Suppose that you are the
chief of maintenance for a large metropolitan hospital.
You are trying to decide from what company to buy your
next 5-year supply of light bulbs. Would you look to the
company whose light bulbs have the greatest mean or
the greatest median life? Explain your reasoning.
greatest mean would refer to the highest average life of each light bulb, while the greatest median when looking at a 5 year supply is not as relevant, half your light bulbs would have a lifespan below the median and half would have a life span above. Compare this to all light bulbs lasting roughly the same amount of time.
What would you choose?
The mean and median are both measures of central tendency. In a normal distribution, they would be essentially the same.
However, in a skewed distribution (one tail significantly longer than the other), the mean will be greatly influenced by the deviant scores. If it is positively skewed (longer tail for the higher values), the mean would be higher than the median. The opposite is true for a negatively skewed distribution.
I hope this helps you make your decision. Thanks for asking.
When deciding from which company to buy your next 5-year supply of light bulbs, you would generally want to look at the company whose light bulbs have the greatest median life rather than the greatest mean life. Here's the reasoning behind it:
Mean and median are two measures of central tendency that provide different insights into the distribution of a set of values.
The mean is the average value calculated by summing up all the values in a dataset and dividing it by the number of values. The mean is sensitive to outliers, meaning that if there are a few light bulbs with extremely long or short lifespans, it can significantly distort the average.
On the other hand, the median is the middle value in a sorted dataset. It represents the point where exactly half of the values are below and half are above. The median is not affected by extreme values or outliers and provides a more reliable measure of central tendency when the data is skewed.
In the case of light bulbs, we are concerned about the overall lifespan of the bulbs in the company's product line. If a company's light bulbs have a few outliers with extremely long lifespans, it could significantly inflate the mean lifespan. However, since outliers are not uncommon in any manufacturing process, it is not an ideal representation of the typical light bulb's lifespan.
By looking at the median lifespan, you get a better idea of a light bulb's typical lifespan without the influence of outliers. It represents the middle value, indicating that half of the light bulbs in the company's product line have a longer lifespan and the other half have a shorter lifespan.
Therefore, when making a decision on which company to buy your next 5-year supply of light bulbs, it is advisable to look for the company whose light bulbs have the greatest median life. This will provide you with a more accurate representation of the typical lifespan of the bulbs, giving you a better indication of the overall quality and reliability of the company's products.