Pollyanna's third book 'A Brush With Wildlife' tells the story of the wildlife sanctuary which Pollyanna ran from her home for fifteen years.
This limited edition was published to commemorate the release of the book 'On Top of the World', and features a mother polar bear leading her young cub through the arctic ice. This lavishly illustrated book, tells the remarkable story of Pollyanna's unique journey into China to study and paint the giant panda. A model of a frequency distribution is an algebraic expression describing the relative frequency (height of the curve) for every possible score. The belief that a few algebraic expressions can adequately model a large number of very different real world phenomena underlies much statistical thought.
In almost all cases in the social sciences, it is not feasible to collect data on the entire population in which the researcher is interested. For example, suppose that the distribution of shoe sizes collected from a sample of fifteen individuals resulted in the following relative frequency polygon. Because there are no individuals in the sample who wear size eight shoes, does that mean that the store owner should not stock the shelves with any size eight shoes?
The alternative is a model of the frequency distribution, sometimes called a probability model or probability distribution. The probability model attempts to capture the essential structure of the real world by asking what the world might look like if an infinite number of scores were obtained and each score was measured infinitely precisely. The statistician has at his or her disposal a number of probability models to describe the world.
If the uniform distribution was used to model shoe size, it would mean that between the two extremes, each shoe size would be equally likely. The negative exponential distribution is often used to model real world events which are relatively rare, such as the occurrence of earthquakes.

It may be useful for describing some real world phenomena, but exactly what that would be is not known for sure. In order for an algebraic expression to qualify as a legitimate model of a distribution, the total area under the curve must be equal to one.
Although probability is a common term in the natural language, meaning likelihood or chance of occurrence, statisticians define it much more precisely. Hey friends – Remember how Bekah went to The Host signing in Philadelphia and reported back on how great Stephenie looked and how cute Max and Jake were (cause, hello!) and then remember how we both chatted about seeing The Host in prescreenings? Lavishly illustrated with sketches, paintings and photographs on every page, it tells the heart-warming, amusing and inspirational stories of many of the birds and animals cared for by Pollyanna and her team of helpers. It will enchant art and nature lovers alike while providing an insight into the an area of the world which is shrouded in mystery.
Lavishly illustrated with sketches, paintings and photographs on every page, it tells the heart-warming, amusing and inspirational stories of many of the birds and animals cared for by Pollyanna. The questions that sometimes come to the mind of the student is "What is the advantage of this level of abstraction? For instance, the individual opening a shoe store might want to know the shoe sizes of all persons living within a certain distance from the store, but not be able to collect all the data. If a different sample was taken, would an individual who wore a size eight likely be included? If the store owner was ordering shoes, it would mean that an equal number of each shoe size would be ordered. It is very important in the social sciences and will be described in detail in the next chapter. Recalling from the chapter on models, parameters are variables within the model that must be set before the model is completely specified.

This property is necessary for the same reason that the sum of the relative frequencies of a sample frequency table was equal to one. The probability of an event is the theoretical relative frequency of the event in a model of the population. That is, every score on the continuum of scores is possible, or there are an infinite number of scores.
If data from a subset or sample of the population of interest is used rather than the entire population, then repeating the data collection procedure would most likely result in a different set of numbers. Because the answer to both of the above questions is yes, some method of ordering shoes other than directly from the sample distribution must be used. However, a probability model often describes the world well enough to be useful in making decisions.
In most cases this would be a very poor model of the real world, because at the end of the year a large number of large or small shoe sizes would remain on the shelves and the middle sizes would be sold out. This property must hold true no matter what values are selected for the parameters of the model. The use of parameters allows a single general purpose model to describe a wide variety of real world phenomena. Then once you’ve recovered from fainting after Max says your name send us your pictures and your experiences!

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