Lets go option by option

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

Range is the difference between the maximum and minimum values in a distribution. In this case maximum number of family members vs minimum number. Clearly both towns have the same maximum number of family member.

Since the width of both the graphs are same.

False2.Families in Town Y are more likely to have sizes within 1 family member of the mean than are families in Town X.

Look at the figure below. Say the line parallel to the y axis represent 1 family member family member in both graphs.

Attachment:

paint.jpg [ 25.96 KiB | Viewed 510 times ]
So area under the curve bounded by the line is the total number of families with one family member or less (shown in red). Note that the line parallel to y axis is at the same distance from y axis in both cases.

Now area should be larger in Graph x is larger since graph x is more spread out than graph y and the median value is same for both (i.e. point on x axis where y is maximum).

True3. The data for Town X has a larger standard deviation than the data for Town Y

Standard deviation is the thickness of the graph. Larger the standard deviation more spread out the graph would be. In this case X is more spread out than Y.

True.
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Sandy

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