Question

Suppose that in a small town of 50 people, one person earns $5,000,000 per year and the other 49 each earn $30,000. Which is the better measure of the "center": the mean or the median?

Answer 1

The median is a better measure of the center than the mean in this scenario because it is not affected by extreme values.

Step-by-step explanation:

The median is a better measure of the center than the mean in this scenario. This is because the mean can be heavily influenced by extreme values, such as the person who earns $5,000,000 per year in this case. Since there is a significant difference between this outlier and the other values, the mean would be skewed towards the higher end.

On the other hand, the median is not affected by extreme values, so it gives a more accurate representation of the center of the data. In this case, the median is $30,000, which is the income earned by 49 people, making it a better measure of the center.

Answer 2

The median is the better measure of the "center" in this scenario.

Step-by-step explanation:

In this small town with 50 residents, the mean and median are two statistical measures that provide insights into the central tendency of income distribution. The mean, or average, is calculated by summing up all incomes and dividing by the number of people. In this case, the mean income would be calculated as:

[ text{Mean} = frac{Sigma text{Income}}{text{Number of People}} ]

Substituting the values, we get:

[ text{Mean} = frac{(1 times 5,000,000) + (49 times 30,000)}{50} ]

After calculating, the mean income turns out to be $125,800. While the mean provides a single numerical representation of income, it can be heavily influenced by extreme values, such as the $5,000,000 income in this case. This extreme value significantly skews the mean higher than the majority of incomes.

On the other hand, the median is the middle value when all incomes are arranged in ascending order. In this scenario, the median income would be $30,000, as it falls right in the middle when the incomes are sorted. The median is less sensitive to extreme values and provides a better representation of the typical income in the town. Therefore, in situations with skewed distributions like this, the median is a more reliable measure of central tendency.