Statistics: common use of σ rather than s

The tutor continues his discussion about population standard deviation, denoted σ, versus sample standard deviation, denoted s. In yesterday’s post I gave the formulas for σ and s. Of course, many people use their hand calculators to find the standard …

Statistics: variance and standard deviation for population versus sample

The tutor indicates the formula for calculating population standard deviation versus that for sample standard deviation. The population variance, σ2, has calculation formula σ2=Σ1N(xi-μ)^2/N where N is the total count of the population, while μ is the mean. The population …

Statistics: goodness-of-fit test with Chi-square distribution

The tutor returns to a more academic focus with today’s post on goodness-of-fit. In business, as well as in science, people often try to fit data to a mathematical equation. The obvious advantage of doing so is being able to …

Standard deviation: a forestry example

The tutor offers a case study in statistics. Around here, forestry might be the leading industry.  Of course, I hardly ever see evidence of it; up in the hills is where the work is done. As I understand, one angle …

Statistics: standard deviation shortcut using frequencies

The tutor shows a convenient way to estimate the standard deviation. Let’s imagine the following list of 20 test scores: 43, 44, 49, 51, 52, 55, 57, 58, 61, 64, 68, 73, 74, 76, 77, 82, 84, 85, 87, 91 …

Statistics: how to enter a list, then find its mean, standard deviation, and median on the TI-83 Plus

Tutoring high school statistics, some of my students use the TI-83 Plus.  The tutor shows one way to find the mean, median, and standard deviation on it. Of course, to find the mean, median, or standard deviation of a list …

Statistics: what is a z-score?

Tutoring some high school math courses, statistics is prominent.  The tutor introduces an important definition.   Statistics focuses on the mean and the standard deviation. But why is that? The reason is that while most phenomena follow a normal distribution, …

Statistics: normal distribution calculations with the Sharp EL-520W

The tutor continues to find handy features on the Sharp EL-520W.  Today: probability associated with the normal distribution. The Sharp EL-520W just keeps on giving.  Sometimes I wonder, “Will it do that?” Usually, it turns out that it does. Relating …

Statistics: standard deviation comparison: formal vs range/6

Following up from the previous post, the tutor tries out the standard deviation estimator range/6.  Standard deviation is a common topic during high school math tutoring. Imagine the following results from a fictional midterm: 56, 42, 71, 66, 45, 81, …

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Statistics: an easy estimate of the standard deviation

Tutoring statistics, I’m happy to add this method to my repertoire.  The tutor brings forth a shortcut for finding the standard deviation. According to my source listed below, the standard deviation (σ) can be estimated as follows: σ=range/6 The range …