Data Analysis and Probability - SSAT Middle Level Quantitative

The mean is equal to the sum of the values divided by the total number of values.

First add all the numbers:

Then, divide that number by 7:

Answer: The mean is 9156

First, add all the amounts:

Then, divide by 4:

Answer: The average is 45.31

First, add the numbers:

Then, divide by 7:

The mode is the number that occurs most often in the list. Since 12 appears three times, and no other number shows up as often, the mode is 12.

First, add all the numbers in this set:

Then, divide by 7 (the amount of numbers in this set):

Answer: The mean is 3795

Since the first sock that Dave pulls out is black, there are 17 remaining socks in the drawer, 8 blue and 9 black. The probability that Dave will choose another black is sock is therefore 9 out of 17.

Wihtout the clubs, the deck comprises 39 cards, 26 of which are red.

The probability that the first card will be red will be . The probability that the second will then also be red will be . Multiply the probabilities, and result is

There are three possible multiples of 4 that can come out: 4, 8, and 12. There are 36 equally probable outcomes; the following will result in a multiple of 4:

These are 9 outcomes out of 36, making the probability

There are four possible multiples of 3 that can come out: 3,6,9, and 12. There are 36 equally probable outcomes; the following will result in a multiple of 3:

These are 12 outcomes out of 36, making the probability

There are 20 balls in the hat. All but four - that is, sixteen - are blue, so the probability of a draw resulting in a non-blue ball is

The removal of two red jacks - and no black cards - results in there being fifty cards, twenty-six of them black. Therefore, the probability of a randomly drawn card being black is .

The addition of two red threes from another deck results in the deck comprising fifty-four cards, twenty-eight of which are red. Therefore, the probability of a randomly drawn card being red is

There are four cards of each rank in a standard deck; since three ranks - jacks, queens, kings - are considered face cards, this makes twelve face cards out of the fifty-two. But two more face cards - two red queens - have been introduced, so now there are fourteen face cards out of fifty-four. This makes the probability of a randomly drawn card being a face card

The probability of drawing a blue marble on the first try is , since there are blue marbles out of a total of marbles. The probability of drawing a second blue marble is , since now there are blue marbles remaining out of a total of remaining marbles. The probability of drawing two blue marbles in a row is the product of the individual probabilities: .

If Mark flips a coin, the chance that it will land on heads is . On a die, there are 2 out of 6 numbers that are a multiple of 3 (3 and 6); therefore, there is a chance that the dice will be a multiple of 3.

The probability that the coin will land on heads and that the dice will be a multiple of 3 is:

There are two possibilities every time you flip a coin and only one outcome. Therefore the probability for flipping either heads or tails each time is . When you have multiple trials in a row you multiply the probabilities of each outcome by each other.

The number of balls in the box is

;

The number of odd-numbered balls is

.

Therefore, there are balls that are not marked with an odd number, making the probability that one of these will be drawn .

Each whole number from one to ten will be represented by a red ball, for a total of ten balls; each even number will be represented by a green ball, for a total of five balls; there will also be five unmarked yellow balls. The number of balls in the box will be , 5 of which are green, making the probability of a random draw resulting in a green ball

.

The number of balls in the box is

.

The number of balls with even numbers is

.

Therefore, if a ball is drawn at random, the probability that an even-numbered ball will be selected is