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INTRODUCTION TO STATISTICS THROUGH RESAMPLING METHODS AND MICROSOFT OFFICE EXCEL phần 3

Tập thể dục 1,15. Có nghĩa là tổng của độ lệch của các quan sát từ số học của họ là gì? Điều đó có nghĩa là, những gìVấn đề với việc sử dụng phương sai rằng nếu quan sát của chúng tôi, vào nhiệt độ ví dụ, trong độ C, sau đó phương sai sẽ được thể hiện ở các mức độ vuông, bất cứ điều gì đây là những. | CHAPTER 1 VARIATION OR WHAT STATISTICS IS ALL ABOUT 35 Exercise 1.15. What is the sum of the deviations of the observations from their arithmetic mean That is what is  -1 X - Xi. The problem with using the variance is that if our observations on temperature for example are in degrees Celsius then the variance would be expressed in square degrees whatever these are. More often we report the standard deviation Ơ the square root of the variance as it is in the same units as our observations. Reporting the standard deviation has the further value that if our observations come from a normal distribution like that depicted in Fig. 1.29 then we know that the probability is 68 that an observation taken from such a population lies within plus or minus one standard deviation of the population mean. If we have two samples and aren t sure whether they come from the same population one way to check is to express the difference in the sample means the between-sample variation in terms of the within-sample variation or standard deviation. We ll investigate this approach in Chapter 3. If the observations do not come from a normal distribution then the standard deviation is less valuable. In such a case we might want to report as a measure of dispersion the sample range. which is just the maximum minus the minimum or the interquartile range which is the distance between the 75th and 25th percentiles. From a boxplot of our data we FIGURE 1.29 Bell-shaped symmetric curve of a normally distributed population. 36 STATISTICS THROUGH RESAMPLING METHODS AND MICROSOFT OFFICE EXCEL can get eyeball estimates of the range as the distance from whisker end to whisker end and the interquartile range which is the length of the box. Of course to obtain exact values we would use R s quantile function. Exercise 1.16. What are the variance standard deviation and interquartile range of the classroom data What are the 90th and 5th percentiles This next exercise is only for those familiar with .