Data Analysis and Probability - ISEE Middle Level Quantitative Reasoning

Card 0 of 3783

Question

Find the mode of this set of numbers:

Answer

Find the most recurring number:

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Question

Find the mode of the set of numbers:

Answer

The mode is the number that appears most frequently in the data set:

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Question

Find the mode in this set of numbers:

7435, 8976, 2784, 7435, 1289, 8976, 2110, 8992, 8976, 2784.

Answer

Find the most recurring number in the set.

The answer is

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Question

Two standard decks of fifty-two cards, one with a red backing and one with a purple backing, are presented to you. The red deck has all of its aces removed; the purple deck has all of its kings removed. Which is the greater quantity?

(A) The probability that a card randomly drawn from the red deck is a seven

(B) The probability that a card randomly drawn from the purple deck is a seven

Answer

Both modified decks still have four sevens, and both modified decks have forty-eight cards. Therefore, the probability of drawing a seven from the red deck is the same as the probability of drawing a seven from the purple deck: $\frac{4}{48} = \frac{1}{12}$ .

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Question

Find the mean in this set of numbers:

5570, 4886, 5226, 4120, 6561, 4120, 6008

Answer

First, add all the numbers in this set:

Then, divide that amount by the total number in the set:

$36491\div 7=5213$

Answer: The mean is 5213.

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Question

Find the mean in this set of numbers:

9078, 9008, 9800, 9099, 9009, 9090, 9008

Answer

First add all the numbers:

Then, divide that number by 7:

$64,092\div 7=9156$

Answer: The mean is 9156

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Question

Find the average of these amounts:

$34.78, $21. 69, $76.89, $47.88

Answer

First, add all the amounts:

Then, divide by 4:

$181.24\div 4=45.31$

Answer: The average is 45.31

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Question

Find the mean of the following set of numbers: 227, 215, 206, 238, 249

Answer

Add the numbers, and divide by 5:

$\frac{ 227 + 215 +206+238+ 249}{5} = \frac{1,135}{5} = 227$

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Question

Find the mean in this set of numbers:

210, 120, 110, 220, 120

Answer

First, add up all of the numbers in the set:

Then, divide: $780 \div 5=156$

Answer: The mean is 156.

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Question

Refer to the above diagram. The top row gives a sequence of figures. Which figure on the bottom row comes next?

Answer

The square with the diagonal line alternates between the square on the left and the square on the right. Therefore, the next figure in the sequence will have its diagonal line in the rightmost square, eliminating Figures (b) and (d) and leaving Figures (a) and (c).

Also, the shaded square moves one position to the right from figure to figure, so in the next figure, the shaded square must be the one at the extreme right. Figure (c) matches that description.

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Question

Patricia is shopping for a coat. She is considering three coats. Each costs $85.98, $93.29 and $88.99, respectively. What is the average price of a coat she is considering?

Answer

First, add up all of the prices:

Then, divide $268.26 \div 3= 89.42$ .

Answer: The average price of a coat is $89.42.

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Question

An arithmetic sequence begins:

Which is the greater quantity?

(a)

(b) The tenth term of the sequence

Answer

The common difference of the sequence is . The tenth term of the sequence is $100 + (10-1) (-11) = 100 + 9 \cdot (-11) = 100 - 99 = 1$ .

This makes (b) greater.

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Question

Find the range in this set of numbers:

9881, 9889, 9818, 9981, 9891, 9918, 9989, 9889, 9198

Answer

First, order the numbers from least to greatest:

Then, find the difference of the largest and smallest number:

Answer: The range is 791.

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Question

Find the mode in this set of numbers:

22, 24, 28, 23, 27, 24, 29, 35, 23, 42, 42, 24, 26, 25, 26.

Answer

Find the number that appears most frequently.

Answer: The mode is 24.

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Question

Two fair six-sided dice are thrown. What is the probability that the product is greater than or equal to 20?

Answer

The rolls that yield a product greater than or equal to 20 are:

$\begin{matrix} \textrm{Roll} & \textrm{Prod} \ (4,5) &20 \ (4,6) &24 \ (5,4) &20 \ (5,5) & 25\ (5,6) & 30\ (6,4) &24 \ (6,5) &30 \ (6,6) &36 \end{matrix}$

These are 8 out of 36 rolls, so the probability of getting one of them is $\frac{8}{36} = \frac{2}{9}$

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Question

Using the information given in each question, compare the quantity in Column A to the quantity in Column B.

A pair of regular dice (with sides numbered from 1-6) is thrown.

Column A Column B

the odds of the odds of

rolling a total of 8 rolling a total of 7

Answer

Consider the different ways in which you could roll an 8 or a 7.

You could roll 8 by the following combinations:

2-6, 3-5, 4-4, 5-3, 6-3

so the odds of rolling 8 are $\frac{5}{36}$ .

You could roll 7 by the following combinations:

1-6, 2-5, 3-4, 4-3, 5-2, 6-1

so the odds of rolling 7 are $\frac{6}{36}=\frac{1}{6}$ .

The answer, therefore, is that Column B is greater.

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Question

A card is drawn at random from a deck of 53 cards - the standard deck including the joker. Which is the greater quantity?

(a) The probability of drawing a black card

(b) $\frac{1}{2}$

Answer

26 of the 53 cards are black (the joker counts as neither).

Half of 53 is

$53 \times \frac{1}{2} = 26 \frac{1}{2}$

26 is less than this, so black cards comprise less than half the deck, and the probability of drawing a black card is less than $\frac{1}{2}$ .

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Question

A standard deck of fifty-two cards is altered by removing the tens and replacing them with the queens from another deck. A card is drawn at random from the altered deck.

Which is the greater quantity?

(a) The probability that the card is a face card

(b) $\frac{1}{3}$

Note: a face card is a jack, a queen, or a king.

Answer

With the replacement of the tens with the queens, there are still 52 cards in the deck, but now, there are four jacks, eight queens, and four kings - 16 face cards. The probability that a random card is a face card is

$\frac{16}{52} = \frac{16 \div 4}{52\div 4} = \frac{ 4}{13}$

$\frac{ 4}{13} = \frac{12}{39} < \frac{13}{39} = \frac{1}{3}$

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Question

A standard deck of fifty-two cards is altered by removing the black aces. A card is drawn at random from the altered deck.

Which is the greater quantity?

(a) The probability that a face card will be drawn

(b) $\frac{1}{4}$

Note: a face card is a jack, a queen, or a king.

Answer

The removal of the two black aces leaves a deck of 50 cards, with all 12 face cards remaining. The probability that a randomly drawn card is a face card is therefore

$\frac{12}{50 } = 0.24$

Since $\frac{1}{4} = 0.25$ , the probability is less than $\frac{1}{4}$ .

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Question

Two fair dice are thrown. Which is the greater quantity?

(a) The probability that the sum wiil be 5 or less

(b) $\frac{1}{4}$

Answer

For the sum of the dice to be 5 or less, one of the following rolls must be thrown:

(1,1). (1,2), (2,1), (1,3), (2,2), (3,1), (1,4), (2,3), (3,2), (4,1)

This makes 10 out of 36 rolls. Since one-fourth of 36 is 9, the probability of throwing a 5 or less is greater than $\frac{1}{4}$ .

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