Statistics - Mean, Median, Mode

SOURCE:COMPETITION
Number of Problems: 9. : (Book)

An iterative average of the numbers 1, 2, 3, 4, and 5 is computed the following way. Arrange the five numbers in some order. Find the mean of the first two numbers, then find the mean of that with the third number, then the mean of that with the fourth number, and finally the mean of that with the fifth number. What is the difference between the largest and smallest possible values that can be obtained using this procedure?

$extbf{(A)} frac{31}{16}qquad extbf{(B)} 2qquad extbf{(C)} frac{17}{8}qquad extbf{(D)} 3qquad extbf{(E)} fra...$

The median of the list $n, n + 3, n + 4, n + 5, n + 6, n + 8, n + 10, n + 12, n + 15$ is $10$ . What is the mean?

$extbf{(A) }4qquad extbf{(B) }6qquad extbf{(C) }7qquad extbf{(D) }10qquad extbf{(E) }11$

The mean, median, unique mode, and range of a collection of eight integers are all equal to 8. The largest integer that can be an element of this collection is

$ext{(A) }11qquad ext{(B) }12qquad ext{(C) }13qquad ext{(D) }14qquad ext{(E) }15$

The mean of a set of five different positive integers is 15. The median is 18. The maximum possible value of the largest of these five integers is

$ext{(A)} 19 qquad ext{(B)} 24 qquad ext{(C)} 32 qquad ext{(D)} 35 qquad ext{(E)} 40$

The average (mean) of $20$ numbers is $30$ , and the average of $30$ other numbers is $20$ . What is the average of all $50$ numbers?

$mathrm{(A) } 23qquad mathrm{(B) } 24qquad mathrm{(C) } 25qquad mathrm{(D) } 26qquad mathrm{(E) } 27$

The Dunbar family consists of a mother, a father, and some children. The average age of the members of the family is $20$ , the father is $48$ years old, and the average age of the mother and children is $16$ . How many children are in the family?

$ext{(A)} 2 qquad ext{(B)} 3 qquad ext{(C)} 4 qquad ext{(D)} 5 qquad ext{(E)} 6$

The average of the numbers $1, 2, 3,cdots, 98, 99,$ and $x$ is $100x$ . What is $x$ ?

$extbf{(A)} dfrac{49}{101} qquad extbf{(B)} dfrac{50}{101} qquad extbf{(C)} dfrac{1}{2} qquad extbf{(D)} df...$

$extbf{(A)} frac{31}{16}qquad extbf{(B)} 2qquad extbf{(C)} frac{17}{8}qquad extbf{(D)} 3qquad extbf{(E)} fra...$