Could you please explain Test #8, calculator-allowed section, number 28?


You have to evaluate both range and standard deviation here. The former you can calculate. The latter you just evaluate visually; You will never have to actually calculate a standard deviation on the SAT.

Let’s talk about range first. To calculate range you just subtract the smallest number in the set from the biggest number. In this case, that means that r_1=88-56=32 and r_2=112-80=32. The numbers in the second set are obviously higher, but the range in both sets is the same: the highest number is 32 greater than the lowest number. Therefore, you really only need to look at choices A and D—the only choices that say r_1=r_2.

Like range, standard deviation is a measure of variability—the bigger the standard deviation, the more spread out the values in a set are from the mean. Visually, you can look at both dot plots in this question and see that the distributions are quite different. In the first plot, there are a couple outliers, but generally the pulse rates are pretty tightly concentrated around the mean of 72.  In the second plot, the dots are much more spread out—if you picked a dot randomly in the second plot, you’d be just as likely to land on an extreme data point like 80 or 112 as you would on the mean of 96. Therefore, you can conclude that the standard deviations of the two sets are not the same (it will be bigger in the second plot). That makes choice D the only option.

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