iran-konkur 2022 Q129

iran-konkur · Other · konkur-riazi_1401_specialized Measures of Location and Spread
129. The mean of six statistical data is a natural number, and the variance of these data is $1$, $9$, $b^2$, $5$, $\pi^2$, $9$. If the variance of these data equals $4$, what is the value of $ab$? $(a, b \in \mathbb{Z})$
(1) $-4$ (2) $4$ (3) $2$ (4) $-2$
*130. In isosceles triangle $ABC$, point $M$ is the midpoint of $AB$, and the perpendicular bisector of $AB$ cuts side $AC$ at point $N$. If $\widehat{NBC} = 54°$, what is the measure of angle $\widehat{MNB}$?
(1) $48$ (2) $56$ (3) $66$ (4) $78$
\textbf{129.} The mean of six statistical data is a natural number, and the variance of these data is $1$, $9$, $b^2$, $5$, $\pi^2$, $9$. If the variance of these data equals $4$, what is the value of $ab$? $(a, b \in \mathbb{Z})$

\begin{center}
(1) $-4$ \hspace{2cm} (2) $4$ \hspace{2cm} (3) $2$ \hspace{2cm} (4) $-2$
\end{center}

\textbf{*130.} In isosceles triangle $ABC$, point $M$ is the midpoint of $AB$, and the perpendicular bisector of $AB$ cuts side $AC$ at point $N$. If $\widehat{NBC} = 54°$, what is the measure of angle $\widehat{MNB}$?

\begin{center}
(1) $48$ \hspace{2cm} (2) $56$ \hspace{2cm} (3) $66$ \hspace{2cm} (4) $78$
\end{center}