If the mean of $a, b, c$ is $M$ and $a b+b c+c a=0,$ then the mean of $a^{2}, b^{2}, c^{2}$ is
$M ^{2}$
$3 M ^{2}$
$6 M ^{2}$
$9 M ^{2}$
The average weight of $36$ students is $50 \,kg$. It was found later that the figure of $37 \,kg$ was misread as $73 \,kg.$ What is the correct average? (in $kg$)
$3 \,years$ ago the average age of a family of $5 \,members$ was $17 \,years,$ with the birth of a new baby, the average age of six members remains the same even today. Find the age of the new baby in $year$.
A man spends $Rs.\,1800$ monthly on an average for the first four months and $Rs.\,2000$ monthly for the next eight months and saves $Rs.\,5600$ a $year$. His average monthly income is (in $Rs.$)
A number, $x,$ equals $80 \%$ of the average of $5,7,$ $14$ and a number $y$. If the average of $x$ and $y$ is $26$ then value of $y$ is
In a class, the average height of $35$ girls was measured $160 \,cm$. Later, on it was discovered that height of one of the girls was misread as $144\, cm ,$ while her actual height was $104 \,cm.$ What was the actual average height of the girls in the class? (in $cm$) (rounded off to two digits after decimal)