Standard Deviation in Normal Distribution (with only mean and unknown division)

normal distributionstandard deviationstatistics

My question comes when I revise the topic.
If the mean and simple information is given, how can I find the standard deviation?
i.e. For normally distributed data, let's say mean = 65, and only 5 % or the samples are >=90. How can I find the standard deviation within so lack of information. Is it possible? Thanks to anyone who can suggest and share your idea.

Best Answer

Hint:

$\Phi^{-1}(0.95)\approx 1.644854$ for a standard normal distribution
so $5\%$ of a normal distribution is more than about $1.644854$ standard deviations above the mean
and you know the mean

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[Math] Calculating mean and standard deviation of very large sample sizes

Posting as an answer in response to comments.

Here's a way to compute the mean and standard deviation in one pass over the file. (Pseudocode.)

n = r1 = r2 = 0;
while (more_samples()) {
    s = next_sample();
    n += 1;
    r1 += s;
    r2 += s*s;
}
mean = r1 / n;
stddev = sqrt(r2/n - (mean * mean));

Essentially, you keep a running total of the sum of the samples and the sum of their squares. This lets you easily compute the standard deviation at the end.

[Math] If 100% of data fall within first two standard deviations of the mean, is the distribution Normal

The naive approach would be to expect 5 samples of 100 outside 2 SD, with a standard deviation on that of $\sqrt 5 \approx 2.2$, so getting 0 is only a 2 SD event (and maybe not that bad as the measured SD is probably a bit low).

Best Answer

Related Solutions

[Math] Calculating mean and standard deviation of very large sample sizes

[Math] If 100% of data fall within first two standard deviations of the mean, is the distribution Normal

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