With Q3 on the 2010 MC exam, the simplest way of estimating the SD without using any formulas would be to look at the graph. You know that 68% lie within 1 SD of the mean right? Or even 34% either side?
Well, if you look at the graph and you use the median 180 (rather than calculating the mean, as it's approx. symmetrical so it shouldn't matter too much) all you need to do it count 34% either side of 180 which will give you ~178 and ~182 and there you have it, a SD of 2!
how come it is a SD of 2 from 178 - 182?
Ok, looking at the histogram given at the start, and knowing that roughly 68% of the data is within 1 Sdev of the mean, we can calculate the Sdev, what I personally did was after noticing that the y axis was %, I added up some bars together, starting from the mean, adding both the bars to left and right of 180, giving me roughly 38% (22+16%), then adding the other two next to each of them, gave me another 29% (14+15%), together equalling roughly 67%, and from that I concluded that between 178 and 182 was the mean +- 1 Sdev, and the difference between 178/182 and 180 was 2. Therefore Sdev of 2.
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