taiwan-gsat 2020 Q3

taiwan-gsat · Other · ast__math-b 6 marks Bivariate data
To understand whether IQ and brain volume are related, a small study used magnetic resonance imaging to measure the brain volume (in units of 10,000 pixels) of 5 people, along with their IQ listed in the table below:
Brain Volume $( X )$90959188106
$\mathrm { IQ } ( Y )$9010011280103

It is known that the mean of $X$ in the table above is $\mu _ { X } = 94$ , the mean of $Y$ is $\mu _ { Y } = 97$ , and the correlation coefficient between brain volume ($X$) and IQ ($Y$) is $r _ { X , Y }$ . Based on the table above, determine which of the following options is most likely the value of $r _ { X , Y }$ ?
(1) $r _ { X , Y } \leq - 1$
(2) $- 1 < r _ { X , Y } < - 0.5$
(3) $r _ { X , Y } = 0$
(4) $0 < r _ { X , Y } < 0.5$
(5) $r _ { X , Y } \geq 1$
To understand whether IQ and brain volume are related, a small study used magnetic resonance imaging to measure the brain volume (in units of 10,000 pixels) of 5 people, along with their IQ listed in the table below:

\begin{center}
\begin{tabular}{ | c | c | c | c | c | c | }
\hline
Brain Volume $( X )$ & 90 & 95 & 91 & 88 & 106 \\
\hline
$\mathrm { IQ } ( Y )$ & 90 & 100 & 112 & 80 & 103 \\
\hline
\end{tabular}
\end{center}

It is known that the mean of $X$ in the table above is $\mu _ { X } = 94$ , the mean of $Y$ is $\mu _ { Y } = 97$ , and the correlation coefficient between brain volume ($X$) and IQ ($Y$) is $r _ { X , Y }$ . Based on the table above, determine which of the following options is most likely the value of $r _ { X , Y }$ ?\\
(1) $r _ { X , Y } \leq - 1$\\
(2) $- 1 < r _ { X , Y } < - 0.5$\\
(3) $r _ { X , Y } = 0$\\
(4) $0 < r _ { X , Y } < 0.5$\\
(5) $r _ { X , Y } \geq 1$