FTCE Prep Grade 5-9
Competency 7
Solutions to Practice Questions #82-94:
82. Find the median of the following set of data: 14 3 7 6 11 20
Solution: The median is the middle number. First arrange the numbers in
order: 20 14 7 6 3 1. Find the middle number 20 14 11 7 6 3.
You can see there are two middle numbers. Add them and divide by 2. That
is the median (7 + 11)/2 = 18/2 = 9
83. Compute the median for the following data set: {12, 19, 13, 16, 17, 14}
Solution: The median is the middle number. First arrange the numbers in
order, then find the middle number(s) : 19 17 16 14 13 12. Since
there are two, add them and divide by 2. 16+14 = 30/2 = 15
84. Corporate salaries are listed for several employees. Which would be the
best measure of central tendency?
$24,000
$24,000
$26,000
$28,000
$30,000
$120,000
Solution: Mean is the average of all 6 numbers, so the high salary of
$120,000 would skew the data – that is out. The mode for this set would be
$24,000, which is the lowest salary, therefore the answer is B Median.
85. Half the students in a class scored 80% on an exam, most of the rest
scored 85%, except for one student who scored 10%. Which would be
the best measure of central tendency for the test scores?
Solution: Use 10 test scores as an example; 5 score 80%, 4 score 85% and
1 scores 10%. Mode would give you an answer of 80%. Median would give
you (85, 85, 85, 85, 80, 80, 80, 80, 80, 10) 80% also. The mean would be the
average of the 10 numbers, which the 10% would lower ….Therefore the D
is an answer choice (although the outlier – 10% makes B the best
answer).
86. A student scored in the 87th percentile on a standardized test. Which
would be the best interpretation of his score?
Solution: The student scored better 87% of the group who took the test or
you can say 13% scored higher than the student. A is the answer.
87. Which statement is true about George’s budget?
Solution: By looking at the picture, you can see that George spends
approximately 50% on mortgage, 25% on utilities, 12.5% on food and 12.5%
on misc. That means that choice C – George spends twice as much on
utilities than on food is correct.
FTCE Prep Grade 5-9
Competency 7
88. What conclusion can be drawn from the graph below?
40
30
20
Girls
10
Boys
0
K
1
2
3
Solution: Choice A is untrue as there are not more students in 1st grade than
2nd grade. Choice C is untrue as there is NOT more girls than boys in 1 st
grade. Choice D is untrue as Grade 3 does NOT have the most students.
Choice B is the correct answer.
89. Given a drawer with 5 black socks, 3 blue socks, and 2 red socks, what
is the probability that you will draw two black socks in two draws in a
dark room?
Solution: There are 10 socks in the drawer, 5 are black. The probability of
drawing black sock is 5/10 or ½. There are now 9 socks in the drawer and 4
are black. The probability of drawing a black sock is now 4/9. The probability
of drawing 2 black socks is ½ x 4/9 or 4/18 or 2/9. Choice A is the correct
answer.
90. A sack of candy has 3 peppermints, 2 butterscotch drops, and 3
cinnamon drops. One candy is drawn and replaced, then another candy
is drawn; what is the probability that both will be butterscotch?
Solution: There are 8 pieces of candy and 2 are butterscotch. The probability
of drawing a butterscotch is 2/8 or ¼. That candy is put back in the sack, so
there are still 8 pieces of candy and 2 are butterscotch. The probability of
drawing a butterscotch is 2/8 or ¼. The probability of drawing 2 butterscotch
(with replacement) is ¼ x ¼ or 1/16. Choice D is the answer.
91. Given a spinner with the numbers one through eight, what is the
probability that you will spin an even number or a number greater than
four?
Solution: There are 8 number choices with 4 of them being even (and 4 are
odd). There are four numbers greater than 4 (5, 6, 7 & 8). There are 4 even
numbers and of the numbers greater than four – we look at those that are not
even (5 & 7) for a total of 6 choices out of a total of 8. Therefore the
probability is 6/8 or ¾. The answer choice is C.
92. If a horse will probably win three races out of ten, what are the odds
that he will win?
Solution: Odds is defined as favorable events compare to unfavorable.
Three is favorable with 7 as unfavorable. Odds is 3:7. Answer choice is C.
FTCE Prep Grade 5-9
Competency 7
93. How many ways are there to choose a potato and two green vegetables
from a choice of three potatoes and seven green vegetables?
Solution: Possible outcomes are
Potatoes: P1, P2, P3
Vegetables: V1, V2, V3, V4, V5, V6, V7
You can use 3 potatoes with any of the 7 vegetables, so you get 3 x 7 ways
with one potato and 1 vegetable. Now to add a second vegetable (there are 6
left) 3 x 7 x 6 ways or 126 different ways. Choice A is the answer.
94. Determine the number of subsets of set K. K ={4, 5, 6, 7}
Solution: Subsets of a set is defined and 2n, where n is the number of objects
in he set. The number of subsets you can make is therefore 24 or 16.
Choice B is the answer.