Discuss the considerations that determine the selection of a suitable average. Explain with the help of suitable examples.
Answers
Answer:
Model selection is the task of selecting a statistical model from a set of candidate models, given data. In the simplest cases, a pre-existing set of data is considered. However, the task can also involve the design of experiments such that the data collected is well-suited to the problem of model selection. Given candidate models of similar predictive or explanatory power, the simplest model is most likely to be the best choice (Occam's razor).
Answer:
The average is a simple term with several meanings. The type of average to use depends on whether you’re adding, multiplying, grouping or dividing work among the items in your set.
Quick quiz: You drove to work at 30 mph, and drove back at 60 mph. What was your average speed?
Hint: It’s not 45 mph, and it doesn’t matter how far your commute is. Read on to understand the many uses of this statistical tool.
Explanation:
But What Does It Mean?
Let’s step back a bit: what is the “average” all about?
To most of us, it’s “the number in the middle” or a number that is “balanced”. I’m a fan of taking multipleviewpoints, so here’s another interpretation of the average:
The average is the value that can replace every existing item, and have the same result. If I could throw away my data and replace it with one “average” value, what would it be?
One goal of the average is to understand a data set by getting a “representative” sample. But the calculation depends on how the items in the group interact. Let’s take a look.
The Arithmetic Mean
The arithmetic mean is the most common type of average:
\displaystyle{\text{average} = \frac{\text{sum}}{\text{number}}}
Arithmetic mean
Let’s say you weigh 150 lbs, and are in an elevator with a 100lb kid and 350lb walrus. What’s the average weight?
The real question is “If you replaced this merry group with 3 identical people and want the same load in the elevator, what should each clone weigh?”
In this case, we’d swap in three people weighing 200 lbs each [(150 + 100 + 350)/3], and nobody would be the wiser.
Pros:
It works well for lists that are simply combined (added) together.
Easy to calculate: just add and divide.
It’s intuitive — it’s the number “in the middle”, pulled up by large values and brought down by smaller ones.
Cons:
The average can be skewed by outliers — it doesn’t deal well with wildly varying samples. The average of 100, 200 and -300 is 0, which is misleading.
The arithmetic mean works great 80% of the time; many quantities are added together. Unfortunately, there’s always those 20% of situations where the average doesn’t quite fit.