encyclopedia of statistics (gerald diaz)

[...]... with the single exception of the levels of the independent variable Sample Surveys Sample surveys involve the selection and study of a sample of items from a population A sample is just a set of members chosen from a population, but not the whole population A survey of a whole population is called a census Examples of sample surveys: Phoning the fifth person on every page of the local phonebook and... Geometric Mean is calculated by taking the nth root of the product of a series of data For example, if the series of data was: 1,2,3,4,5 The geometic mean would be calculated like this: Of course, if you have a large N, this can be difficult to calculate Taking advantage of two properties of the logarithm: We find that by taking the logarithmic transformation of the geometric mean, we get: Which leads us... overwhelm the estimate of scale and give a misleading description of the spread of the data Another robust estimator of scale is the "median absolute deviation", or mad As the name implies, the estimate is calculated as the median of the absolute deviation from an estimate of location Often, the median of the data is used as the estimate of location, but it is not necessary that this be so Note that if... 70 Everything else we can get from the table: Using software, we calculate the actual value of f(63) to be 1.669402, a difference of around 0.00013 Close enough for our purposes Different Types of Data Data are assignments of values onto observations of events and objects They can be classified by their coding properties and the characteristics of their domains and their ranges Identifying data type... actual mathematical manipulation of the data and deriving results Summary Statistics Summary Statistics The most simple example of statistics “in practice” is generating summary statistics Let us consider the example where we are interested in the weight of eighth graders in a school (Maybe we’re looking at the growing epidemic of child obesity in America!) Our school has 200 eighth graders so we gather... are two types of data Qualitative data Qualitative—measurement expressed not in terms of numbers, but rather by means of a natural language description In statistics it is often used interchangably with “categorical” data For example: favourite colour = “blue” height = “tall” Although we may have categories, the categories may have a structure to them When there is not a natural ordering of the categories,... be useful to express how much this number varies—after all, eighth graders come in a wide variety of shapes and sizes! In reality, we can probably reduce this set of 200 weights into at most four or five numbers that give us a firm comprehension of the data set Range of the Data The range of a sample (set of data) is simply the maximum possible difference in the data, i.e the difference between the maximum... available, which can calculate s directly at the touch of a key, there is no longer much need for such expedients, though students of statistics should be familiar with them Quartiles Quartiles The quartiles of a data set are formed by the two boundaries on either side of the median, which divide the set into four equal sections The lowest 25% of the data being found below the first quartile value,... This value is then the average of 12 and 24 resulting in 18 as the true median (which is closer to the mean of 19 2/3 The same process is then applied to the lower and upper quartiles, giving 6.5, 18, and 29 This is only an issue if the data contains an even number of elements with an even number of equally divided sections, or an odd number of elements with an odd number of equally divided sections Inter-Quartile... had an odd number of points, determining the central position was easy - it will have the same number of points before it as after it But what if our data set has an even number of points? Let’s take the same data set, but add a new number to it: {1,2,10,14,68,85,99,100} What is the median of this set? When you have an even number of points, you must determine the two central positions of the data set . are some of the many real-world examples that require the use of statistics. General Definition Statistics, in short, is the study of data. It includes descriptive statistics (the study of methods. “collection of data involving the State”. Gradually, the term came to be used to describe the collection of any sort of data. History Statistics as a subset of mathematics As one would expect, statistics. modern statistics and some practical applications of statistics. We will also lay out some of the background mathematical concepts required to begin studying statistics. Subjects in Modern Statistics