A frequency distribution graph sounds more complex than it is. It merely tells how often certain values showed up. For example, in Quantity A's graph, the values 10, 20, 40, and 50 all showed up 3 times each, but 30 showed up 6 times.
Standard deviation, basically, is a measure of how spread out data is, or the average distance from the mean. There's a long, complicated way to calculate it exactly, but that would be the wrong way to approach this problem.
If you compare the graphs directly, you can see which is more spread out. Notice that both graphs are symmetrical. That means that the middle value is also the average. Now since we're looking for the average distance from the mean, we can ignore the 2nd and 4th columns, since they're the same in both graphs and therefore the same distance from the average.
Let's compare the middle column. Since the middle column on the lefthand graph is much higher, we see that there are many more values that actually are the average, meaning their distance from the average is zero. This will reduce the average distance from the mean.
Conversely, the 1st and 5th columns on the left are smaller than the same two columns on the right, meaning that there are fewer values that are far from the mean. This would also reduce the standard deviation.
Thus, the standard deviation in Quantity B is higher, so B is the answer.
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