normally distributed sampling distribution, the sample mean, quantiles of the normal distribution and standard error can be used in the calculation of the population mean’s confidence intervals.**

Standard Error Formula Calculator

You can use the following Standard Error Formula Calculator

s
√n
Standard Error Formula

 

 

Standard Error Formula =
s =
√n
0 = 0
0

Recommended Articles

This is a guide to Standard Error Formula. Here we discuss how to calculate Standard Error along with practical examples and a downloadable excel template. You may also look at the following articles to learn more –

  1. Formula for Sample Size
  2. Examples of Standard Deviation
  3. How to calculate Percentage Change
  4. Calculation of Marginal Benefit

All in One Financial Analyst Bundle (250+ Courses, 40+ Projects)

250+ Online Courses

40+ Projects

1000+ Hours

Verifiable Certificates

Lifetime Access

Learn More

0 Shares
Share
Tweet
Share
Primary Sidebar
Finance Blog
  • Finance Formula
    • Fixed Asset Turnover Ratio Formula
    • Deferred Annuity Formula
    • Capital Investment Formula
    • Ratio Analysis Formula
    • Loss Ratio Formula
    • Benefit-Cost Ratio Formula
    • Probability Distribution Formula
    • Cash Conversion Cycle Formula
    • Accrued Income
    • DCF Excel summary
    • Price to Earning Ratio Formula
    • Current Yield of Bond Formula
    • Earnings Per Share Formula
    • Manufacturing Overhead Formula
    • FCFF Formula
    • Predetermined Overhead Rate Formula
    • Times Interest Earned Ratio Formula
    • Bank Efficiency Ratio Formula
    • Capital Expenditure Formula
    • Expense Ratio Formula
    • WACC Formula
    • Activity Ratio Formula
    • Standard Error Formula
    • Forward Rate Formula
    • Gearing Formula
    • Prime Cost Formula
    • Productivity Formula
    • t-Test Formula
    • Risk Free Rate Formula
    • Tax Shield Formula
    • Sortino Ratio
    • Reserve Ratio Formula
    • Bond Formula
    • Annualized Rate of Return Formula
    • Conditional Probability Formula
    • Financing Formula
    • Future Value of an Annuity Formula
    • For Profit vs Non Profit
    • Deadweight Loss Formula
    • Inflation Formula
    • Amortized Loan Formula
    • Horizontal Analysis Formula
    • Marginal Utility Formula
    • Kurtosis Formula
    • Macaulay Duration Formula
    • Multiplier Formula
    • Modified Duration Formula
    • Operating Leverage Formula
    • Payout Ratio Formula
    • Statistics Formula
    • Sampling Error Formula
    • Trend Analysis Formula
    • Taylor Rule Formula
    • Put Call Parity Formula
    • Annual Return Formula
    • Discount Rate Formula
    • Cash Flow Formula
    • Dilution Formula
    • Attrition Formula
    • Operating Expense Formula
    • Interpolation Formula
    • Annuity Due Formula
    • Bond Yield Formula
    • Turnover Ratio Formula
    • Efficiency Formula
    • Revenue Per Employee
    • Regression Line Formula
    • Yield to Maturity
    • Pearson Correlation Coefficient Formula
    • Accounting Formula
    • Fiscal Deficit Formula
    • Tax Multiplier Formula
    • Efficiency Ratio Formula
    • Demand Elasticity Formula
    • Gross Margin Formula
    • Elasticity Formula
    • Marginal Benefit Formula
    • Depreciation Formula
    • Cost-Benefit Analysis Formula
    • Percentage Change Formula
    • Levered Beta Formula
    • Shares Outstanding Formula
    • Capital Gain Formula
    • Convexity Formula
    • Gross Income Formula
    • Net Exports Formula
    • Producer Surplus Formula
    • Accounting Rate of Return Formula
    • Net Cash Flow Formula
    • Labor Force Participation Rate Formula
    • Moving Average Formula
    • Net Worth Formula
    • Accounting Profit Formula
    • Disposable Income Formula
    • Discount Formula
    • Average Variable Cost Formula
    • Total Variable Cost Formula
    • Product Cost Formula
    • Marginal Product Formula
    • Break-Even Sales Formula
    • Return on Sales Formula
    • Cost of Goods Manufactured Formula
    • Average Fixed Cost Formula
    • Stock Turnover Ratio Formula
    • Operating Ratio Formula
    • Equity Ratio Formula
    • Net Present Value Formula
    • Aggregate Demand Formula
    • Volatility Formula
    • Marginal Product of Labor Formula
    • Z Test Statistics Formula
    • Standard Cost Formula
    • Velocity of Money Formula
    • Invested Capital Formula
    • Unlevered Beta Formula
    • Bank Reconciliation Formula
    • Portfolio Return Formula
    • Central Tendency Formula
    • Accumulated Depreciation Formula
    • Intrinsic Value Formula
    • Decile Formula
    • Vector Cross Product Formula
    • Effective Annual Rate Formula
    • CAGR Formula
    • Mode Formula
    • Arithmetic Mean Formula
    • Real GDP Formula
    • Gini Coefficient Formula
    • Expected Value Formula
    • Price Elasticity of Supply Formula
    • Net Operating Income Formula
    • Profit Percentage Formula
    • GDP Per Capita Formula
    • Altman Z Score
    • Quartile Deviation Formula
    • Return on Capital Employed Formula
    • Consumer Price Index Formula
    • Economic Profit Formula
    • Market Share Formula
    • Real Interest Rate Formula
    • Income Elasticity of Demand Formula
    • Income From Operations Formula
    • Indexation Formula
    • Sales Formula
    • Money Multiplier Formula
    • GDP Deflator Formula
    • Residual Income Formula
    • Effective Interest Rate Formula
    • Coupon Bond Formula
    • Current Account Formula
    • Total Cost Formula
    • Total Expense Ratio Formula
    • Net Sales Formula
    • Percentage Decrease Formula
    • Uncertainty Formula
    • Nominal GDP Formula
    • Effect Size Formula
    • Delta Formula
    • Cost of Sales Formula
    • Fixed Cost Formula
    • Unemployment Rate Formula
    • Present Value of Annuity Formula
    • Compounding Formula
    • Geometric Distribution Formula
    • National Income Formula
    • Accounts Receivables Turnover Formula
    • Integer Formula
    • Ending Inventory Formula
    • Owner's Equity Formula
    • Capacity Utilization Rate Formula
    • Interest Formula
    • Nominal Interest Rate Formula
    • Risk Premium Formula
    • Interest Coverage Ratio Formula
    • Gross Profit Margin Formula
    • Diluted EPS Formula
    • Return On Average Equity Formula
    • Return on Average Assets Formula
    • Working Capital Formula
    • Revenue Per Employee Ratio Formula
    • Capital Employed Formula
    • Rule of 72 Formula
    • Inventory Turnover Ratio Formula
    • Preferred Dividend Formula
    • Retention Ratio Formula
    • Present Value Factor Formula
    • Equity Multiplier Formula
    • Continuous Compounding Formula
    • Return on Assets (ROA) Formula
    • Portfolio Variance Formula
    • Weighted Average Formula
    • Net Working Capital Formula
    • Tax Equivalent Yield Formula
    • Poisson Distribution Formula
    • Current Ratio Formula
    • Debt Ratio Formula
    • Quick Ratio Formula
    • Payback Period Formula
    • Marginal Cost Formula
    • Debt to Income Ratio Formula
    • Book Value Per Share Formula
    • Asset Turnover Ratio Formula
    • Perpetuity Formula
    • Bid-Ask Spread Formula
    • Price to Book Value Formula
    • Capital Gains Yield Formula
    • Net Profit Margin Formula
    • DuPont Formula
    • Bond Pricing Formula
    • Binomial Distribution Formula
    • Sustainable Growth Rate Formula
    • Average Collection Period Formula
    • Net Income Formula
    • CAPM Formula
    • Cost of Goods Sold Formula
    • Economic Order Quantity (EOQ) Formula
    • Amortization Formula
    • Enterprise Value Formula
    • Beta Formula
    • Cost of Equity Formula
    • Rate of Return Formula
    • Revenue Formula
    • Markup Price Formula
    • Cash Flow from Operations Formula
    • Simple Interest Rate Formula
    • Consumer Surplus Formula
    • Asset to Sales Ratio Formula
    • Debt Service Coverage Ratio Formula
    • Capitalization Rate Formula
    • Cost of Debt Formula
    • Straight Line Depreciation Formula
    • Variable Costing Formula
    • Return on Invested Capital Formula
    • Profitability Index Formula
    • Expected Return Formula
    • Cost of Capital Formula
    • Price Index Formula
    • Average Total Cost Formula
    • Discount Factor Formula
    • Price Elasticity Formula
    • Profitability Ratios Formula
    • Financial Leverage Formula
    • Contribution Margin Formula
    • Time Value of Money Formula
    • Balance Sheet Formula
    • Opportunity Cost Formula
    • Current Assets Formula
    • Operating Cycle Formula
    • Operating Margin Formula
    • Bond Equivalent Yield Formula
    • Marginal Revenue Formula
    • Sales Revenue Formula
    • Net Debt Formula
    • Times Interest Earned Formula
    • Gordon Growth Model Formula
    • Required Rate of Return Formula
    • Break Even Analysis Formula
    • Inventory Formula
    • Marginal Propensity to Consume Formula
    • Debt to Asset Ratio Formula
    • Solvency Ratio Formula
    • Interest Expense Formula
    • Leverage Ratio Formula
    • Dividend Payout Ratio Formula
    • Operating Profit Margin Formula
    • PEG Ratio Formula
    • Net Interest Margin Formula
    • Return on Equity (ROE) Formula
    • Overhead Ratio Formula
    • Future Value Formula
    • Days in Inventory Formula
    • Market Capitalization Formula
    • Sharpe Ratio Formula
    • Cash Ratio Formula
    • Retained Earnings Formula
    • Average Rate of Return Formula
    • Current Liabilities Formula
    • Equity Value Formula
    • Relative Risk Reduction Formula
    • Capital Adequacy Ratio Formula
    • Debtor Days Formula
    • DPMO Formula
    • Average Formula
    • Exponential Growth Formula
    • Net Realizable Value Formula
    • Range Formula
    • Shareholders' Equity Formula
    • Sinking Fund Formula
    • Doubling Time Formula
    • Salvage Value Formula
    • Coupon Rate Formula
    • Simple Interest Formula
    • Correlation Formula
    • R - Squared Formula
    • MTBF Formula
    • Change in Net Working Capital Formula
    • Midrange Formula
    • Normal Distribution Formula
    • Mean Formula
    • Population Mean Formula
    • Median Formula
    • Central Limit Theorem Formula
    • Free Cash Flow Formula
    • Stockholder's Equity Formula
    • Acid-Test Ratio Formula
    • Percentile Rank Formula
    • Purchasing Power Parity Formula
    • Harmonic Mean Formula
    • Relative Standard Deviation Formula
    • T Distribution Formula
    • Normalization Formula
    • Operating Income Formula
    • Markup Percentage Formula
    • Relative Change Formula
    • Maturity Value Formula
    • Salary Formula
    • High Low Method
    • Income Statement Formula
    • Market to Book Ratio Formula
    • Dividends Per Share Formula
    • Daily Compound Interest Formula
    • Working Capital Turnover Ratio Formula
    • Weighted Mean Formula
    • Compounded Annual Growth Rate Formula
    • Regression Formula
    • Margin of Error Formula
    • Hypergeometric Distribution Formula
    • Standard Normal Distribution Formula
    • NOPAT Formula
    • Effective Tax Rate Formula
    • Degree of Operating Leverage Formula
    • Outliers Formula
    • Information Ratio Formula
    • Percent Error Formula
    • Hypothesis Testing Formula
    • Activity Based Costing Formula
    • Coverage Ratio Formula
    • Market Risk Premium Formula
    • Degree of Financial Leverage Formula
    • Absorption Costing Formula
    • Future Value of Annuity Due Formula
    • Internal Growth Rate Formula
    • F-Test Formula
    • Covariance Formula
    • Population Variance Formula
    • Coefficient of Determination Formula
    • Adjusted R Squared Formula
    • Compound Interest Formula
    • Gross Profit Formula
    • Accounting Equation Formula
    • Sample Size Formula
    • Sample Standard Deviation Formula
    • Quartile Formula
    • Variance Analysis Formula
    • Correlation Coefficient Formula
    • Z Score Formula
    • Variance Formula
    • Present Value Formula
    • Coefficient of Variation Formula
    • Net Asset Value Formula
    • Profit Margin Formula
    • Holding Period Return Formula
    • Capital Asset Pricing Model Formula
    • Present Value of Annuity Due Formula
    • Depreciation Expenses Formula
    • Annuity Formula
    • Taxable Income Formula
    • Profit Formula
    • Monthly Compound Interest Formula
    • Equity Formula
    • Return on Total Assets Formula
    • Alpha Formula
    • Debt to Equity Ratio Formula
    • EBITDA Formula
    • Accrued Interest Formula
    • Dividend Formula
    • Common Stock Formula
    • Mortgage Formula
    • Growth Rate Formula
    • Absolute Value Formula
  • Accounting fundamentals (614+)
  • Asset Management Tutorial (181+)
  • Banking (43+)
  • Corporate Finance Basics (248+)
  • Credit Research Fundamentals (6+)
  • Economics (44+)
  • Financial Modeling in Excel (13+)
  • Investment Banking Basics (114+)
  • Investment Banking Careers (26+)
  • Trading for dummies (67+)
  • valuation basics (27+)
Finance Blog Courses
  • Finance for Non Finance Managers Training Course
  • Investment Banking Online Course
  • Financial Modeling Certification
Footer
About Us
  • Blog
  • Who is EDUCBA?
  • Sign Up
  • Live Classes
  • Corporate Training
  • Certificate from Top Institutions
  • Contact Us
  • Verifiable Certificate
  • Reviews
  • Terms and Conditions
  • Privacy Policy
  •  
Apps
  • iPhone & iPad
  • Android
Resources
  • Free Courses
  • Investment Banking Jobs Offer
  • Finance Formula
  • All Tutorials
Certification Courses
  • All Courses
  • Financial Analyst All in One Bundle
  • Investment Banking Training
  • Financial Modeling Course
  • Equity Research Course
  • Private Equity Training Course
  • Business Valuation Course
  • Mergers and Acquisitions Course

© 2022 - EDUCBA. ALL RIGHTS RESERVED. THE CERTIFICATION NAMES ARE THE TRADEMARKS OF THEIR RESPECTIVE OWNERS.

EDUCBA
Free Investment Banking Course

Corporate Valuation, Investment Banking, Accounting, CFA Calculator & others

*Please provide your correct email id. Login details for this Free course will be emailed to you

By signing up, you agree to our Terms of Use and Privacy Policy.

EDUCBA
Free Investment Banking Course

Corporate Valuation, Investment Banking, Accounting, CFA Calculator & others

*Please provide your correct email id. Login details for this Free course will be emailed to you

By signing up, you agree to our Terms of Use and Privacy Policy.

Let’s Get Started

By signing up, you agree to our Terms of Use and Privacy Policy.

Loading . . .
Quiz
Question:

Answer:

Quiz Result
Total QuestionsCorrect AnswersWrong AnswersPercentage

Explore 1000+ varieties of Mock tests View more

EDUCBA Login

Forgot Password?

By signing up, you agree to our Terms of Use and Privacy Policy.

This website or its third-party tools use cookies, which are necessary to its functioning and required to achieve the purposes illustrated in the cookie policy. By closing this banner, scrolling this page, clicking a link or continuing to browse otherwise, you agree to our Privacy Policy

EDUCBA

Download Standard Error Formula Excel Template

EDUCBA

*Please provide your correct email id. Login details for this Free course will be emailed to you

By signing up, you agree to our Terms of Use and Privacy Policy.

Special Offer - Finance for Non Finance Managers Training Course Learn More