No doubt, every day we are exposed to statistics. They influence nearly every as

Question

No doubt, every day we are exposed to statistics. They influence nearly every aspect of our lives. Unfortunately, often times the statistics presented to us are incomplete, misleading, or difficult to interpret meaningfully. For example, in the MATH110 course that many of you may have completed, you were asked to compute the cost per mile of operating your vehicle. Naturally, that statistic is dependent on a number of factors including your car payment, maintenance costs, miles driven, etc. The important thing to keep in mind when using that statistic is that there may be situations in which it would be completely misleading to compare Person A's cost per mile with Person B's cost per mile. For example, suppose Person A has a monthly car payment of $350 while Person B has no car payment at all. No doubt, all other things being equal, Person A's cost per mile would be higher than Person B's, because of the monthly car payment that Person A has each month. Clearly, in this case, comparing the cost per mile of Person A with that of Person B would be inappropriate.

As a second example, we often encounter situations in which advertisers claim, for example, "You can save 15% by switching to company C." But, in such situations no reference is established and the question that remains unanswered is: Save 15% compared to what? Statistics play a role in nearly every thing that we encounter during our daily lives. They help determine what we eat, what we watch on TV, who we vote for, what colors are used in the fabrics our clothes are made from, what music we hear, and what movies make it to the big screen. But, there are times when statistics can be misleading or incomplete.

Please share with us a statistic that you feel is misleading or confusing. Be sure to clearly define the statistic you have identified and clearly articulate why you find it to be misleading or confusing

Explanation / Answer

EXAMPLE OF A STASTISTIC THAT IS MISLEADING OR CONFUSING:

Step 1:

Definition of the statistic identified:
Measure of Central Tendency - Application of Arithmetic Mean

Step 2:

How Arithmetic Mean can be misleading or confusing in certain situations:

It is well known that Arithmetic Mean is used generally in all situations as a measure of Central Tendency. But, in highly skewed distributions, Arithmetic Mean gives mesleading or confusing result. For example, suppose we are interested in the average salary of the emplyess of a particular company. As the salaries of the employees are quite varied - the lowest paid attender to the top management - taking the Arithmetic Mean will not really represent the data.

Consider the salaries of 4 employees: 10,20,30 and 1000. Here, 10, 20 and 30 are the salaries of middle level management, whereas 1000 is the salary of the top boss, which is naturally very high. Taking such Arithmetic Mean is misleading or cofusing. The remedy in this case is to apply Median of the salaries.

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