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South African Mathematics Olympiad

South Africa statistics

Problem

The list of numbers 16; 19; 24; 25; 30; 31; 32; 46; has the same median and mean. If is greater than , then the value of is (A) 47 (B) 48 (C) 53 (D) 50 (E) 57
Solution
The median is the middle number, which is , so the mean is also . The sum of all nine numbers is therefore , which means that .
Final answer
A

Techniques

Mathematical Statistics