II. Probability and Statistics for Reliability
A. Basic concepts
1. Statistical terms (Apply)
Define and use terms such as population, parameter, statistic, sample, the central limit theorem, etc., and compute their values.
This lesson takes a close look at various measures of variation within the data.
Additional References
Variance (article)
Statistical Terms about Variation (article)
Quick Quiz
1-41. Laboratory tests of a new dental amalgam have yielded the following proportions of a critical compound: 41.2, 42.1, 44.7, and 41.9 ppm. Calculate the sample standard deviation.
(A) 1.327
(B) 1.443
(C) 1.533
(D) 1.666
(C) 1.533
The key element here is the calculation is for a sample, not a population. Thus be sure your calculator is providing the sample standard deviation result, based on this formula
$$ s=\sqrt{\frac{\sum\limits_{i=1}^{n}{{{\left( {{X}_{i}}-\bar{X} \right)}^{2}}}}{n-1}}$$
and not the formula for the population standard deviation.
$$ s=\sqrt{\frac{\sum\limits_{i=1}^{n}{{{\left( {{X}_{i}}-\bar{X} \right)}^{2}}}}{n}}$$
The difference of dividing by n or n-1 does make a difference for small sample. At about n = 30 there is little difference in the results.
why n-1? small correction. You say n=2 but it should be n=1 that makes sample variance undefined
Hi Satya,
Just listened to the lecture and right at the end (orange screen) – you are right as I misspoke. Do determine a sample variance we need a minimum of two points, thus divide by 1.. with only one point of data we are not able to calculate variance as the single point is the mean and thus zero… and with the n-1 for samples, we further divide by zero…
So, min number of data points is 2, not 3.
When I get a chance I’ll record the ending and update the lecture.
thanks for the listening so closely.
Cheers,
Fred