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standart deviation in statistics

Standard Deviation: A Vital Metric for Evaluating Data Variability and Spread


By gobrain

Jan 1st, 2024

INTRODUCTION

The standard deviation is a statistical indicator that reflects the variability or spread of a set of data. Standard deviation is widely used across various industries, including finance, engineering and education etc.

In this article, we will discuss standard deviation from many aspects including its importance and calculation. First, let's get started with what standard deviation is.

What is Standard Deviation

Simply put, the standard deviation is a measure of how much the values in a data set differ from the mean of the data. Standard deviation of a dataset:

  • is high if many values are far from the mean and

  • is low if they are close to the mean.

  • is zero, it means that all numbers in the data set are equal.

Importance Of Standard Deviation

Standard deviation enables us to make general conclusions from a smaller sample drawn from a large data set. It also contributes to identifying outliers when utilized in combination with other statistical measures.

For instance, in psychology studies, standard deviation can be utilized to analyze test scores of a sample of the entire population, allowing us to make generalizations about the overall situation of the population.

And also, standard deviation is a key component of many probability distributions, including the normal distribution. This allows for the calculation of probabilities and confidence intervals, which can be used in statistical inference and hypothesis testing.

AREAS OF USE OF VARIANCE

Some of the common areas of use of variance are:

  • In economics, variance is used to measure the variability of economic indicators like inflation, GDP and unemployment rates.

  • Engineering: In engineering, variance is used to measure the variability of the dimensions and specifications of a product. It helps to ensure that the product meets the desired tolerances and specifications

  • Social Sciences: In social sciences, variance is used to measure the variability of data collected from surveys, experiments, and other research methods. It helps to assess the reliability of the data and to test hypotheses

Calculating Of Standard Deviation

The standard Deviation of a data set easily can be calculated by following the steps below.

  • Calculate the mean of the dataset
  • Subtract the mean from each value in set
  • Square the values found in the second step and sum all the values
  • Divide the sum by the number of values in set
  • Take the square root of the last result

Formula: SD = √(Σ(x - μ)^2 / n)

For:

  • x is a data in set,
  • μ is the mean,
  • n is the number of values in set,
  • Σ is the sum of

For example, for a given set of 2,6,7

  • mean: (2 + 6 + 7) / 3 = 5
  • SD = (2-5)^2 + (6-5)^2 + (7-5)^2 = 14
  • SD = √ (14 / 3)
  • SD = 2.160...

Standart Deviation: Sample vs Population

Since it is usually difficult to collect data for the whole population, a sample from the whole population is taken and the standard deviation can be calculated. In this case, there will be a small change in the formula as below

SD = √(Σ(x - μ)^2 / (n-1))

The new standart deviation for the set above will be :

  • SD = √ (14 / 2)
  • SD = 2.645

Conclusion

In conclusion, standard deviation is a statistical measure of the spread of a set of data values. Standard deviation is useful because it allows us to make inferences about a population based on a sample and helps us understand the variability of data.

Thank you for reading.