- Statistics Tutorial
- Home
- Adjusted R-Squared
- Analysis of Variance
- Arithmetic Mean
- Arithmetic Median
- Arithmetic Mode
- Arithmetic Range
- Bar Graph
- Best Point Estimation
- Beta Distribution
- Binomial Distribution
- Black-Scholes model
- Boxplots
- Central limit theorem
- Chebyshev's Theorem
- Chi-squared Distribution
- Chi Squared table
- Circular Permutation
- Cluster sampling
- Cohen's kappa coefficient
- Combination
- Combination with replacement
- Comparing plots
- Continuous Uniform Distribution
- Continuous Series Arithmetic Mean
- Continuous Series Arithmetic Median
- Continuous Series Arithmetic Mode
- Cumulative Frequency
- Co-efficient of Variation
- Correlation Co-efficient
- Cumulative plots
- Cumulative Poisson Distribution
- Data collection
- Data collection - Questionaire Designing
- Data collection - Observation
- Data collection - Case Study Method
- Data Patterns
- Deciles Statistics
- Discrete Series Arithmetic Mean
- Discrete Series Arithmetic Median
- Discrete Series Arithmetic Mode
- Dot Plot
- Exponential distribution
- F distribution
- F Test Table
- Factorial
- Frequency Distribution
- Gamma Distribution
- Geometric Mean
- Geometric Probability Distribution
- Goodness of Fit
- Grand Mean
- Gumbel Distribution
- Harmonic Mean
- Harmonic Number
- Harmonic Resonance Frequency
- Histograms
- Hypergeometric Distribution
- Hypothesis testing
- Individual Series Arithmetic Mean
- Individual Series Arithmetic Median
- Individual Series Arithmetic Mode
- Interval Estimation
- Inverse Gamma Distribution
- Kolmogorov Smirnov Test
- Kurtosis
- Laplace Distribution
- Linear regression
- Log Gamma Distribution
- Logistic Regression
- Mcnemar Test
- Mean Deviation
- Means Difference
- Multinomial Distribution
- Negative Binomial Distribution
- Normal Distribution
- Odd and Even Permutation
- One Proportion Z Test
- Outlier Function
- Permutation
- Permutation with Replacement
- Pie Chart
- Poisson Distribution
- Pooled Variance (r)
- Power Calculator
- Probability
- Probability Additive Theorem
- Probability Multiplecative Theorem
- Probability Bayes Theorem
- Probability Density Function
- Process Capability (Cp) & Process Performance (Pp)
- Process Sigma
- Quadratic Regression Equation
- Qualitative Data Vs Quantitative Data
- Quartile Deviation
- Range Rule of Thumb
- Rayleigh Distribution
- Regression Intercept Confidence Interval
- Relative Standard Deviation
- Reliability Coefficient
- Required Sample Size
- Residual analysis
- Residual sum of squares
- Root Mean Square
- Sample planning
- Sampling methods
- Scatterplots
- Shannon Wiener Diversity Index
- Signal to Noise Ratio
- Simple random sampling
- Skewness
- Standard Deviation
- Standard Error ( SE )
- Standard normal table
- Statistical Significance
- Statistics Formulas
- Statistics Notation
- Stem and Leaf Plot
- Stratified sampling
- Student T Test
- Sum of Square
- T-Distribution Table
- Ti 83 Exponential Regression
- Transformations
- Trimmed Mean
- Type I & II Error
- Variance
- Venn Diagram
- Weak Law of Large Numbers
- Z table
- Statistics Useful Resources
- Statistics - Discussion

- Selected Reading
- UPSC IAS Exams Notes
- Developer's Best Practices
- Questions and Answers
- Effective Resume Writing
- HR Interview Questions
- Computer Glossary
- Who is Who

# Statistics - Standard Error ( SE )

The standard deviation of a sampling distribution is called as standard error. In sampling, the three most important characteristics are: accuracy, bias and precision. It can be said that:

The estimate derived from any one sample is accurate to the extent that it differs from the population parameter. Since the population parameters can only be determined by a sample survey, hence they are generally unknown and the actual difference between the sample estimate and population parameter cannot be measured.

The estimator is unbiased if the mean of the estimates derived from all the possible samples equals the population parameter.

Even if the estimator is unbiased an individual sample is most likely going to yield inaccurate estimate and as stated earlier, inaccuracy cannot be measured. However it is possible to measure the precision i.e. the range between which the true value of the population parameter is expected to lie, using the concept of standard error.

## Formula

$SE_\bar{x} = \frac{s}{\sqrt{n}}$

Where −

${s}$ = Standard Deviation

and ${n}$ = No.of observations

### Example

**Problem Statement:**

Calculate Standard Error for the following individual data:

Items | 14 | 36 | 45 | 70 | 105 |
---|

**Solution:**

Let's first compute the Arithmetic Mean $\bar{x}$

Let's now compute the Standard Deviation ${s}$

Thus the Standard Error $SE_\bar{x}$

The Standard Error of the given numbers is 15.63.

The smaller the proportion of the population that is sampled the less is the effect of this multiplier because then the finite multiplier will be close to one and will affect the standard error negligibly. Hence if the sample size is less than 5% of population, the finite multiplier is ignored.