You are part of a school and have to report the results of standardized test scores. Which measure of central tendency would you use? Assume that you don't know how your students will perform; so consider the general effects of outliers on the three measures of central tendency. Research and summarize the general effects that outliers have on each of the measures of central tendency. Then, using some real values, provide an example of how the three measures of central tendency vary due to outlier effects.
Mean, functioning as a fulcrum, is most effected by outliers.
When reporting standardized test scores for a school, it is crucial to understand the measures of central tendency and how outliers can impact them. The three common measures used are the mean, median, and mode.
The mean is the sum of all the values divided by the total number of values. It is sensitive to outliers since it takes into account the magnitude of each data point. Outliers, which are extreme values far from the rest of the data, can disproportionately impact the mean. Even a single outlier can greatly skew the mean towards that extreme value.
The median is the middle value in a dataset when it is arranged in ascending or descending order. It is less sensitive to outliers as it only considers the position of the data points rather than their magnitude. A few outliers often do not significantly affect the median, especially if they are far away from the majority of the data.
The mode is the value that appears most frequently in a dataset. It is least affected by outliers as it looks for the highest frequency rather than the values themselves. Outliers typically have minimal impact on the mode unless they occur frequently and affect the most common value.
Here's an example to illustrate the impact of outliers on these measures. Let's say we have the following test scores for a class of 10 students: 75, 80, 85, 88, 88, 90, 92, 98, 100, 100. The mean of this dataset is 89.6, the median is 88.5, and the mode is 88.
Now, let's introduce an outlier into the dataset. If we add a score of 50 to the list, the new dataset becomes: 50, 75, 80, 85, 88, 88, 90, 92, 98, 100, 100. The mean drops to 85.4, the median remains at 88.5, and the mode is still 88. As you can see, the mean is drastically affected by the outlier, while the median and mode remain relatively stable.
When reporting standardized test scores, it is essential to consider the effects of outliers on the measures of central tendency. To accurately represent the overall performance, it may be wise to report multiple measures, such as the mean and median, or even provide a visual representation like a box plot to show the distribution of scores.