You are a manager working for an insurance company. Your job entails processing
ID: 3268987 • 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.
Draw a conclusion as to why you might be observing this difference in the data.
Evaluate whether this information might be useful for determining if the claims data is normally distributed.
If you conclude that the data is likely normally distributed, explain why. If not, suggest another distribution that might best describe the data. Explain why this distribution would be a more accurate representation of the data.
Given the large difference between the two measures of central tendency, which of the two measures would you rely on in describing the average claim cost and why? Support your discussion with relevant examples, research, and rationale.
Explanation / Answer
solution:
This difference occurs because there are a few data points (important word is FEW) whose values are much larger than most of the values.
No data is not normally distributed. because in normal distribution, median is equal to mean (Since it is a symmetric distribution)
I believe lognormal distriibution is a good fit, because it is a skewed distribution with mean > median
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.
examples
NORMAL: Company inventory, Company sales figure, Company revenue
Not Normal: 1. Sale price 2. Shares price of the company. 3. profits over the year.
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