Sets X, Y, and Z are shown below. What is the average (arithmetic mean) of the elements of set Z?X = {1,2,3,4} Y = {2,4,6,8} Z = X ∪ Y Choices: a. 5/2 b. 3 c. 15/4 d. 4 e. 5

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samhouston's profile pic

Posted on

X = {1,2,3,4}

Y = {2,4,6,8}

Z = X ∪ Y

∪ means the union of the 2 sets.  Therefore, set Z is made up of the elements that are in sets X or Y.  Note that repeating elements are not written twice.

Z = {1, 2, 3, 4, 6, 8}

To find the arithmetic mean, find the sum of the elements and then divide by the number of elements in set Z.

(1 + 2 + 3 + 4 + 6 + 8) / 6

24 / 6 = 4

The arithmetic mean of set Z is 4.

justaguide's profile pic

Posted on

The set X = {1, 2, 3, 4}

Y = {2, 4, 6, 8}

Z = X U Y = {1, 2, 3, 4, 6, 8}

The arithmetic mean of all the elements of Z is (1 + 2 + 3 + 4+ 6+ 8)/6

=> 24/6

=> 4

The correct answer is choice d or 4.

rnk's profile pic

Posted on

Since Z = XUY

therefore z = {1,2,3,4,6,8}

Mean = (1+2+3+4+6+8)/6

= 24/6

=4

Ans.)d

Top Answer

giorgiana1976's profile pic

Posted on

To determine the arithmetic mean of the elements of the set Z, we'll have to determine what are the elements of Z.

We notice that the set Z is the result of union of the sets X and Y. We'll recall that the resulting set Z consists of all distinct elements of X and Y.

We notice that all distinct elements of Z are: Z = {1,2,3,4,6,8}.

Now, we'll recall the definition of the arithmetic mean: the sum of all elements divided by the number of elements.

In this case, the sum of distinct elements is: 1+2+3+4+6+8 = 24

The number of elements of Z is 6.

a.m. = (1+2+3+4+6+8)/6

a.m. = 24/6

a.m. = 4

We notice that the arithmetic mean is a.m. = 4, therefore the right option is d.4.

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