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The term variance is a statistical concept related to the spread or dispersion of a set of data. Second to the mean, it a common value we may calculate.
We find standard deviation easier to understand and use (it uses the same units as the data) whereas variance uses the units squared.
We use variance in quite a few different ways. Let’s review just a few. [Read more…]
There are two basic ways to consider the central limit theorem. First consider a random variable, X, which has a mean, μ, and variance σ2. If we take a random sample from f(X) of size n and calculate the sample mean, X̄, then as n increases the distribution of the sample means, X̄’s approaches a normal distribution with mean, μ, and variance σ2/√n̄. The original data, X, may have any distribution and when n is suitably large the distribution of the averages will approach a normal distribution. [Read more…]
The basic measures of central tendency are mean, median, and mode.
Given a collection of data, a common question is about where the data resides. Knowing the center or mid-point or average is a starting point as we consider the data. [Read more…]
In statistics and reliability, we use distributions to describe time to failure patterns. The four functions commonly used in reliability engineering include
We often use terms like, mean, variance, skewness, and kurtosis to describe distributions (along with shape, scale, and location). The mean is defined as the use of a moment generating function. First though let’s first back up to the concept of center of gravity (cog) from mechanics. [Read more…]
In another post, I started the discussion about variability and interquartile range. This is part 2 of that discussion and will focus on variance.
With rare exception, most distributions or groups of data require more than one parameter (or statistic) to fully describe both the location and spread (scale and shape) of the group of data. Is the data clumped tightly about some value, or spread out over a wide range. [Read more…]
“Statistics is the language of variation.” I’m sure that is a quote by someone, not me, though. It is true. Statistics is all about variation. In this post let’s explore some of the ways statisticians talk about data and specifically the amount of dispersion in the data. [Read more…]
This is hopefully completely a review. The mastery of basic statistical terms is important as many of the questions on the CRE are statistical in nature and rely on your understanding the terms. Let’s simply review the terms, and do let me know if you have any questions.
Let’s take a random sample from a population. Given a [Read more…]
Generally, I do not talk about statistics before 10am – it’s not polite.
As a reliability professional, statistics is a central feature of the value I bring to the team. And, not just the reliability statistics, all stats. It continues to amaze me how many engineers, scientists, and professionals tend to avoid statistics. [Read more…]
Understanding the math is critical not only for the exam, but it is also important for your ability to function as a reliability professional.
Most of us did not enjoy our undergraduate statistics course. It was just another course to endure as part of being in an engineering or science track.
The basic concepts and approaches to working with data are fundamental for some many situations. [Read more…]