Five coins were simultaneously tossed $1000$ times and at each toss the number of heads were observed. The number of tosses during which$0,1,2,3,4$ and $5$ heads were obtained are shown in the table below. Find the mean number of heads per toss

$No. of heads per toss$	$No. of tosses$
$0$	$38$
$1$	$144$
$2$	$342$
$3$	$287$
$4$	$164$
$5$	$25$
$Total$	$1000$

 

The mean of the following data is $20.6$. Find the value of $p.$

$\begin{array}{llllll}x:& 10& 15& \mathrm{p}& 25& 35\\ f:& 3& 10& 25& 7& 5\end{array}$

If the mean of the following data is $15,$ find $p$

$\begin{array}{llllll}x:& 5& 10& 15& 20& 25\\ f:& 6& p& 6& 10& 5\end{array}$

Find the value of $p$ for the following distribution whose mean is $16.6 .$

$\begin{array}{cccccccc}x\text{ : }& 8& 12& 15& \mathrm{p}& 20& 25& 30\\ f:& 12& 16& 20& 24& 16& 8& 4\end{array}$

Find the missing value of $p$for the following distribution whose mean is $12.58 .$

$\begin{array}{llllllll}x:& 5& 8& 10& 12& p& 20& 25\\ f:& 2& 5& 8& 22& 7& 4& 2\end{array}$

Find the missing frequency$\left(p\right)$ for the following distribution whose mean is $7.68 .$

$\begin{array}{lllllll}x:& 3& 5& 7& 9& 11& 13\\ f:& 6& 8& 15& p& 8& 4\end{array}$

Find the value of $p,$ if the mean of the following distribution is $20 .$

$\begin{array}{cccccc}x:& 15& 17& 19& 20+p& 23\\ f:& 2& 3& 4& 5p& 6\end{array}$

Candidates of four schools appear in a mathematics test. The data were as follows:

If the average score of the candidates of all the four schools is $66,$ find the number of candidates that appeared from school $\mathrm{III}$.

Find the missing frequencies in the following frequency distribution if it is known that the mean of the distribution is $50$