Finance

Standard Error vs. Standard Deviation

Standard Error vs. Standard Deviation

Standard Error & Standard Deviation are two important concepts of statistics, which are widely used in the field of research. The Standard Error is a mathematical tool used in statistics to measure variability. It measures how precisely a sampling distribution represents a population. It is the approximate standard deviation of a statical sample population. A sample mean deviates from the actual mean of a population this deviation is the standard error of the mean. It can be applied in statistics, economics and is especially useful in the field of econometrics where researchers use it in performing regression analyses and hypothesis testing. This article highlights the concept of Standard Error vs. Standard Deviation.

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The Standard Deviation is a statistic that measures the dispersion of a dataset relative to its mean and is calculated as the square root of the variance by determining each data point’s deviation relative to the mean. It is most widely used and practiced in portfolio management services. Fund managers often use this basic method to calculate and justify their variance of returns in a particular portfolio.

What do they indicate?

Standard deviation can be difficult to interpret as a single number on its own. A small standard deviation means that the values in a statistical data set are close to the mean of the data set on average and a large standard deviation means that the values in the data set are farther away from the mean. In situations where just observation is required and the data is recorded a large standard deviation isn’t necessarily a bad thing it just reflects a large amount of variation in the group that is being studied. Similar to mean outliers affect the standard deviation.

The standard error tells how accurate the mean of any given sample from that population is likely to be compared to the true population mean. As the standard deviations increase it signifies that the mean is more spread out thus it becomes more likely that any given mean is an inaccurate representation of the true population means.

Calculation:

STANDARD ERROR OF MEAN

The standard error(SE) is expressed as σ͞x.

The steps to calculate standard error are as follows

  • STEP 1 – Calculate the mean by adding all the samples and dividing by the number of samples.
  • STEP 2 – Each measurement deviation from the mean is supposed to be calculated (mean minus the individual measurement).
  • STEP 3 – Square each deviation from the mean
  • STEP 4 – Sum the squared deviations from step 3.
  • STEP 5 – Divide the sum from step 4 by one less than the sample (n-1).
  • STEP 6 – Take the square root of the number got in step 5.
  • STEP 7 – Divide the standard deviation by the square root of the sample size(n), which will give the standard error.

Standard deviation:

  • x = Value of each data point
  • x̄ = Mean
  • n = Number of data points

Steps to calculate standard deviation are as follows-

  • STEP 1 – Find the mean
  • STEP 2 – For each data point, find the square of its distance from the mean.
  • STEP 3 – sum the values from step 2.
  • STEP 4 – divide by the number of data points
  • STEP 5 – take the square root.

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Importance & Uses in Real- Life:

  • Standard deviation
    • It is helpful in analyzing the overall risk and return which is a matrix of the portfolio and is historically helpful. The correlation and weights of the stocks of the portfolio have an impact on the standard deviation of the portfolio. Also, it is widely used in the industry.
    • When the correlation of the two asset classes in a portfolio reduces the risk if the portfolio, in general, reduces however it is not necessary all the time that the equally weighted portfolio provides the least risk among the universe.
    • A measure of volatility can be a fund with a high standard deviation but it does not necessarily mean that it is worse than a fund with a lower standard deviation.
  • Standard error of the mean
    • A sample is always taken from a higher population which comprises a larger size of variables. The standard error tends to be higher if the sample size taken is small. It helps the statistician to determine the credibility of the sample mean with respect to the population mean.
    • A presence of a large variation in the sample with respect to the population tells the statistician that there is a large standard error and the sample is not uniform with respect to the population mean. In a similar way, a small standard of error tells that the sample is uniform with respect to the population means and that there is a presence of no or small variation in the sample with respect to the population.
    • The standard error should not be confused with standard deviation because standard eros is calculated for the sample to mean whereas standard deviation is calculated for the entire population.

Conclusion:

This was the overview of Standard Error vs. Standard Deviation. Standard deviations are a very useful tool in quantifying how risky an investment is actually. By actively monitoring a portfolio’s standard deviation and making adjustments will allow investors to tailor their investments to their personal risk attitude.

The standard error offers a useful way for the quantification of a sampling error and represents the total amount of sampling errors that are associated with the sampling process. It can be understood as the statistic or parameter of the mean.

Author -Sanjana Rau

About the author- Started my journey of self even when the odds were against me, keen observation, a cool temper, and sports worked the best for me.

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