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The frequency distributions shown above represent two groups

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The frequency distributions shown above represent two groups [#permalink] New post 21 Nov 2017, 13:09
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The frequency distributions shown above represent two groups of data. Each of the data values is a multiple of 10.

Quantity A
Quantity B
The standard deviation of distribution A
The standard deviation of distribution B


A. Quantity A is greater.
B. Quantity B is greater.
C. The two quantities are equal.
D. The relationship cannot be determined from the information given.
[Reveal] Spoiler: OA

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Re: The frequency distributions shown above represent two groups [#permalink] New post 08 Feb 2018, 08:06
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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 left-hand 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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Re: The frequency distributions shown above represent two groups [#permalink] New post 16 Feb 2018, 15:42
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Carcass wrote:
Attachment:
distribution.jpg


The frequency distributions shown above represent two groups of data. Each of the data values is a multiple of 10.

Quantity A
Quantity B
The standard deviation of distribution A
The standard deviation of distribution B


A. Quantity A is greater.
B. Quantity B is greater.
C. The two quantities are equal.
D. The relationship cannot be determined from the information given.


Based on the symmetry of the two distributions, we can see that each has a mean of 30.

In Distribution A, the most values (6 in total) are EQUAL to the mean, and the rest are AWAY from the mean.
In Distribution B, the most values (10 in total) are AWAY to the mean, and a few are EQUAL to the mean.

As such, Distribution B has a greater standard deviation.

Answer: B

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Re: The frequency distributions shown above represent two groups   [#permalink] 16 Feb 2018, 15:42
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