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| Student Work / Activities - Mechatronics 3 - Pattern Recognition By Automated systems |
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| During the data collection exercise in Chapter 2, a wide range of raw results were collected from the colour environment being investigated. Review the following data collected from a similar experiment. Evaluate the results obtained and identify possible problems with the data collected. |
| 6.12 |
5.47 |
5.09 |
5.02 |
4.83 |
4.71 |
4.50 |
4.34 |
| 4.83 |
4.43 |
4.18 |
4.18 |
4.19 |
4.11 |
4.07 |
4.24 |
| 4.62 |
4.36 |
4.25 |
4.14 |
4.13 |
4.09 |
3.93 |
4.00 |
| 4.46 |
4.14 |
4.07 |
4.07 |
3.97 |
4.01 |
3.94 |
3.99 |
| 4.59 |
4.32 |
4.24 |
4.25 |
4.31 |
4.40 |
4.17 |
4.17 |
| 4.29 |
4.09 |
4.09 |
3.99 |
4.04 |
4.11 |
4.06 |
4.24 |
| 5.20 |
5.24 |
5.06 |
4.79 |
4.76 |
4.73 |
4.53 |
4.54 |
| 5.54 |
5.00 |
4.99 |
4.96 |
4.97 |
4.84 |
5.1 |
4.69 |
|
Patterns discovered
Use the following information provided to analyze your data, and plot the results using Excel. A suitable plot would be Number of samples v Voltage Range.
Example 4.000 to 4.099, 4.100 to 4.199 etc. select an appropriate range for you study.
Process this data and find the average =
Now use Excel to analyze this data
Is it possible to confidently predict the colour of the card used from the peak value obtained??? |
Standard Deviation - Variance and standard deviation (1 of 2)
The variance is a measure of how Spread out a distribution is. It is computed as the average squared deviation of each number from its mean. For example, for the numbers 1, 2, and 3, the mean is 2 and the variance is: |
σ 2 = 
The formula (in Summation Notation) for the variance in a Populationis
where μ is the mean and N is the number of scores.
When the variance is computed in a sample, the statistic
(where M is the mean of the sample) can be used. S 2 is a biasedestimate of σ 2, however. By far the most common formula for computing variance in a sample is:
which gives an unbiased estimate of σ 2. Since samples are usually used to estimate parameters, s 2 is the most commonly used measure of variance. Calculating the variance is an important part of many statistical applications and analyses.
Standard Deviation
The formula for the standard deviation is very simple: it is the square root of the variance. It is the most commonly used measure of spread.
An important attribute of the standard deviation as a measure of spread is that if the mean and standard deviation of a normaldistribution are known, it is possible to compute the percentile rank associated with any given score. In a normal distribution, about 68% of the scores are within one standard deviation of the mean and about 95% of the scores are within two standards deviations of the mean.
The standard deviation has proven to be an extremely useful measure of spread in part because it is mathematically tractable. Many formulas in inferentialstatistics use the standard deviation. Although less sensitive to extreme scores than the range, the standard deviation is more sensitive than the semi-inter quartile range. Thus, the standard deviation should be supplemented by the semi-inter quartile range when the possibility of extreme scores is present.
If variable Y is a linear transformationof X such that: Y = bX + A, then the variance of Y is:  where  is the variance of X. The standard deviation of Y is b σ x where σ x is the standard deviation of X.
Standard Deviation as a Measure of Risk
The standard deviation is often used by investors to measure the risk of a stock or a stock portfolio. The basic idea is that the standard deviation is a measure of volatility: the more a stock's returns vary from the stock's average return, the more volatile the stock. Consider the following two stock portfolios and their respective returns (in per cent) over the last six months. Both portfolios end up increasing in value from $1,000 to $1,058. However, they clearly differ in volatility. Portfolio A's monthly returns range from -1.5% to 3% whereas Portfolio B's range from -9% to 12%. The standard deviation of the returns is a better measure of volatility than the range because it takes all the values into account. The standard deviation of the six returns for Portfolio A is 1.52; for Portfolio B it is 7.24.
Yellow
| 1.96 |
2.03 |
2.12 |
2.22 |
2.00 |
1.95 |
1.88 |
1.81 |
| 2.01 |
2.05 |
2.13 |
2.28 |
1.86 |
2.30 |
1.95 |
1.91 |
| 2.03 |
1.92 |
1.86 |
2.01 |
2.32 |
2.25 |
1.84 |
1.86 |
| 2.05 |
2.16 |
1.93 |
2.08 |
2.26 |
1.88 |
1.98 |
1.81 |
| 2.11 |
1.78 |
2.37 |
2.32 |
2.41 |
2.16 |
1.81 |
1.79 |
| 1.98 |
2.03 |
1.95 |
1.84 |
1.83 |
1.74 |
1.79 |
1.82 |
| 1.74 |
1.96 |
2.14 |
2.13 |
2.28 |
1.91 |
2.25 |
2.21 |
| 2.16 |
2.11 |
1.90 |
1.85 |
2.05 |
2.41 |
2.32 |
2.20 |
| 1.70 |
1.65 |
1.69 |
1.74 |
1.85 |
1.89 |
1.93 |
1.88 |
| 1.99 |
2.05 |
2.04 |
2.16 |
2.19 |
2.23 |
2.20 |
2.28 |
| 1.62 |
1.64 |
1.91 |
2.01 |
2.00 |
1.96 |
2.09 |
2.14 |
| 2.45 |
2.29 |
2.34 |
2.30 |
2.28 |
2.24 |
2.17 |
2.14 |
| 2.01 |
2.00 |
1.94 |
1.96 |
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Pink
| 0.88 |
0.86 |
0.86 |
0.85 |
0.84 |
0.87 |
0.85 |
0.82 |
0.83 |
0.87 |
| 0.88 |
0.90 |
0.85 |
0.86 |
0.87 |
0.83 |
0.84 |
0.85 |
0.89 |
0.86 |
| 0.87 |
0.91 |
0.84 |
0.89 |
0.87 |
0.83 |
0.81 |
0.82 |
0.85 |
0.83 |
| 0.86 |
0.87 |
0.89 |
0.85 |
0.89 |
0.84 |
0.85 |
0.85 |
0.86 |
0.89 |
| 0.87 |
0.84 |
0.86 |
0.85 |
0.88 |
0.88 |
0.88 |
0.87 |
0.89 |
0.84 |
| 0.88 |
0.85 |
0.86 |
0.84 |
0.89 |
0.88 |
0.87 |
0.86 |
0.84 |
0.86 |
| 0.85 |
0.88 |
0.87 |
0.86 |
0.85 |
0.86 |
0.84 |
0.85 |
0.87 |
0.86 |
| 0.88 |
0.85 |
0.84 |
0.88 |
0.89 |
0.86 |
0.82 |
0.87 |
0.84 |
0.89 |
| 0.81 |
0.84 |
0.87 |
0.89 |
0.86 |
0.85 |
0.86 |
0.86 |
0.87 |
0.87 |
| 0.86 |
0.89 |
0.89 |
0.88 |
0.88 |
0.87 |
0.84 |
0.84 |
0.86 |
0.82 |
| 0.84 |
0.83 |
0.85 |
0.83 |
0.88 |
0.87 |
0.86 |
0.84 |
0.89 |
0.85 |
| 0.85 |
0.84 |
0.83 |
0.81 |
0.80 |
0.90 |
0.85 |
0.84 |
0.87 |
0.86 |
| 0.86 |
0.84 |
0.89 |
0.82 |
0.82 |
0.86 |
0.84 |
0.87 |
0.87 |
0.91 |
| 0.86 |
0.84 |
0.81 |
0.82 |
0.80 |
0.83 |
0.83 |
0.85 |
0.86 |
0.84 |
| 0.90 |
0.90 |
0.81 |
0.91 |
0.84 |
0.87 |
0.86 |
0.95 |
0.84 |
0.88 |
Green
| 9.9k |
8.1k |
5.4k |
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6.28k |
5.9k |
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6.9k |
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| 5.6k |
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6.9k |
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Blue sheet
| 1.61 |
1.62 |
1.64 |
1.67 |
1.62 |
1.47 |
1.45 |
1.30 |
1.25 |
1.25 |
| 1.60 |
1.43 |
1.45 |
1.34 |
1.35 |
1.37 |
1.44 |
1.31 |
1.30 |
1.32 |
| 1.92 |
1.48 |
1.45 |
1.43 |
1.40 |
1.38 |
1.38 |
1.28 |
1.24 |
1.45 |
| 1.52 |
1.36 |
1.38 |
1.27 |
1.31 |
1.33 |
1.31 |
1.26 |
1.37 |
1.34 |
| 1.41 |
1.32 |
1.30 |
1.30 |
1.31 |
1.25 |
1.35 |
1.42 |
1.21 |
1.24 |
| 1.26 |
1.45 |
1.25 |
1.23 |
1.12 |
1.28 |
1.25 |
1.23 |
1.23 |
1.27 |
| 1.23 |
1.28 |
1.20 |
1.14 |
1.22 |
1.24 |
1.24 |
1.33 |
1.25 |
1.23 |
| 1.22 |
1.24 |
1.20 |
1.21 |
1.25 |
1.29 |
1.20 |
1.21 |
1.18 |
1.20 |
| 1.32 |
1.34 |
1.24 |
1.26 |
1.23 |
1.22 |
1.20 |
1.31 |
1.16 |
1.10 |
| 1.09 |
1.26 |
1.18 |
1.14 |
1.32 |
1.24 |
1.31 |
1.43 |
1.11 |
1.37 |
| 1.23 |
1.34 |
1.23 |
1.15 |
1.34 |
1.21 |
1.24 |
1.23 |
1.23 |
1.35 |
| 1.28 |
1.39 |
1.32 |
1.18 |
1.31 |
1.23 |
1.25 |
1.56 |
1.26 |
1.36 |
| 1.11 |
1.42 |
1.34 |
1.23 |
1.29 |
1.20 |
1.36 |
1.23 |
1.24 |
1.39 |
| 1.15 |
1.51 |
1.31 |
1.25 |
1.26 |
1.25 |
1.25 |
1.28 |
1.29 |
1.20 |
| 1.18 |
1.21 |
1.21 |
1.25 |
1.26 |
1.23 |
1.31 |
1.09 |
1.24 |
1.19 |
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