Learning Objectives: Students will be able to... 1. Correctly use an analytical balance to measure mass and calculate th
Posted: Sun Jul 10, 2022 4:17 pm
- Learning Objectives Students Will Be Able To 1 Correctly Use An Analytical Balance To Measure Mass And Calculate Th 1 (55.37 KiB) Viewed 34 times
1. Determine the average, standard deviation, and relative standard deviation of your data (if you determined a data point should be rejected, then do not include it in your calculations). Show your work to receive credit. Average Standard Deviation Relative Standard Deviation (5pts) (5pts) (5pts) 2. Given the accepted mass of a U.S. penny is 2.5 g, calculate the %error and comment on the accuracy and precision of your data.(15 pts) 3. Provide an explanation for any discrepancy you find in lines 2 through 4 of your data sheet.(3 pts)
Q-Test Datum Rejection We may be in a situation where one data value apparently has a strong influence on the mean of a set of data. Assume we have 6 data points to analyze to be sure that each point is a viable part of the set; in other words, it's not "way off" from the rest of the data. Consider the data set: 44.7 43.3 46.2 45.1 46.5 69.2 The 69.2 value appears to be out of class, i.e., it comes from a different population. Notice how this number affects the calculated mean: 44.7+ 43.3 + 46.2+ 45.1 + 46.5 + 69.2 Whereas 44.7+ 43.3 + 46.2 + 45.1 +46.5 5 45.16 Since the mean obtained using 69.2 is very different from most of the data, we "suspect" it is out of class. The Q-test is often used to test this hypothesis. Like Student's t-test, we calculate a Q value under a null hypothesis; i.e., data are the same, and then compare it to a statistical table value using the logical scheme if calculated < Qtable, then null hypothesis is correct. The data is kept. if Qcalculated > Qtables then null hypothesis is wrong. The data is rejected. The RANGE and the GAP are 6 RANGE= GAP and the calculated Q value is The Q value is calculated using this formula: Qcalc GAP RANGE where the GAP is difference between the suspect datum (the one that looks out of place) and its nearest neighbor. The RANGE is the difference between the maximum and minimum data in the set. Rearranging the data set from minimum to maximum gives us: 43.3 44.7 Minimum value Number of Data (N) Rejection Quotient largest value minus smallest value = 69.243.3 = 25.9 = = 49.17 45.1 46.2 46.5 69.2 Maximum value 22.7 Qcale= = 0.876 25.9 suspect datum minus its nearest neighbor = 69.2 46.5 = 22.7 To determine if this value is acceptable, we look at the Table 1, a list of Q Values for the number of measurement data. Table 1: Q Test Statistics (Rejection Quotients) 3 4 5 6 0.94 0.76 0.64 0.56 7 0.51 8 0.47 9 0.44 10 0.41
The mean or average result, X, is calculated by summing the individual results and dividing this sum by the number (n) of individual values: The standard deviation is a measure of how precise the average is, that is, how well the individual numbers agree with each other. It is a measure of a type of error called random error-the kind of error people can't control very well. It is calculated as follows: standard deviation, S = mean, x = mean, X = The relative standard deviation (RSD) is often more convenient. It is expressed in percent and is obtained by multiplying the standard deviation by 100 and dividing this product by the average. relative standard deviation, RSD = ³ × 100% Example: Here are 4 measurements: 51.3, 55.6, 49.9 and 52.0. Calculate the mean, standard deviation, and relative standard deviation. standard deviation, S = = X1 + X₂ + X3 + X4 + ... n 51.3 + 55.6 + 49.9 +52 4 = (x₁ - x)² + (x₂-x)² + (x3 - x)² +... n-1 = 2.4 √5.9 = [0.81 +11.56 +5.29 +0.04 3 208.8 (51.3 - 52.2)² + (55.6 - 52.2)² + (499-52.2)²+(520-52.2)² 4-1 (-0.9)² + (34)² + (-2.3)² + (-0.2)² 3 = 52.2
= 2.4 relative standard deviation, RSD = X 100% = 4.6% Our final result for this example can be written as 52.2±2.4 or 52.2±4.6%.