Hiding items in student's handout using beamer duplicate slides

Motivation: giving lectures using beamer, I would like to hide answers from the students’ handout. On one slide, I want to ask a question, show the answer after a pause, ask a second question after a pause, then show the answer, etc. I applied three solutions found on StackExchange (hideit, only<beamer>, and mode<beamer>).

As the MWE below will show, the PDF when compiled with beamer contains more slides that it should (slides 6 and 10). Indeed, those two slides display all the information and do not make use of the pause. When using handout, everything is as I want it. I would like the slides under Atmospheric pressure to behave like under Standard Climate Statistics. I am not sure where the code goes awry in the second frame.

documentclass[xcolor={dvipsnames},t,serif,mathserif,aspectratio=1610]{beamer}

%%% To create a handout version of the presentation 
%documentclass[xcolor={dvipsnames},handout,serif,mathserif,aspectratio=1610]{beamer}

mode<presentation>
{
    usetheme{Goettingen}
    usecolortheme{seagull}
}

%To hite text in handout from https://tex.stackexchange.com/questions/266116/trying-to-hide-blocks-of-text-in-beamer
newcommandhideit[1]{%
  only<0| handout:1>{mbox{}}%
  invisible<0| handout:1>{#1}}
    
begin{document}

section{Climate statistics}
%%----------------------------------------------------------%
begin{frame}[c]{Standard climate statistics}

begin{itemize}
    item textcolor{ForestGreen}{Arithmetic mean} (or average)
    
    pause
    item Sum of the values, x$_i$, divided by the number of observations, N
end{itemize}

begin{align}
    hideit{bar{x_i} = dfrac{sum x_i}{N}}
end{align}

%begin{align}
%   only<beamer>{bar{x_i} = dfrac{sum x_i}{N}}
%end{align}

%mode<beamer>{%
%begin{align}
%   bar{x_i} = dfrac{sum x_i}{N}
%end{align}
%}

pause
begin{itemize}
    item A measure of variability such as textcolor{ForestGreen}{standard deviation}, S$_n$
end{itemize}

pause
begin{align}
    hideit{S_n = sqrt{dfrac{1}{N} sum^N_{i=1} (x_i - bar{x_i})^2}}
end{align}

%begin{align}
%   only<beamer>{S_n = sqrt{dfrac{1}{N} sum^N_{i=1} (x_i - bar{x_i})^2}}
%end{align}

%mode<beamer>{%
%begin{align*}
%   S_n = sqrt{dfrac{1}{N} sum^N_{i=1} (x_i - bar{x_i})^2}
%end{align*}
%}
end{frame}

%%----------------------------------------------------------%
begin{frame}[c]{Atmospheric pressure}

begin{itemize}
    item How can we calculate the dry air density, $rho_{air}$?
end{itemize}

pause
begin{align}
    hideit{rho_{air} =pause dfrac{m_{air}}{V_{air}}}
end{align}

%begin{align}
%   only<beamer>{rho_{air} =pause dfrac{m_{air}}{V_{air}}}
%end{align}

%mode<beamer>{%
%begin{align}
%       rho_{air} =pause dfrac{m_{air}}{V_{air}}
%end{align}
%}  

pause
begin{itemize}
    item How can we calculate the mass of a given dry air parcel, $m_{air}$?
end{itemize}

pause
begin{align}
    hideit{m_{air} =pause n_{air} MM_{air}}
end{align}

%begin{align}
%   only<beamer>{m_{air} =pause n_{air} MM_{air}}
%end{align}

%mode<beamer>{%
%begin{align}
%   m_{air} =pause n_{air} MM_{air}
%end{align}
%}
end{frame}
end{document}