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ISEE Middle Level Quantitative : Data Analysis and Probability

Study concepts, example questions & explanations for ISEE Middle Level Quantitative

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All ISEE Middle Level Quantitative Resources

6 Diagnostic Tests 110 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : Data Analysis

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?

Possible Answers:

$3\textup,890$

$7\textup,431$

$3\textup,966$

$1\textup,565$

$7\textup,916$

Correct answer:

$7\textup,916$

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.

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Example Question #1 : Range

Which is the greater quantity?

(A) The midrange of the data set $\left\{ 1, 10, 100, 1000, 10000 \right \}$

(B) The midrange of the data set $\left\{ 80, 90, 100, 110, 120 \right \}$

Possible Answers:

(A) and (B) are equal

(B) is greater

It is impossible to determine which is greater from the information given

(A) is greater

Correct answer:

(A) is greater

Explanation:

The midrange of a data set is the mean of its least and greatest elements. The midrange of the first data set is $\left (10,000 + 1 \right ) \div 2 = 5,000.5$ ; that of the second data set is $(80 + 120) \div 2 = 100$ . (A) is greater.

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Example Question #2 : Range

Set is defined as:

6,13,4,10,4,1

Set is made by doubling the values in set .

What is the range of values in set ?

Possible Answers:

9.5

Correct answer:

Explanation:

To find the range of a set of numbers, you do not even have to put them in order. You merely need to subtract the smallest value from the largest. Given the way of constructing set by doubling set 's values, the largest and smallest values in will directly correlate to the same in set :

Smallest: 1 => 2

Largest: 13=>26

Therefore, the range is: 26-2=24

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Example Question #3 : Range

The members of set are defined as the values for:

f(x)=x^2+3

For values of between and .

What is the range of set ?

Possible Answers:

169

172

170

Correct answer:

169

Explanation:

To find the range of a set of numbers, you do not even have to put them in order. You merely need to subtract the smallest value from the largest. Given the way that we construct set from the function f(x) , we merely need to use that function to find the smallest and largest values. Luckily, that is pretty easy for this question. The smallest will be f(0) and the largest will be f(13)

Smallest: f(0) = 0^2 + 3 = 3

Largest: f(13) = 13^2 + 3 = 172

Therefore, the range is: 172 - 3 = 169

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Example Question #4 : Range

Set is defined as:

13,-1,4,1,-9,10

The members of set are defined by the function:

f(x) = x^2 - 3x , where is a member of set .

So, for instance, set T contains 130 because for , we get:

f(13)=13^2-3*13=169-39=130

What is the range of set ?

Possible Answers:

132

128

Correct answer:

132

Explanation:

We first need to determine the members of set . Using our function, we will get:

f(13) = 130

f(-1) = (-1)^2-3(-1)=1+3=4

f(4) = (4)^2-3(4)=16-12=4

f(1) = (1)^2-3(1)=1-3=-2

f(-9) = (-9)^2-3(-9)=81+27=108

f(10) = (10)^2-3(10)=100-30=70

Our largest value is 130 , and our smallest value is ; therefore, the range is 130-(-2)= 130+2=132

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Example Question #5 : Range

Given the below set of numbers find the range:

4, 8, 9, 7, 12, 15, -2, 3, 0, 10

Possible Answers:

Correct answer:

Explanation:

Range for a set of data is defined as the difference between the biggest and smallest number.

First we find the biggest number which is 15, we then subtract the smallest number in this set which is negative 2 as shown below:

15-(-2) = 15 + 2 = 17

Remember, when subtracting a negative number we must add the numbers.

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Example Question #5 : Range

Given the below set of numbers, find the range:

$\frac{4}{5}, \ \frac{5}{8},\ \frac{1}{3},\ \frac{1}{10}$

Possible Answers:

$\frac{3}{5}$

$\frac{1}{5}$

$\frac{7}{10}$

$\frac{3}{10}$

Correct answer:

$\frac{7}{10}$

Explanation:

In order to find the range, we must subtract the smallest number from the biggest number.

$Biggest\ Number = \frac{4}{5}$

$Smallest\ Number = \frac{1}{10}$

$\frac{4}{5}-\frac{1}{10}$

We must convert the fractions to have a common denominator which is 10.

$\frac{8}{10}-\frac{1}{10}=\frac{7}{10}$

Therefore, the range of this set is

$\frac{7}{10}$ .

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Example Question #3 : Data Analysis

Given the below set of numbers, find the range:

$\frac{4}{5}, \ \frac{5}{8},\ \frac{1}{3},\ \frac{1}{10}$

Possible Answers:

$\frac{3}{5}$

$\frac{1}{3}$

$\frac{3}{10}$

$\frac{7}{10}$

$\frac{1}{5}$

Correct answer:

$\frac{7}{10}$

Explanation:

In order to find the range, we must subtract the smallest number from the biggest number.

$Biggest\ Number = \frac{4}{5}$

$Smallest\ Number = \frac{1}{10}$

$\frac{4}{5}-\frac{1}{10}$

We must convert the fractions to have a common denominator which is 10.

$\frac{8}{10}-\frac{1}{10}=\frac{7}{10}$

Therefore, the range of this set is

$\frac{7}{10}$ .

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Example Question #7 : Find Range

Find the range of the data set provided:

Screen shot 2016 04 05 at 8.55.18 am

Possible Answers:

Correct answer:

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:

26,26,26,27,28,28,28,29,30,30,30,31,32,33,34,34,34,34,35,36

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

$\frac{\begin{array}[b]{r}36\\ -\ 26\end{array}}{ \ \ \ \space 10}$

The range for this data set is

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Example Question #8 : Find Range

Find the range of the data set provided:

Screen shot 2016 04 05 at 9.44.17 am

Possible Answers:

Correct answer:

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:

11,11,13,14,14,14,14,15,18,19,20,20,21,22,27

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

$\frac{\begin{array}[b]{r}27\\ -\ 11\end{array}}{ \ \ \ \space 16}$

The range for this data set is

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ISEE Middle Level Quantitative : Data Analysis and Probability

Study concepts, example questions & explanations for ISEE Middle Level Quantitative

All ISEE Middle Level Quantitative Resources

Example Questions

Example Question #1 : Data Analysis

Example Question #1 : Range

Example Question #2 : Range

Example Question #3 : Range

Example Question #4 : Range

Example Question #5 : Range

Example Question #5 : Range

Example Question #3 : Data Analysis

Example Question #7 : Find Range

Example Question #8 : Find Range

All ISEE Middle Level Quantitative Resources

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