More often than not, when we are presented with statistics we are given only a m

Question

More often than not, when we are presented with statistics we are given only a measure of central tendency (such as a mean). However, lots of useful information can be gleaned about a dataset if we examine the variance, skew, and the kurtosis of the data as well.

Choose a statistic that recently came across your desk where you were just given a mean. If you can't think of one, come up with an example you might encounter in your life. How would knowing the variance, the skew, and/or the kurtosis of the data give you a better idea of the data? What could you do with that information?

Example: Say you are an executive in an automobile manufacturer, and you are told that, for a particular model of new car that you sell, buyers have on average 2.2 warrantee claims over the first three years of owning the car. What would additional information on the shape of your data tell you? If the variance was low, you’d know that just about every car had 2 or 3 warrantee claims, while if it was high you’d know that you have a lot of cars with no warrantee claims and a lot with more than 2.2. The skew would provide similar information; with a high level of right skew, you’d know that the average is being brought up by a few lemons; with left skew you’d know that very few of the cars have no warrantee claims. The kurtosis (thickness of the tails) would help you get an idea as to just how prevalent the lemon problem is. If you have high kurtosis, it means you have a whole bunch of lemons and a whole bunch of perfect cars. If you have low kurtosis, it means that you have few lemons but few perfect cars.

Explanation / Answer

Solution:

Sherlock Holmes has led us the two important statistical ideas such as average and variation. We know that the value of mean or average only does not explain the numerical phenomenon in detail (Brase, 2010). For explaining the phenomenon detail we need some more values of measures of central tendency or dispersion. By knowing the value of the mode for the data we get the idea about the most repeated observations. Also, by using the value of the standard deviation or the variance we understood the pattern of variation. The coefficients of skewness and Kurtosis help us to determine the nature of the overall data and its spread (Babbie, 2009). There are several examples in our life that we need to analyze and we cannot analyze these examples only help of average values but we need other values of central tendency and dispersion for understanding the numerical concept. For example, in share market we cannot judge the increment only by describing the average values but we also need the values of the variation, skewness, etc. These values will help us in understanding the nature and trend of the values related to the share market. Let us consider simple example of average height of the persons in our city. By knowing the value of the average height of the persons in our city we cannot judge overall idea but if we know the variation pattern, then we get the idea of the average height in detail. We can also consider the examples of the average mileage of the cars, average price of the gold, etc.

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