CHEM%20140L%20Session%2003

CHEM%20140L%20Session%2003 - Session 03 Data Analysis in...

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3-1 Session 03 Data Analysis in Excel Topics In this session the following spreadsheet concepts will be explored: 1. Basic Statistics in Science Distributions Mean Variance and Standard Deviation Method of Least Squares 2. Basic Statistical Functions in Excel AVERAGE COUNT •M A X I N 3. Linear Regression Techniques in Excel Linear regression functions (SLOPE, INTERCEPT, CORREL and RSQ) Linear regression using TRENDLINE Linear regression using LINEST •T R E N D 4. Standard Deviation and Error Bars in Excel Standard Deviation Error Bars
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CHEM 140L Session 3 - Data Analysis in Excel 3-2 Basic Statistics in Science Experimental measurements always have some sort of error. This means no conclusion can be made with complete certainty. Statistics provide the tools to accept experimental results that have a high probability of being correct or to reject experimental results that fall beyond acceptable confidence limits. This session will address the basic statistics used in science. = Distributions Consider the example, that a food manufacturer claims that there are 100 mg of sodium in a can of soup. Five cans of soup were tested and it was found that the sodium content was 108.6 mg, 104.2 mg, 96.1 mg, 99.6 mg and 102.2 mg. Each can of soup is known as a sample . As we can see no individual sample contains the exact sodium content reported by the manufacturer, but all the values are close to 100 mg. The discrepancy between the sodium content of an individual sample and the reported sodium content is due to some degree of random error or fluctuation in the system. If the measurements were repeated enough times, we would expect a spread of results or a distribution of the values. The distribution of a few measurements would look like the plot shown in Figure 3.2. The frequency is the number of times that a particular results occurs. Figure 3.1 : Population versus sample.
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CHEM 140L Session 3 - Data Analysis in Excel 3-3 With the example shown in Figure 3.2, we see that the values are distributed relatively evenly around a point somewhere between 1.2 and 1.6. You can see the probability distribution plot has a “bell shape”. This type of distribution is known as a bell-curve or normal distribution . A normal distribution implies that a large number of measurements were made for the same system. = Mean As you can see from Figure 3.3, as we increase the number of measurements, the shape of the probability plot begins to resemble the normal distribution. The mean (or average) of a set of measurements is located at the centre of the normal distribution. The mean can be thought of as the expected outcome of an event, such that if a measurement was performed multiple times, the average values would be the most common outcome. If an infinite number of measurements are made, the average of the infinite measurements is known as the population mean ( μ ). The population means represents the “true” value of a measurement. Since it is impossible to measure directly a population mean, normally a
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CHEM%20140L%20Session%2003 - Session 03 Data Analysis in...

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