Lecture_Statistics_Spring_2013b

Random error vs precision the measurement has high

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Unformatted text preview: ng the true value. *Random error vs. Precision The measurement has high precision if the random errors are small. There is no necessary relationship between accuracy and precision. Precision DOES NOT necessarily imply accuracy, since an experiment with small random errors may still give inaccurate results due to large systematic errors. See Example in the next slide I. Accuracy and Precision × ×× A × × × × × × B C Three targets for three different guns and three different marksmen. Target A: reasonable accuracy and precision. Target B: poor precision, although the average is about the center of the target. Target C: excellent precision, but poor accuracy. II. Means and Standard Deviations A sample represents some subset of a population A population represents every member of a group Population Mean, µ ȹ N ȹ µ = ȹ ∑ x i ȹ N ȹ ȹ ȹ i =1 Ⱥ Population Variance, σ2 Sample Mean, ȹ N ȹ x = ȹ ∑ x i ȹ N ȹ ȹ ȹ i =1 Ⱥ Sample Variance, s2 ȹ N 2 ȹ s = ȹ ∑ (x i − x ) ȹ ȹ ȹ ȹ i =1 Ⱥ ȹ N 2 ȹ σ = ȹ ∑ (x i − µ ) ȹ N ȹ ȹ ȹ i =1 Ⱥ 2 2 2 σ=x 2 −x 2 x s2 = (N − 1) N ȹ N ȹȹ 2 2 σ 2 = ȹ x − x ȹ ȹ ȹȹ ȹ Ⱥ N −1 ȹ N − 1 Ⱥ Variance describes the distribution of values ar...
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