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

Expert Answers
samhouston eNotes educator| Certified Educator

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 eNotes educator| Certified Educator

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 | Student

Since Z = XUY

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

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

= 24/6

=4

Ans.)d

giorgiana1976 | Student

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.