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The graph on the left above represents the number of family
[#permalink]
30 Jul 2018, 09:12

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The graph on the left above represents the number of family members per family in Town X, while the graph on the right above represents the number of family members per family in Town Y. The median family size for Town X is equal to the median family size for Town Y. The horizontal and vertical dimensions of the boxes above are identical and correspond to the same measurements. Which of the following statements must be true?

Indicate all such statements.

A. The range of family sizes measured as the number of family members is larger in Town X than in Town Y.

B. Families in Town Y are more likely to have sizes within 1 family member of the mean than are families in Town X.

C. The data for Town X has a larger standard deviation than the data for Town Y.

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Re: The graph on the left above represents the number of family
[#permalink]
11 Aug 2018, 14:26

3

Note that the spread of graph Y appears smaller than the spread of graph X. This tells us that the standard deviation of X is greater than the standard deviation of Y.

A: We don't know anything about the range. It appears that they are roughly equal, based on the width of the two graphs.

B: Based on the graphs, it does indeed appears that more of population Y is closer to the mean of the graph. This fits with what we said about the spread before. If the spread is smaller, more of the population would be closer to the mean.

C: As stated in the beginning, graph X has greater spread, so it has a greater standard deviation than Y.

A: We don't know anything about the range. It appears that they are roughly equal, based on the width of the two graphs.

B: Based on the graphs, it does indeed appears that more of population Y is closer to the mean of the graph. This fits with what we said about the spread before. If the spread is smaller, more of the population would be closer to the mean.

C: As stated in the beginning, graph X has greater spread, so it has a greater standard deviation than Y.

Re: The graph on the left above represents the number of family
[#permalink]
30 Apr 2020, 22:24

1

Romang67 wrote:

Note that the spread of graph Y appears smaller than the spread of graph X. This tells us that the standard deviation of X is greater than the standard deviation of Y.

A: We don't know anything about the range. It appears that they are roughly equal, based on the width of the two graphs.

B: Based on the graphs, it does indeed appears that more of population Y is closer to the mean of the graph. This fits with what we said about the spread before. If the spread is smaller, more of the population would be closer to the mean.

C: As stated in the beginning, graph X has greater spread, so it has a greater standard deviation than Y.

A: We don't know anything about the range. It appears that they are roughly equal, based on the width of the two graphs.

B: Based on the graphs, it does indeed appears that more of population Y is closer to the mean of the graph. This fits with what we said about the spread before. If the spread is smaller, more of the population would be closer to the mean.

C: As stated in the beginning, graph X has greater spread, so it has a greater standard deviation than Y.

If SD of Town x is greater than Town y, then range of Town x should also be greater than that of Town y. Because the range of a normal distribution is 6xSD

Re: The graph on the left above represents the number of family
[#permalink]
22 Jun 2020, 18:13

I want explanation for point B please

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Re: The graph on the left above represents the number of family
[#permalink]
22 Jun 2020, 21:44

I didn't get it. Can you give me some more details?

Re: The graph on the left above represents the number of family
[#permalink]
28 Jun 2020, 23:58

1

What we know here is that the median for X= median for Y and from the graph we see for variability for town X than town Y, indicating that s.d of X> s.d of Y. Lets move on to the options now.

A- This is not necessarily true. Range is simply max–min and while the variability differs, they can still have similar max and min values or different ones so this is incorrect.

B- True, since town Y has values more concentrated around the µ than town X.

C- True. This has been already inferred.

A- This is not necessarily true. Range is simply max–min and while the variability differs, they can still have similar max and min values or different ones so this is incorrect.

B- True, since town Y has values more concentrated around the µ than town X.

C- True. This has been already inferred.

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