# How to understand this Standard Deviation question?

Here’s the question:

The lengths of a sample of tiger canines were measured. 68 % of the lengths fell within a range between 15 mm and 45 mm. The mean was 30 mm. What is the standard deviation of this sample?

A. 5 mm

B. 15 mm

C. 7.5 mm

D. 30 mm

I just don’t really understand how to calculate the SD if I don’t have the number of values in the sample. Thanks!

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## 10 Answers

So, this question is related to the definition of standard deviation, rather then having to calculate it. I refer you to wikipedia, which has a decent write-up. Specifically the “rules for normally distributed data”. I’m not sure what level the class is, so if the math there is too high-level, just take a good look at the plot on the right.

Here’s a hint. A certain percentage of data points in a group of data fall within 1 standard deviation of the mean, another particular percentage fall within 2 SD, etc.

Does the number 68% mean anything to you? Think hard…

Here’s an image that shows how one SD (from +1 sigma to -1 sigma) encompasses 68% of the sample in a normal distribution.

2 SD includes 95%, 3 SD covers 99.7% of the total sample, and so on—thinning out rapidly into long, sparse tails as you deviate on either side of the mean. A standard deviation of 30 centered around a mean of 30 implies a range of 15–45. It’s the width of the hump.

This question is easy because 68% is a magic number.

I’m taking an Introduction to Statistics class at the moment, so I was excited because I could answer this question, but a bunch of people beat me to it =[

@gasman Just to say, usually straight answering of a homework question is frowned upon.

@Hobbes Oy, good luck with that.

@BhacSsylan

Hey, be positive :>)

Stats was my favorite math subject *ever*! I actually used to work out stats problems for fun…

I used to teach the science fair project class for our school, and I had 7th and 8th graders doing t-tests and chi-square. The great thing about stats is that it’s *usable* in the real world. If you really understand statistics, it makes so many things more comprehensible. My favorite essay on this subject is Steven Jay Gould’s The Median Isn’t the Mesage. – it should be required reading.

@BhacSsylan Understood. I wouldn’t work a whole batch of homework problems just dumped onto the site, as often goes on at other Q&A boards. Sometimes people don’t “get” a concept, however, until they see a problem or two worked out for them, perhaps with an explanation from a fresh perspective. One-time help may be genuinely appreciated in the spirit of helpfulness. Sometimes I think Fluther’s anti-homework policy is counter-productively overzealous.

@crisw thanks for the link—Gould was one of my favorite authors.

@gasman That’s fair. And I’m also not a mod, so, you know, feel free to ignore me :-p. In general more obtuse, “here’s how you figure it out” answers are preferred. And to be fair, yours is not a direct answer, just more direct then is usually offered, so sorry if i came off more gruff then I intended. After all, my wiki link says the same thing, just a little more obtuse.

@crisw Well, yes, stats can be both extremely powerful and useful, no debating that. But you do have to have a certain mindset to be good at them. Since pure math is not my strong point, an actual stats class would tear me to shreds, probably. My stats training i got through my chemistry courses, and so while I don’t have the best training, it works for what i need to do. Makes it a little harder to relate, though :-p.

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