Discuss why Most parametric statistics require that the variables being studied are normally distributed.

Most parametric statistics require that the variables being studied are normally distributed. The normal curve has a symmetrical or equal distribution of scores around the mean with a small number of outliers in the two tails. The first step to determining normality is to create a frequency distribution of the variable(s) being studied. A frequency distribution can be displayed in a table or figure. A line graph figure can be created whereby the axis consists of the possible values of that variable, and the axis is the tally of each value. The frequency distributions presented in this Exercise focus on values of continuous variables. With a continuous variable, higher numbers represent more of that variable and the lower numbers represent less of that variable, or vice versa. Common examples of continuous variables are age, income, blood pressure, weight, height, pain levels, and health status (see ).The frequency distribution of a variable can be presented in a which is a way of organizing the data by listing every possible value in the first column of numbers, and the frequency (tally) of each value as the second column of numbers. For example, consider the following hypothetical age data for patients from a primary care clinic. The ages of 20 patients were: 45, 26, 59, 51, 42, 28, 26, 32, 31, 55, 43, 47, 67, 39, 52, 48, 36, 42, 61, and 57.First, we must sort the patients\’ ages from lowest to highest values:Next, each age value is tallied to create the frequency. This is an example of an ungrouped frequency distribution. In an , researchers list all categories of the variable on which they have data and tally each datum on the listing. In this example, all the different ages of the 20 patients are listed and then tallied for each age.Because most of the ages in this dataset have frequencies of “1,” it is better to group the ages into ranges of values. These ranges must be mutually exclusive (i.e., a patient\’s age can only be classified into one of the ranges). In addition, the ranges must be exhaustive, meaning that each patient\’s age will fit into at least one of the categories. For example, we may choose to have ranges of 10, so that the age ranges are 20 to 29, 30 to 39, 40 to 49, 50 to 59, and 60 to 69. We may choose to have ranges of 5, so that the age ranges are 20 to 24, 25 to 29, 30 to 34, etc. The grouping should be devised to provide the greatest possible meaning to the purpose of the study. If the data are to be compared with data in other studies, groupings should be similar to those of other studies in this field of research. Classifying data into groups results in the development of a grouped frequency distribution. presents a grouped frequency distribution of patient ages classified by ranges of 10 years. Note that the range starts at “20” because there are no patient ages lower than 20, nor are there ages higher than 69. also includes percentages of patients with an age in each range; the cumulative percentages for the sample should add up to 100%. This table provides an example of a percentage distribution that indicates the percentage of the sample with scores falling into a specific group. Percentage distributions are particularly useful in comparing this study\’s data with results from other studies.As discussed earlier, frequency distributions can be presented in figures. The common figures used to present frequencies include graphs, charts, histograms, and frequency polygons. is a line graph of the frequency distribution for age ranges, where the axis represents the different age ranges and the axis represents the frequencies (tallies) of patients with ages in each of the ranges.