Statistics for Dummies: 104

Prajwal Khairnar
4 min readAug 4, 2023

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Photo by Volodymyr Proskurovskyi on Unsplash

Measures of Variability: Range, Variance, and Standard Deviation

Introduction to Measures of Variability

In this lesson, you will learn about measures of variability. These are used to describe the dispersion or spread of a set of data.

Variability is the extent to which values differ from one another in a set of observations. It can be thought of as how far apart individual scores are from each other on average or at any time. Variability is also called dispersion because it describes how widely dispersed scores are within a distribution (or group).

Range: The simplest way to measure variability is by calculating range, which is simply the maximum value minus minimum value:

Range = Max — Min

Variance: Another common method for measuring variability involves looking at squared deviations between each data point and its mean (average), then taking an average over all points in order to get an estimate for standard deviation (the most commonly used measure). This process involves adding up all squared deviations between each observation and its mean; while making sure they add up correctly so you don’t double count any terms like x² = 2x; then dividing by N-1 where N=total number of items being measured

Defining the Range: The Difference Between the Maximum and Minimum Values

The range is the difference between the largest and smallest values in a data set. It’s often used as an alternative to standard deviation, which we’ll talk about later. The range is not a good measure of variability because it doesn’t take into account how much each value differs from its mean; instead, it simply measures how far apart they are from one another. For example, if you have two sets of numbers — one with values 0 through 5 and another with values 100 through 105 — you would expect that their standard deviations would be different because their means were so far apart (50 versus 100). However, both sets have identical ranges: 5–0 = 5.

Understanding Variance: A Measure of the Spread of a Data Set

Variance is a measure of the dispersion or variability of a data set. It is defined as the average squared difference between each data point and its mean, which can be calculated by taking the sum of all of your observations, squaring them, then dividing by n minus 1 (where n is how many data points you have).

In other words:

Variance = Sum(x²)/(n-1)

Calculating Standard Deviation: A Measure of the Amount of Variation or Dispersion Around the Mean

Standard deviation is a measure of how far the items in a data set are from their mean. It measures the spread of data around its mean, or average. The standard deviation is calculated by taking the square root of variance (the average squared difference between each value and its mean).

Standard deviation is one way to measure dispersion, or how much variation there is between observations within your dataset. You should use this statistic when you want to know if there’s enough variability within your sample set so that it makes sense for further analysis (i.e., whether or not your results are statistically significant).

Interpreting Variance and Standard Deviation: Understanding the Results

Interpreting the results of your data analysis is an important part of the process. It’s critical to understand how much variability there is in your data, and whether or not this amount of variability is considered normal.

  • A high standard deviation means that there is a lot of variation within your sample population — for example, if you measure everyone’s height and then calculate their average height, they could all be different heights but still fall within one standard deviation from each other. This would indicate that most people have similar heights but some are taller than others (or shorter).
  • A low standard deviation means that there isn’t much variation within your sample population — for example, if every person had exactly the same height (and weight), then there wouldn’t be any difference between them at all! This would indicate that everyone has a very similar personality type or lifestyle choice because it hasn’t been affected by outside influences like location or upbringing; instead of having many different kinds of people living together peacefully like we do today here on Earth…

The Effect of Outliers on Variance and Standard Deviation

The effect of outliers on the range and variance is quite straightforward. Outliers are extreme values, so their presence will increase your range and variance. The standard deviation, however, doesn’t change much when you have outliers in your data set because it measures variability within a distribution rather than between distributions.

Conclusion

In this article, we’ve covered the basics of measures of variability. Variance and standard deviation are important statistics because they can help you understand how much a set of data varies from its mean and whether or not there are any outliers that may affect your conclusions. In addition, they can be used to make decisions in real life situations by providing information about the degree of certainty associated with a particular outcome based on previous results.

If you’re looking for more information on statistics related topics such as the mean, median and mode then check out my other articles!

Journey Links

I will keep updating the list here when new articles are published in the series. Keep an eye on it!

  1. Statistics for Dummies: 101
    Introduction to Statistics
  2. Statistics for Dummies: 102
    Types of Data: Nominal, Ordinal, Interval, and Ratio Scales
  3. Statistics for Dummies: 103
    Measures of Central Tendency: Mean, Median, and Mode
  4. Statistics for Dummies: 104
    Measures of Variability: Range, Variance, and Standard Deviation
  5. Statistics for Dummies: 105
    Probability: Definition and Basic Concepts
  6. Statistics for Dummies: 106
    Mastering Discrete and Continuous Probability Distributions: Key Concepts and Applications
  7. Statistics for Dummies: 107
    Unlocking the Power of Sampling Distributions: Key Insights for Statistical Analysis
  8. Statistics for Dummies: 108
    Demystifying Hypothesis Testing: Essential Concepts for Statistical Analysis

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Prajwal Khairnar
Prajwal Khairnar

Written by Prajwal Khairnar

Data Scientist | IT Engineer | Research interests include Statistics | NLP | Machine Learning, Data Science and Analytics, Clinical Trials

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