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| represent the simplest level of measurement. Objects are usually placed into mutually exclusive categories or types, and there is often no necessary quantitative or statistical meaning to numbers assigned to these categories, except as a convenience in distinguishing groups. |
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| contain all the properties of nominal variables, but they also enable the placement of objects into ranks, that is, highest to lowest. |
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| contain all the elements of nominal and ordinal data and also assume equal distance between objects on a scale. It not only provides a ranking of objects, but also reflects equal intervals or a standard unit between scale scores. (body temps) |
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not only assume the interval quality of data, but they also have a
fixed meaningful zero point. Such data enable one to show how many times greater one value is
than another. Some examples of ratio variables are variables such as age, weight, income, education,
number of children, and frequency of crime commission. |
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| How to Calculate Relative & Absolute Error |
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Relative error is a number that compares how incorrect a quantity is from a number considered to be true. Unlike absolute error, where the error has the units of what is being measured, relative error is expressed as a percentage, defined as the absolute error divided by the true value.
1) To begin, a measurement has to take place: counting the money in a coin jar, measuring the length of a desk, so on and so forth. After determining what needs to be measured, the tool has to be determined. For counting coins, there is no real tool needed, but for measurements of length or temperature, then a tool is required. For example, to measure the long side of a sheet of letter paper, a ruler is used to measure the length. The measurement shows the paper length is 11.25 inches.
2)Error is a comparison between the measured value and true value. For the example, a sheet of letter paper is 8.5 inches times 11 inches. So the long side is 11 inches.
3)To compute the absolute error, the difference between measurement and the real value is taken. The example continues by the determination of the absolute error of .125 inches in the measurement.
4) The relative error is then computed by dividing the absolute error by the true value. In the example, .125inches/11inches yields a relative error of ~.011364.
5) To convert to percentage, multiply by 100. The relative error in the measurement in percent is 1.1364 percent. |
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Mean, median, and mode are three kinds of "averages". There are many "averages" in statistics, but these are, I think, the three most common, and are certainly the three you are most likely to encounter in your pre-statistics courses, if the topic comes up at all.
The "mean" is the "average" you're used to, where you add up all the numbers and then divide by the number of numbers. The "median" is the "middle" value in the list of numbers. To find the median, your numbers have to be listed in numerical order, so you may have to rewrite your list first. The "mode" is the value that occurs most often. If no number is repeated, then there is no mode for the list. |
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| The "range" is just the difference between the largest and smallest values. |
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| How to Find the Standard Deviation |
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After finding an average, sometimes it's helpful to find the way other numbers and results are distributed around that average. We use the standard deviation to measure the size of that distribution. This calculation comes in handy for determining grades, results of case studies, and many other real-life applications.
1) First, find the average of your set of numbers. This can be done by adding all your numbers together, and dividing the sum by the number of values. For example, if you had 4 numbers in your list, you would divide the sum of all numbers by 4.
2) Next, subtract the average from each number in the original list. These new values are called 'deviations from the average'.
3) To find the standard deviation, we are going to use the process called R.M.S., or root-mean-square. To start this process, square all of the deviations individually.
4) After each value has been squared, add all the new values together.
5) Divide the sum by the amount of numbers in the original list.
6) Take the square root of this number, and this will be your standard deviation value. |
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A histogram is "a representation of a frequency distribution by means of rectangles whose widths represent class intervals and whose areas are proportional to the corresponding frequencies."
Sounds complicated . . . but the concept really is pretty simple. We graph groups of numbers according to how often they appear. Thus if we have the set {1,2,2,3,3,3,3,4,4,5,6}, we can graph them like this:
This graph is pretty easy to make and gives us some useful data about the set. For example, the graph peaks at 3, which is also the median and the mode of the set. The mean of the set is 3.27—also not far from the peak. The shape of the graph gives us an idea of how the numbers in the set are distributed about the mean; the distribution of this graph is wide compared to size of the peak, indicating that values in the set are only loosely bunched around the mean. |
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