You are a manager working for an insurance company. Your job entails processing
ID: 2705441 • Letter: Y
Question
You are a manager working for an insurance company. Your job entails processing individual claims filed by policyholders. In general, few claims are expensive. Each quarter, you compile a report summarizing key claim statistics, such as the number of claims submitted, the average cost per claim, and the total cost of submitted claims. In the last quarter's report, you notice a large difference between the mean and the median claim cost, the mean cost being much higher than the median cost. What do you attribute this difference to? Do you think the claims data is normally distributed? If so, why? If not, what distribution might best describe the data and why? Given the large difference between the two measures of central tendency, which of the two would you rely on in describing the average claim cost and why?
Explanation / Answer
Solution : Problem is : a large difference between the mean and the median claim cost, the mean cost being much higher than the median cost. (i) The larger difference between Mean and median cost is due to Existence of very "FEW" Data points or very few cases with much larger value than most of other values. (ii) No data is not normally distributed. because in normal distribution, median is equal to mean (Since it is a symmetric distribution), but here the mean is larger than medain. (iii) As larger difference in mean and median is seen so lognormal distriibution is a good fit, because it is a skewed distribution with mean > median. (iv) Median is a better measure because the larger valued samples (when they are less). have the potential to disrupt the nature. These values are like outliers, whose effects on the actual data should be minimized. Hence, mean which gives equal weightage to all the data points is not a good measure.
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