Question

commuting justine asked all of her co - workers for the distance they commute to work. the commute (in miles): 5.4, 8.1, 0.5, 10.3, 6.7, 7.2, 9.5, 6.3, 7.8, 5.9, 0.2, 6.4, 7.1, 7.5, 5.7. which measure of center best describes the data? mean only median only mean and median median and mode

Explanation:

Step1: Check for outliers

The data set is \(5.4,8.1,0.5,10.3,6.7,7.2,9.5,6.3,7.8,5.9,0.2,6.4,7.1,7.5,5.7\). The values \(0.2\) and \(0.5\) and \(10.3\) are relatively extreme compared to the rest.

Step2: Recall effect of outliers

The mean is affected by outliers. Since we have outliers in the data - set, the mean will be pulled in the direction of the outliers. The median is the middle - value when the data is arranged in ascending or descending order and is not affected by outliers.

Step3: Determine the best measure

Since the data has outliers, the median is a better measure of central tendency than the mean. There is no mode (no value repeats more frequently than others). So the best measure of center is the median only.

Answer:

Median only