 # One of the main concerns in the field of statistics

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One of the main concerns in the field of statistics is how accurately a statistic estimates a parameter. The accuracy reallydepends on how well the sample represents the population. The sample must contain the characteristics of the populationin order to be arepresentative sample. We are interested in both the sample statistic and the population parameter ininferential statistics. In a later chapter, we will use the sample statistic to test the validity of the established populationparameter.Avariable, or random variable, notated by capital letters such asXandY, is a characteristic of interest for each person orthing in a population. Variables may benumericalorcategorical.Numerical variablestake on values with equal unitssuch as weight in pounds and time in hours.Categorical variablesplace the person or thing into a category. If we letXequal the number of points earned by one math student at the end of a term, thenXis a numerical variable. If we letYbea person's party affiliation, then some examples ofYinclude Republican, Democrat, and Independent.Yis a categoricalvariable. We could do some math with values ofX(calculate the average number of points earned, for example), but itmakes no sense to do math with values ofY(calculating an average party affiliation makes no sense).Dataare the actual values of the variable. They may be numbers or they may be words.Datumis a single value.Two words that come up often in statistics aremeanandproportion. If you were to take three exams in your math classesand obtain scores of 86, 75, and 92, you would calculate your mean score by adding the three exam scores and dividing bythree (your mean score would be 84.3 to one decimal place). If, in your math class, there are 40 students and 22 are men4Chapter 1 | Sampling and DataThis OpenStax book is available for free at
and 18 are women, then the proportion of men students is2240and the proportion of women students is1840. Mean andproportion are discussed in more detail in later chapters.NOTEThe words "mean" and "average" are often used interchangeably. The substitution of one word for the other iscommon practice. The technical term is "arithmetic mean," and "average" is technically a center location. However, inpractice among non-statisticians, "average" is commonly accepted for "arithmetic mean."

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Introductory Statistics
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