Solved – Interpretation of mean in this example

meanstandard deviation

I recently presented a national test and the company in charge of preparing the test then does a standardization to provide the final scores for each person. These are the values they gave at the end of the page where the grades were posted:

N = 259
Mean = 72
StdDev = 7

I don't remember anything about this, and my career doesn't deal with any of this. I want to know how can I interpret these results with those values.

  • What does it mean that the mean was 72?
  • What does it mean that the standard deviation value is 7?
  • What does it mean if, for example, I obtained an 88 or a 78 on the test?

Best Answer

They had a test. The results of that test were 259 measurements. When they average those measurements, the value they come up with is 72. When they compute the standard deviation using the data and the mean, the number they came up with is 7. So far, this is nearly uninformative.

Mean is meant "measure of central tendency". If you are going to bet, and you want to win, if you bet on the average value, then most likely you are going to do better than you would picking any other value.

Standard deviation is a "measure of dispersive tendency". It is how wide a range the values span. It is the "turning radius" of the data - does it take 300 miles, or 1 inch. A smaller stdev means the variation is small. A large stdev means the variation is large.

But there are a lot of assumptions here, and they aren't stated. If the tests was mean body weight between Sudan vs. USA then you are going to get two "bunches" (aka modes) where the average person in the US is much heavier than the average person in Sudan. In that case, guessing the mean is going to be uninformative - you wouldn't want to bet on that. You would want to bet on the means of each of the "bunches". These results don't tell you that.

The sample size isn't bad. More samples means less error in the estimates of "true mean" and "true stdev" using the data. If you only have 1 sample, what if it was a dud? How good of a mean could you get from it? Having many samples can help keep you from really bad results. It doesn't guarantee good results, but it helps.

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