Data Analysis

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ISEE Upper Level Quantitative Reasoning › Data Analysis

Questions 1 - 10

Venn

In the above Venn diagram, the universal set is defined as $U = \left \{ a, b, c, d, e, f, g, h\right \}$ . Each of the eight letters is placed in its correct region. Which of the following is equal to $\overline{A\cup B}$ ?

$\overline{A\cup B} = \left \{ c\right \}$

$\overline{A\cup B} = \left \{ a,c,f\right \}$

$\overline{A\cup B} = \left \{ a,f\right \}$

$\overline{A\cup B} = \left \{ b,c,d,e,g,h\right \}$

$\overline{A\cup B} = \left \{ b,d,e,g,h\right \}$

Explanation

$\overline{A\cup B}$ is the complement of $A\cup B$ - the set of all elements in not in $A\cup B$ .

$A\cup B$ is the union of sets and - the set of all elements in either or . Therefore, $\overline{A\cup B}$ is the set of all elements in neither nor , which can be seen from the diagram to be only one element - . Therefore,

$\overline{A\cup B} = \left \{ c\right \}$

Venn

$\overline{A\cup B} = \left \{ c\right \}$

$\overline{A\cup B} = \left \{ a,c,f\right \}$

$\overline{A\cup B} = \left \{ a,f\right \}$

$\overline{A\cup B} = \left \{ b,c,d,e,g,h\right \}$

$\overline{A\cup B} = \left \{ b,d,e,g,h\right \}$

Explanation

$\overline{A\cup B}$ is the complement of $A\cup B$ - the set of all elements in not in $A\cup B$ .

$\overline{A\cup B} = \left \{ c\right \}$

Venn

$\overline{A\cup B} = \left \{ c\right \}$

$\overline{A\cup B} = \left \{ a,c,f\right \}$

$\overline{A\cup B} = \left \{ a,f\right \}$

$\overline{A\cup B} = \left \{ b,c,d,e,g,h\right \}$

$\overline{A\cup B} = \left \{ b,d,e,g,h\right \}$

Explanation

$\overline{A\cup B}$ is the complement of $A\cup B$ - the set of all elements in not in $A\cup B$ .

$\overline{A\cup B} = \left \{ c\right \}$

What is the mode value in the set below?

$2^{2}, \frac{1}{4}, 3^{1},\sqrt{9}, \frac{8}{2}, \frac{6}{2}$

Explanation

The first step is to convert the expressions in the set $2^{2}, \frac{1}{4}, 3^{1},\sqrt{9}, \frac{8}{2}, \frac{6}{2}$ to their simplified forms. This gives us:

$4, \frac{1}{4}, 3, 3, 4, 3$

While the value of 4 appears twice, given that the value 3 appears 3 times, it is the mode in this set.

Use the following data set to answer the question:

Find the median.

Explanation

To find the median of a data set, we will first arrange the numbers in ascending order. Then, we will locate the number in the center of the data set.

So, given the data set

we will arrange the numbers in ascending order. To do that, we will arrange them from smallest to largest. So, we get

Now, we will locate the number in the center of the data set.

$3, 3, 4, 5, {\color{Red} 6}, 6, 6, 8, 8$

We can see that it is 6.

Therefore, the median of the data set is 6.

Find the median of the following data set:

Explanation

Find the median of the following data set:

To find the median, first put the numbers in increasing order

Now, identify the median by choosing the middle term

$12,12,12,33,44,{\color{Green} 44},55,65,65,79,99$

In this case, it is 44, because 44 is in the middle of all our terms.

Find the median of the following data set:

Explanation

Find the median of the following data set:

To find the median, first put the numbers in increasing order

Now, identify the median by choosing the middle term

$12,12,12,33,44,{\color{Green} 44},55,65,65,79,99$

In this case, it is 44, because 44 is in the middle of all our terms.

Use the following data set to answer the question:

Find the median.

Explanation

To find the median of a data set, we will first arrange the numbers in ascending order. Then, we will locate the number in the center of the data set.

So, given the data set

we will arrange the numbers in ascending order. To do that, we will arrange them from smallest to largest. So, we get

Now, we will locate the number in the center of the data set.

$3, 3, 4, 5, {\color{Red} 6}, 6, 6, 8, 8$

We can see that it is 6.

Therefore, the median of the data set is 6.

What is the mode value in the set below?

$2^{2}, \frac{1}{4}, 3^{1},\sqrt{9}, \frac{8}{2}, \frac{6}{2}$

Explanation

The first step is to convert the expressions in the set $2^{2}, \frac{1}{4}, 3^{1},\sqrt{9}, \frac{8}{2}, \frac{6}{2}$ to their simplified forms. This gives us:

$4, \frac{1}{4}, 3, 3, 4, 3$

While the value of 4 appears twice, given that the value 3 appears 3 times, it is the mode in this set.

Find the median of the following data set: