Question

Arsenic is toxic to humans, and people can be exposed to it through contaminated drinking water, food, dust, and soil. Scientists have devised an interesting new way to measure a person's level of arsenic poisoning: by examining toenail clippings. In a recent study,1 scientists measured the level of arsenic (in mg/kg) in toenail clippings of eight people who lived near a former arsenic mine in Great Britain. The following levels were recorded: 0.8, 1.9, 2.7, 3.4, 3.9, 7.1, 11.9, 26.0
Do you expect the mean or the median of these toenail arsenic levels to be larger?

Answer 1

Answer:

The mean, because the outlier values are above the mean.

Step-by-step explanation:

Mean of a data-set:

The mean of a data-set is given by the sum of all values of the data-set divided by the number of values.

Median:

The median of a data-set is the value that separates the lower 50% from the upper 50% of the sorted set.

0.8, 1.9, 2.7, 3.4, 3.9, 7.1, 11.9, 26.0

Finding the median, since it is easier.

8 values, the median is the mean between the 4th and the 5th values. (3.4+3.9)/2 = 3.65

The values below the median are quite close to it, while those above it are considerably more distant, considered outliers, which means that we should expect the mean to be larger than the median.