19. Just average the smallest and the largest terms. AVERAGE OF EVENLY SPACED TERMS
20.
21. Arrange the terms in ascending or descending order:
•the number in the middle of the list,
•the average (arithmetic mean) of the two numbers in the middle of the list. AVERAGE OF EVENLY SPACED TERMS
30. The girl’s average score is 30. The boy’s
average score is 24. If there are twice as
many boys as girls, what is the overall
average?
1 30 2 24
3
26
average
average
57. The 20th percentile is the value (or score) below which 20 percent of the observations may be found.
58.
59. DECILE AND PERCENTILEThe 20th percentile (2nd decile) is the value (or score) below which 20 percent of the observations may be found. D1D2D3D4D5D6D7D8D910%20%30%40%50%60%70%80%90%
60. QuartilesAre the three points that divide the data set into four equal groups, each representing a fourth of the population being sampled.
65. INTERQUARTILE RANGE
- IQR
Is a measure of statistical dispersion,
being equal to the difference between
the upper and the lower quartiles.
3 1 IQR Q Q
93. ! n n P n
3-distinct color
patterns
3! 321 6
94. 4! 4321 24
! n n P n
4-distinct color patterns
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
95. 21 21 P 21!
! n n P n
51,090,942,171,709,440,000
96. How many different 4-letter arrangements can be formed with all the letters A, B, C, and D?
ABCD
ABDC
ACBD
ACDB
ADBC
ADCB
BACD
BADC
BCAD
BCDA
BDAC
BDCA
CABD
CADB
CBAD
CBDA
CDAB
CDBA
DABC
DACB
DBAC
DBCA
DCAB
DCBA444! 432124P
97. There are three marbles: 1 blue, 1 red
and 1 green. In how many ways is it
possible to arrange marbles in a row?
3 3 3!
3 2 1
6
P
98. There are three marbles: 1 blue, 1 red and 1 green. In how many ways is it possible to arrange marbles in a row if red marble have to be left to blue marble?
104. How many different 3-letter arrangements
can be formed with all the letters A, B, C,
D, E, F, and G?
7 3
7! 7!
210
7 3 ! 4!
P
!
! n r
n
P
n r
116. 52 5
52!
5! 52 5 !
C
!
! ! n r
n
C
r n r
2,598,960
117. How many different 3-letter combinations
can be formed with all the letters A, B, C,
D, E, F, and G?
7 3
7!
3! 7 3 !
C
!
! ! n r
n
C
r n r
7 3
7!
35
3! 4!
C
121. A variable whose value results from a measurement on some type of random process.
122. Is a numerical description of the outcome of an experiment. RANDOM VARIABLE
123. PROBABILITYFor situations in which the possible outcomes are all equally likely, the probability that an event E occurs, represented by “P(E)”, can be defined as:
FavorableoutcomesofEPETotalnumberofpossibleoutcomes
137. Independent Events
Two events are said to be independent if the occurrence or nonoccurrence of either one in no way affects the occurrence of the other.
138. INDEPENDENT EVENTSTo find the probability of occurrence of both, find each probability separately and multiply consecutive probabilities.
PEandFPEPF
139. A dresser drawer contains one pair of socks with each
of the following colors: blue, brown, red, white and
black. Each pair is folded together in a matching set.
You reach into the sock drawer and choose a pair of
socks without looking. You replace this pair and then
choose another pair of socks. What is the probability
that you will choose the red pair of socks both times?
1 2 p red and red p red p red
1 1
5 5
1
25
140.
141. DEPENDENT EVENTSTo find the probability of occurrence of both, find each probability separately and multiply consecutive probabilities.
PEandFPEPF
142. A card is chosen at random from a standard
deck of 52 playing cards. Without replacing it, a
second card is chosen. What is the probability
that the first card chosen is a queen and the
second card chosen is a jack?
1 2 p queen and jack p queen p jack
4 4
52 51
4
663
143. PE or F PE PFPE and F
PE or F
PE and F
Probability that at least one
of the two events occurs.
Probability that events E
and F both occur.
ADDITION LAW OF
PROBABILITIES
144. A
A
A
A
2
2
2
2
3
3
3
3
4
4
4
4
5
5
5
5
6
6
6
6
7
7
7
7
8
8
8
8
9
9
9
10
10
10
10
J
J
J
J
Q
Q
Q
Q
K
K
K
K
What is the probability of picking a 9 or a club in an standard deck of cards?
DiamondsHeartsClubsSpades
P (9 or ) = P(9)+P() –P(9 and )
= 4/52 + 13/52 –1/52
= 16/52
= 4/13
9
145. If xis to be chosen at random from the set {1, 2, 3, 4} and yis to be chosen at random from the set {5, 6, 7}, what is the probability that xywill be even? x
1
2
3
4y
5
5
10
15
20
6
6
12
18
24
7
7
14
21
28
82123
146. If a person rolls two dice, what is the
probability of getting a prime number as
the sum of the two dice?
15 5
36 12
2, 3, 5, 7, 11
147. If a person rolls two dice, what is the
probability of getting an even number as
the sum of the two dice?
18 1
36 2
170. DEALING WITH GRAPHS & CHARTSBefore even reading the questions based on a graph or table, take 10 or 15 seconds to look it over.
171. Make sure you understand the information that is being displayed, the scales and the units of the quantities involved. DEALING WITH GRAPHS & CHARTS