Need response done for MAT 232 Statisical Literacy need to be 2 seperate answers details below:
You may read in the newspaper that a study of a new drug for cancer “increased survival by an average of eight weeks.” It turns out that this is a median, and it is used for complicated statistical reasons. But in a perfect world, would you prefer to know the increase in mean or median survival?
In a case such as this, I would prefer to know the increase in mean versus median. Our textbook describes the mean as “what most people think of as the average….it represents the balance point for a quantitative data distribution” (Bennett, Briggs & Triola, 2014, p.120). If the increased survival average of eight weeks is a median, then for a medical drug, this just provides a middle ground. For example, if this new drug tested increased survival on the average eight weeks, this means there were some that tested longer, possibly 12-16 weeks and some 1-4 weeks. I would prefer to know the mean. In other words, of all the patients tested, what was the average increase in survival rate? This would paint a clearer picture of what type of results a patient can expect.
In the concept of buying a house, the median would give you the middle price range of houses in a neighborhood whereas the mean could be very offset if the data is non-symmetrical. My brother built a nice home worth about $185,000 but the houses around him are valued at $85,000. In this case, the median and mean are not identical.
If the median house price is $1.9m, does that necessarily mean that half of the houses on the block are worth less than $1.9m and half worth more? How do ties figure in?
In summary, the mean would be the total sum of all numbers that is bothered by outliers. The median is the middle of the numbers, but is not disturbed by outliers. The median and mean gives an idea of a common outlook in a given set of data, but they are different. Median can make house prices seem way higher than what it actually is. If the numbers are something common or normal, then mean can be used, but if there are numbers that have huge differences, then the median will help give a better reality of what you are looking for. If the median price for a home is $1.9 million, then someone would think that half of the houses costs less than $1.9 million and the others cost more than that.
If my neighbor sold his house and wanted double for it, the mean would go up, but the median would not. This is because half the homes are still priced at more than $1.9 million. The situation changes because currently, one of the homes now is prices at way more than $1.9 million.
Mean can be a problem because one or two homes can raise the mean value dramatically, which means that it is not the true representation of the average house price, which is why mean should be used because it would not count the couple of house that are extremely expensive. The couple of extremely expensive houses are known as the outliers.