General Question

jessiecakes's avatar

How to understand this Standard Deviation question?

Asked by jessiecakes (24points) April 19th, 2011

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

BhacSsylan's avatar

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.

Mariah's avatar

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.

roundsquare's avatar

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

gasman's avatar

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.

Hobbes's avatar

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 =[

BhacSsylan's avatar

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

@Hobbes Oy, good luck with that.

crisw's avatar


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.

gasman's avatar

@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.

gasman's avatar

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

BhacSsylan's avatar

@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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