المحاضرة الثالثة 162 معتمدة (1).pdf

‫العنوان الرئيسي هنا‬ ‫العنوان الفرعي هنا‬ ‫عنوان فرعي او تاريخ‬  3-1 Measures of Centre p. 77 Key Concept: The focus of this section is to obtain a value that measures the centre of a data set. We present measures of centre, including mean and median. Our o...

‫العنوان الرئيسي هنا‬ ‫العنوان الفرعي هنا‬ ‫عنوان فرعي او تاريخ‬  3-1 Measures of Centre p. 77 Key Concept: The focus of this section is to obtain a value that measures the centre of a data set. We present measures of centre, including mean and median. Our objective here is not only to find the value of each measure of centre, but also to interpret and make sense of those values. Calculation and Notation of the Mean  Median p. 79 Important Properties of the Median The median does not change by large amounts when we include just a few extreme values, so the median is a resistant measure of center. The median does not directly use every data value. (For example, if the largest value is changed to a much larger value, the median does not change.) Mode p. 80 p. 83 p. 84  p. 89 Variation is the single most important topic in statistics, so this is the single most important section in this book. This section presents three important measures of variation: range, standard deviation, and variance. These statistics are numbers, but our focus is not just computing those numbers but developing the ability to interpret and understand them. This section is not a study of arithmetic; it is about understanding and interpreting measures of variation, especially the standard deviation  Basic Concepts of Variation To visualize the property of variation, see Figure 3-2, which illustrates pulse rates (beats per minute or BPM) for subjects given a treatment and subjects given a placebo. (A high priority is placed on using real data, but these pulse rates are fabricated for the purposes of making an important point here.) Verify this important observation: The pulse rates in the treatment group (top dotplot) have more variation than those in the placebo group (bottom dotplot). Both sets of pulse rates have the same mean of 70.2 BPM, they have the same median of 70.0 BPM, and they have the same mode of 70 BPM. Those measures of center do not “see” the difference in variation. To keep our round-off rules as consistent and as simple as possible, we will round the measures of variation using this rule  Range Important Properties of the Range The range uses only the maximum and the minimum data values, so it is very sensitive to extreme values. The range is not resistant. Because the range uses only the maximum and minimum values, it does not take every value into account and therefore does not truly reflect the variation among all of the data values Standard Deviation of a Sample  Important Properties of Standard Deviation Standard Deviation of a Population p. 94 n-1 Variance of a Sample and a Population  Comparing Variation in Different Samples or Populations p.96 it’s a good practice to compare two sample standard deviations only when the sample means are approximately the same. When comparing variation in samples or populations with very different means, it is better to use the coefficient of variation. Also use the coefficient of variation to compare variation from two samples or populations with different scales or units of values, such as the comparison of variation of pulse rates of men and heights of men. Exercices Homework Sheet #1  ‫شكراً لكم‬ Thank You