taiwan-gsat 2025 Q10

taiwan-gsat · Other · gsat__math-b 5 marks Measures of Location and Spread
A badminton player competes against four opponents: A, B, C, and D, one match each. After the competition, data from these four matches were collected, recording the total number of smashes by each opponent and the average and standard deviation of the time used per smash. The results are shown in the table below. For example, opponent A made 25 smashes in that match, with an average time of 1.2 seconds per smash and a standard deviation of 0.5 seconds.
OpponentNumber of smashes in that matchAverage time per smash (seconds)Standard deviation of time per smash (seconds)
A251.20.5
B141.50.3
C201.70.2
D301.20.4

Based on the above, regarding the performance of opponents A, B, C, and D, select the correct options.
(1) C had the highest average time per smash among the four in that match
(2) D spent the most total time on smashing among the four in that match
(3) A's time per smash in that match was the same as D's for every smash
(4) The range of A's smash times in that match is greater than the range of D's smash times in that match
(5) It is impossible for all of B's smash times in that match to be between 1.4 and 1.6 seconds
A badminton player competes against four opponents: A, B, C, and D, one match each. After the competition, data from these four matches were collected, recording the total number of smashes by each opponent and the average and standard deviation of the time used per smash. The results are shown in the table below. For example, opponent A made 25 smashes in that match, with an average time of 1.2 seconds per smash and a standard deviation of 0.5 seconds.

\begin{center}
\begin{tabular}{|l|l|l|l|}
\hline
Opponent & Number of smashes in that match & Average time per smash (seconds) & Standard deviation of time per smash (seconds) \\
\hline
A & 25 & 1.2 & 0.5 \\
\hline
B & 14 & 1.5 & 0.3 \\
\hline
C & 20 & 1.7 & 0.2 \\
\hline
D & 30 & 1.2 & 0.4 \\
\hline
\end{tabular}
\end{center}

Based on the above, regarding the performance of opponents A, B, C, and D, select the correct options.\\
(1) C had the highest average time per smash among the four in that match\\
(2) D spent the most total time on smashing among the four in that match\\
(3) A's time per smash in that match was the same as D's for every smash\\
(4) The range of A's smash times in that match is greater than the range of D's smash times in that match\\
(5) It is impossible for all of B's smash times in that match to be between 1.4 and 1.6 seconds