Question

In August 2009 , Harris Interactive released the results of the Great Schools survey, in which 1,086 parents of children attending a public or private school were asked approximately how much they had spent on school supplies over the last school year. For this sample, the mean amount spent was \(\$ 235.20\) and the median amount spent was \(\$ 150.00 .\) What does the large difference between the mean and median tell you about this data set?

Short answer

The large difference between the mean and median indicates a positive skewness in this dataset, demonstrating that some parents are spending significantly more on school supplies than others, skewing the average to be higher.

Step-by-step solution

Understanding Mean and Median

The mean is the average of all numbers in a data set while the median is the middle value when the data is organized from least to greatest. It is important to note that the mean is influenced by all values in the data set, including outliers - which are significantly larger or smaller data points compared to the rest of the data. In contrast, the median is not affected by outliers as it's the center value.

Analyzing the Difference in Mean and Median

If the mean is larger than the median, this indicates that the data is skewed to the right (positively skewed). This suggests that there are higher values or outliers in the dataset that are pulling the mean upwards.

Conclusion for this Specific Dataset

In this case, the mean amount spent (\$235.20) is significantly higher than the median (\$150.00). Therefore, it can be concluded that some parents are spending a lot more on school supplies than others, hence pulling up the mean while the median remains relatively low.