Sat 2015 Practice Test #1 Answer Explanations

Choice C is correct.
The average number of seeds per apple is the total 
number of seeds in the 12 apples divided by the number of apples, which 
LV2QWKHJUDSKWKHKRUL]RQWDOD[LVLVWKHQXPEHURIVHHGVSHUDSSOH
and the height of each bar is the number of apples with the corresponding 
QXPEHURIVHHGV7KHƮUVWEDURQWKHOHIWLQGLFDWHVWKDWDSSOHVKDYH
VHHGVHDFKWKHVHFRQGEDULQGLFDWHVWKDWDSSOHVKDYHVHHGVHDFK
the third bar indicates that 1 apple has 6 seeds, the fourth bar indicates 
WKDWDSSOHVKDYHVHHGVHDFKDQGWKHƮIWKEDULQGLFDWHVWKDWDSSOHV
have 9 seeds each. Thus, the total number of seeds for the 12 apples is 
(
––––– DQGWKH
average number of 
seeds per apple is 
12
2IWKHFKRLFHVJLYHQLVFORVHVWWR
Choice A is incorrect; it is the number of apples represented by 
the tallest bar but is not the average number of seeds for the 
12 apples. Choice B is incorrect; it is the number of seeds per apple 
corresponding to the tallest bar, but is not the average number of seeds 
for the 12 apples. Choice D is incorrect; a student might choose this 
YDOXHE\FRUUHFWO\FDOFXODWLQJWKHDYHUDJHQXPEHURIVHHGVEXW
incorrectly rounding up to 7. 

---

QUESTION 13 
Choice C is correct.
)URPWKHWDEOHWKHUHZDVDWRWDORIVXUYH\
UHVSRQGHQWVDQGRIDOOVXUYH\UHVSRQGHQWVLVHTXLYDOHQW
_
19
to 
– UHVSRQGHQWV2IWKHFKRLFHVJLYHQWKHQXPEHU
of males taking Geometry, is closest to 58.9 respondents. 
Choices A, B, and D are incorrect because the number of males taking 
*HRPHWU\LVFORVHUWRZKLFKLVRIWKDQWKHQXPEHURI
respondents in each of these categories. 
48(67,21
Choice C is correct.
7KHUDQJHRIWKHOHQJWKVRIWKHƮVK
UHSUHVHQWHGLQWKHWDEOHLVơ LQFKHVDQGWKHUDQJHRIWKH
UHPDLQLQJOHQJWKVDIWHUWKHLQFKPHDVXUHPHQWLVUHPRYHGLV
ơ LQFKHV7KHUHIRUHDIWHUWKHLQFKPHDVXUHPHQWLVUHPRYHG
the change in range, 8 inches, is much greater than the change in the 
mean or median. 
Choice A is incorrect. Let 
P
be the mean of the lengths, in inches, 
RIWKHƮVK7KHQWKHVXPRIWKHOHQJWKVLQLQFKHVRIWKHƮVK
is 21
P$IWHUWKHbLQFKPHDVXUHPHQWLVUHPRYHGWKHVXPRIWKH
OHQJWKVLQLQFKHVRIWKHUHPDLQLQJƮVKLVPơDQGWKH
_
mean 
OHQJWKLQLQFKHVRIWKHVHƮVKLV
21
P
ơ
, which is a
_
change of
ơP
inches. Since 
P
must be between the smallest
and largest
PHDVXUHPHQWVRIWKHƮVKLWIROORZVWKDWP
from which it can be seen that the change in the mean, in inches, is 
between
ơ
_ 
DQG
ơ
_
= 
_
4
5, and so must be less than the
change in the range, 8 inches. Choice B is incorrect because the median 
OHQJWKRIWKHƮVKUHSUHVHQWHGLQWKHWDEOHLVDQGDIWHUWKHLQFK
PHDVXUHPHQWLVUHPRYHGWKHPHGLDQRIWKHUHPDLQLQJOHQJWKVLV
DOVR7KHUHIRUHWKHFKDQJHLQWKHPHGLDQLVOHVVWKDQWKHFKDQJH
in the range (8). Choice D is incorrect because the changes in the mean, 
PHGLDQDQGUDQJHRIWKHPHDVXUHPHQWVDUHGLƬHUHQW
QUESTION 15