Arnold Williams (notebuyer) wrote,
Arnold Williams

Living with Statistics

There were media reports about the average cost of cell phone minutes, heavily covered this week. Example 1. Example 2.

The hard part? The figure: $3.02/minute. Answer these questions for yourself:

1. What is the rate you pay?
2. Of your friends, who pays more than $1/minute?

Based on your answers to these two questions, you should have an element of doubt about the stories linked to above.

Now think about going to the source of the stories.

Not ready to walk through the 87 page report on your own? Think about taking a guide with you. You've got three stories: the two newspaper articles referred to above, and the "guide" referred to in this paragraph. Use them as a way to read the report.

Oh, and one other thing you'll need: an idea of the problems that arithmetic means have -- the most important of which is the "outlier problem" illustrated this way: if the values are (1, 2, 2, 2, 3, 9), the arithmetic mean is 3.1666, and five of the six values are LOWER than the mean. The mode (the most frequent value) is 2, a better representation of the set. The median is 2, again, a better guess at what the sample looks like than the average.

The method described in the report is not to take the total dollars and divide by the number of minutes (that's lower, so would not serve the purpose of the creators of this study), but to take the amount of each bill and divide by the minutes used and take the arithmetic mean of the result. Not a robust result, but a splashy one. After all, it got picked up by the papers (and by the reporters who wrote on it, all of whom could have asked themselves the two questions we started with).

Take a moment and do the math using the guide above. You'll feel better about how you understand the story.
Tags: statistics

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