Question

Summary of Descriptive Statistics Excel will tabulate a summary of the descriptive statistics for central tendency and using the Data Analysis Pack. Click Data Click Data Analysis .In the pop-up list click on Descriptive Statistics and hit OK . In the pop-up box in the input range type A2:A75 or highlight this region . Click the box next to summary statistics Click OK A box of summary statistics will appear like the one below Mean Standard Error Median Mode Standard Deviation Sample Variance Kurtosis Skewness Range Minimum Maximum Sum Count 134.8108 1.203271 136.5 129 10.35093 107.1418 1.00612 0.043921 41 116 157 9976 74 HOW DOES CENTRAL TENDENCY AND DISPERSION CHANGE IN THE PRESENC OUTLIERS? 4 of 4 HOW DOES CENTRAL TENDENCY AND DISPERSION CHANGE IN THE PRE OUTLIERS? To investigate how an outlier, defined as a value much different than the maj a sample, can affect measures of central tendency and dispersion, let's add a widths in our data set. Go back to sheet 1 and in cell A76 type the value 100 summary statistics as before. 1. Click Data 2. Click Data Analysis 3. In the pop-up list click on Descriptive Statistics and hit OK 4. In the pop-up box in the input range type a2:a76 or highlight this regi 5. Click the box next to summary statistics 6. Click OK You should get summary statistics that look like: Mean Standard Ero115 Median Mode 146.3466667 11.5967764 137 140 100,4310296 Sample Variance 10086.39171 73.37235654 8.520824393 884 116 1000 10976 75 Range Sum Notice the mean and mode are much different but the median does not chang property of the central tendencies that the mean is affected by outliers but th not Notice that the standard error is also highly affected by the outlier. This the standard error Summary of Descriptive Statistics Excel will tabulate a summary of the descriptive statistics for central tendency and using the Data Analysis Pack. Click Data Click Data Analysis .In the pop-up list click on Descriptive Statistics and hit OK . In the pop-up box in the input range type A2:A75 or highlight this region . Click the box next to summary statistics Click OK A box of summary statistics will appear like the one below Mean Standard Error Median Mode Standard Deviation Sample Variance Kurtosis Skewness Range Minimum Maximum Sum Count 134.8108 1.203271 136.5 129 10.35093 107.1418 1.00612 0.043921 41 116 157 9976 74 HOW DOES CENTRAL TENDENCY AND DISPERSION CHANGE IN THE PRESENC OUTLIERS?

Answer 1

Answer

We know that mean and mode are dependent on entire data set and the median is only dependent on the middle value of the data. So, in case of outlier, only mean and mode will change and median will remain same.

In this case, mean and mode are increased due to the presence of outlier and median is same (just a 0.5 point variation due to the total number of data values which is changed from 74 to 75)

Dispersion or standard error is measures the difference between the each individual value and mean value. It is clear that the mean is changed, so there will be an increase in the dispersion or standard error because the sum of squared deviation is increased due to increase in mean.

Therefore, mean, mode and dispersion will increase in presence of outlier, but median will remain same.