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The standard deviation (SD) is a single number that summarizes the variability in a dataset. It represents the typical distance between each data point and the mean. Smaller values indicate that the data points cluster closer to the mean—the values in the dataset are relatively consistent.
It’s helpful to know both the mean and the standard deviation of a dataset because each metric tells us something different. The mean gives us an idea of where the “center” value of a dataset is located.
The standard deviation measures how concentrated the data are around the mean; the more concentrated, the smaller the standard deviation. A small standard deviation can be a goal in certain situations where the results are restricted, for example, in product manufacturing and quality control.
The standard deviation: a way to measure the typical distance that values are from the mean. The variance: the standard deviation squared. Out of these four measures, the variance tends to be the one that is the hardest to understand intuitively. This post aims to provide a simple explanation of the variance.
Next, we will learn how to interpret the numerical summaries to communicate the shape of the distribution. For example, what do you imagine, when you hear that a dataset has the average 50 and the standard deviation 10?
How does the mean and standard deviation describe data? The standard deviation is a measurement in reference to the mean that means: A large standard deviation indicates that the data points are far from the mean, and a small standard deviation indicates that they are clustered closely around the mean.
This article will cover the basic statistical functions of mean, median, mode, standard deviation of the mean, weighted averages and standard deviations, correlation coefficients, z-scores, and p-values.
1. What is Descriptive Statistics? 2. Types of Descriptive Statistics? 3. Measure of Central Tendency (Mean, Median, Mode) 4. Measure of Spread / Dispersion (Standard Deviation, Mean Deviation, Variance, Percentile, Quartiles, Interquartile Range) 5. What is Skewness? 6. What is Kurtosis? 7. What is Correlation?
The standard deviation of \(X\) is the square root of this sum: \(\sigma = \sqrt{1.05} \approx 1.0247\) The mean, μ, of a discrete probability function is the expected value. \[μ=∑(x∙P(x))\nonumber\] The standard deviation, Σ, of the PDF is the square root of the variance. \[σ=\sqrt{∑[(x – μ)2 ∙ P(x)]}\nonumber\]
The standard deviation is the average amount of variability in your dataset. It tells you, on average, how far each value lies from the mean. A high standard deviation means that values are generally far from the mean, while a low standard deviation indicates that values are clustered close to the mean.