Tham khảo tài liệu 'data analysis and presentation skills part 6', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | DESCRIPTIVE STATISTICS 83 Figure Descriptive Statistics functions in Excel true population mean. The equation for the standard error may be seen in Equation standard deviation SEM Equation H number in sample If we wanted to check that the value of the standard error calculated in the Descriptive Statistics function was correct then we would insert the following formula into a cell on the spreadsheet using the data from Group 1 as an example SQRT 9 84 4 PRELIMINARY DATA ANALYSIS Group 1 Group 2 Mean Mean Standard Error Standard Error Median Median Mode 9 Mode Standard Deviation 3694966546 Standard Deviation 1 833333 Sample Variance Sample Variance Kurtosis Kurtosis Skewness Skewness Range 125 Range Minimum Minimum 7 Maximum 20 Maximum Sum 95 Sum Count 9 Count 9 Figure Descriptive Statistics for the television viewing data where is the standard deviation of the sample for which there were nine observations so it could be calculated by STDEV range of values in sample SQRT number in sample When presenting graphs showing mean values it is usually expected that error bars are included by using either the standard deviation values to demonstrate the variability in the sample or the standard error to demonstrate the deviation of the sample from the true population mean. Kurtosis and skewness Values for kurtosis and skewness are also produced by the Descriptive Statistics function. These are used to characterize the data relative to a normal distribution. Skewness is a measure of data are symmetrical about the mean the skewness would be expected to have a value of around 0. If data are skewed to the left or right then the centre of the data is not around the mean and so a negative or positive value for skewness would be obtained. Skewed distributions are further discussed in section . Kurtosis .
