After finding the mean, median, SD and CV, what can be concluded about the performance characteristics of the analysis? Table 1. Chemical Oxygen Demand (COD) (Chemische Sauerstoffbedarf or CSB in German) of three different Quality Control samples measured several times (mg/L)Ifd-NrQC Sample 200QC Sample 50OC Sample 25119350.0519.00219350.0519.00321057.5521.35420455.9020.30519247.659.9520551.5016.30720548.2015.1519953.1514.30920254.7520.101019545.3513.601119450.9011.001220150.5514.001320453.4512.601420453.6519.601529549.2016.301619548.6516.901719446.3015.101819647.2010.751920556.3022.952019545.1012.202120453.3520.852219847.6510.502319552.6517.902420253.0517.25

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Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter7: Distance And Approximation

Section7.3: Least Squares Approximation

Problem 31EQ

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After finding the mean, median, SD and CV, what can be concluded about the performance characteristics of the analysis?

Table 1. Chemical Oxygen Demand (COD) (Chemische Sauerstoffbedarf or CSB in German) of three different Quality Control samples measured several times (mg/L)
Ifd-Nr
QC Sample 200
QC Sample 50
OC Sample 25
1
193
50.05
19.00
2
193
50.05
19.00
3
210
57.55
21.35
4
204
55.90
20.30
5
192
47.65
9.95
205
51.50
16.30
7
205
48.20
15.15
199
53.15
14.30
9
202
54.75
20.10
10
195
45.35
13.60
11
194
50.90
11.00
12
201
50.55
14.00
13
204
53.45
12.60
14
204
53.65
19.60
15
295
49.20
16.30
16
195
48.65
16.90
17
194
46.30
15.10
18
196
47.20
10.75
19
205
56.30
22.95
20
195
45.10
12.20
21
204
53.35
20.85
22
198
47.65
10.50
23
195
52.65
17.90
24
202
53.05
17.25

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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