ISEE Middle Level Quantitative Reasoning - Data Analysis and Probability

Find the mode in this set of numbers:

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

Explanation

Find the number that appears most frequently.

Answer: The mode is 24.

Find the range of the data set provided:

Screen shot 2016 04 05 at 10.19.45 am

Explanation

In order to answer this question correctly, we need to recall the definition of range:

Range: The range of a data set is the difference between the highest value and the lowest value in the set.

In order to find the range, we need to first organize the data from least to greatest to find the lowest and highest values:

Next, we can solve for the difference between the highest value and the lowest value:

$\frac{\begin{array}[b]{r}9\ -\ 1\end{array}}{ \ \ \ \space 8}$

The range for this data set is

Find the mode in this set of numbers:

Explanation

Identify the number that appears most frequently:

Find the mode in this set of numbers:

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

Explanation

Find the number that appears most frequently.

Answer: The mode is 24.

In a dice game, what is the probability of rolling a factor of 5 on a six-sided die?

$\frac{1}{3}$

$\frac{5}{6}$

$\frac{1}{6}$

Explanation

To find the probability of an event, we will use the following formula:

$\text{probability of event} = \frac{\text{number of ways event can happen}}{\text{total number of possible outcomes}}$

Now, given the event of rolling a factor of 5, we can calculate the following.

$\text{number of ways event can happen} = 2$

because there are 2 factors of 5 on a dice:

We can also calculate the following.

$\text{total number of possible outcomes} = 6$

because there are 6 different possible numbers we can roll on a dice:

Knowing this, we can substitute into the formula. We get

$\text{probability of rolling a factor of 5} = \frac{2}{6}$

$\text{probability of rolling a factor of 5} = \frac{1}{3}$

Therefore, the probability of rolling a factor of 5 on a dice is $\frac{1}{3}$ .

Find the mode in this set of numbers:

Explanation

Find the number that appears most frequently in the set:

Venn_3

Define:

Universal set $U =\mathbb{N}$ , the set of all natural numbers.

= { | is a multiple of 3}

= { | is a multiple of 5}

If all of the natural numbers were to be placed in their appropriate places in the above Venn diagram, which of the following would be placed in the gray region?

$7\textup,916$

$1\textup,565$

$3\textup,890$

$7\textup,431$

$3\textup,966$

Explanation

The gray region is the region outside both and and is therefore the set of natural numbers that are multiples of neither 3 nor 5.

1,565 and 3,890 can be eliminated as choices as each is divisible by 5: the former ends in 5 and the latter ends in 0.

7,431 and 3,966 can be eliminated as each is divisible by 3: $7,431 \div 3 = 2,477$ and $3,966 \div 3 = 1,322$ .

7,916 is not divisible by 5 as it ends in 6; it is not divisible by 3 as $7,916 \div 3 =2,638 ; R; 2$ . Therefore, it is the correct choice.

In a dice game, what is the probability of rolling a factor of 5 on a six-sided die?

$\frac{1}{3}$

$\frac{5}{6}$

$\frac{1}{6}$

Explanation

To find the probability of an event, we will use the following formula:

$\text{probability of event} = \frac{\text{number of ways event can happen}}{\text{total number of possible outcomes}}$

Now, given the event of rolling a factor of 5, we can calculate the following.

$\text{number of ways event can happen} = 2$

because there are 2 factors of 5 on a dice:

We can also calculate the following.

$\text{total number of possible outcomes} = 6$

because there are 6 different possible numbers we can roll on a dice:

Knowing this, we can substitute into the formula. We get

$\text{probability of rolling a factor of 5} = \frac{2}{6}$

$\text{probability of rolling a factor of 5} = \frac{1}{3}$

Therefore, the probability of rolling a factor of 5 on a dice is $\frac{1}{3}$ .

A bag contains $\small 2$ red marbles, $\small 7$ pink marbles, and $\small 6$ purple marbles. What is the probability of not choosing a purple marble?

$\small \frac{3}{5}$

$\small \frac{2}{5}$

$\small \frac{2}{3}$

$\small \frac{3}2$

Explanation

The probability (p) is equal to the number of a specific event (purple marbles) divided by the total number of events. The probability of NOT p (called q) is equal to $\small 1-q.$ In this example: