Find the value of $p$ if the Mean of the following distribution is $50$ $x$ $10$ $30$ $50$ $70$ $90$ $y$ $17$ $5p+3$ $32$ $7p-11$ $19$

Using the assumed mean method with the assumed mean as 50, the sum of the deviations multiplied by their respective frequencies equals zero. This yields the equation 17 multiplied by negative 40 plus the quantity 5p plus 3 multiplied by negative 20 plus the quantity 7p minus 11 multiplied by 20 plus 19 multiplied by 40 equals zero. Solving this equation gives negative 680 minus 100p minus 60 plus 140p minus 220 plus 760 equals zero, which simplifies to 40p minus 200 equals 0. Therefore, p equals negative 25/2.

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