For 71.5 and 67: σ=3.182
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It allows you to understand, or comprehend the average fluctuation to the average. example: the average height for adult men in the United States is about 70", with a standard deviation of around 3". This means that most men (about 68%, assuming a normal distribution) have a height within 3" of the mean (67"- 73"), one standard deviation, and almost all men (about 95%) have a height within 6" of the mean (64"-76"), two standard deviations. In summation standard deviation allows us to see the 'average' as a whole.
134 is twice 67, so there is 67 between them.
An IQ test is simply a (somewhat flawed) means of assessing a person's "relative intelligence". It is important that IQ is not extremely important when working with such a measure in psychology. Now, the IQ test is designed such that scores follow a pattern known as a "normal distribution". This is not simply an expected distribution! This distribution is very important in the study of statistics, and has many applications to scientific disciplines (such as psychology). A standard deviation is essentially a measure of distance from the mean. For example, say that the average person lives to be 75, with a standard deviation of 4. This means that a person who lives to be 79 would be one standard deviation above the mean, and a person who lives to be 67 would be two standard deviations below the mean. As a table depicting the normal distribution can show, one standard deviation above the mean is at the 84th percentile, while one standard deviation below the mean is at the 16th percentile (two stds above: 97.5th, two stds below: 2.5th) This means that an IQ score of 115 is at the 84th percentile, while an IQ score of 85 is at the 16th percentile. 68% of all people are within this range, and that is "most" people.
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67