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Data Analysis, Statistics, and Probability

SAT Mean, Median, and Mode

         

The average of \(11\) numbers is \(205.\) When another number is introduced, the average of the \(12\) numbers is also \(205.\) What is the \(12\text{th}\) number?

(A) \(\ \ \frac{11}{205}\)

(B) \(\ \ \frac{12}{11}\)

(C) \(\ \ 11\)

(D) \(\ \ 23\)

(E) \(\ \ 205\)

If the average (arithmetic mean) of \(5, 10, 15, 20,\) and \(x\) is \(53\), what is the value of \(x\)?

(A) \(\ \ 3\)
(B) \(\ \ 50\)
(C) \(\ \ 53\)
(D) \(\ \ 215\)
(E) \(\ \ 265\)

\(9, 80, 3, 25, 3, 25, 25, 9\)

If \(x\) is the median of the list above and \(y\) is the mode, which of the following is \(x+y?\)

(A) \(\ \ 34\)
(B) \(\ \ 39\)
(C) \(\ \ 42\)
(D) \(\ \ 50\)
(E) \(\ \ 97\)

Anna's average (arithmetic mean) on three tests is \(70\). What grade does she need on her fourth test to raise her average to \(75\)?

(A) \(\ \ 70\)
(B) \(\ \ 75\)
(C) \(\ \ 80\)
(D) \(\ \ 85\)
(E) \(\ \ 90\)

Oliver drove \(600\) kilometers at \(60\) km/hr. He then sped up and drove \(1680\) kilometers at \(120\) km/hr. What was his average speed, in km/hr, for the entire trip?

(A) \(\ \ 90\)
(B) \(\ \ 95\)
(C) \(\ \ 100 \)
(D) \(\ \ 105 \)
(E) \(\ \ 420\)

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