Four archers P, Q, R and S try to hit a bull's eye during a tournament consisting of seven rounds. As illustrated in the...

Question

Four archers P, Q, R and S try to hit a bull's eye during a tournament consisting of seven rounds. As illustrated in the figure below, a player receives 10 points for hitting the bull's eye, 5 points for hitting within the inner circle and 1 point for hitting within the outer circle.

The final scores received by the players during the tournament are listed in the table below.

Round | P  | Q  | R  | S
  1   |  1 | 10 |  1 | 10
  2   |  5 | 10 | 10 |  1
  3   |  1 |  1 |  1 |  5
  4   | 10 |  1 |  1 |  5
  5   |  1 |  5 | 10 | 10
  6   |  5 | 10 |  1 |  5
  7   | 10 |  5 |  5 |  1

The most accurate and the most consistent players during the tournament are respectively

A. P and S   B. Q and S   C. Q and R   D. R and Q

Accepted Answer

Q is most accurate (total score 42) and S is most consistent (stdev 3.68). Answer: B. Q and S. Each round a player scores 10 (bull's eye), 5 (inner circle), or 1 (outer circle). 'Most accurate' is the player with the highest total score across all 7 rounds. 'Most consistent' is the player whose scores vary the least from round to round, measured by the standard deviation of their 7 scores.