Question

The sum of four observations is p square+31p.if the mean of this observation is 8, find the value of p, where pe any positive integer

Answer 1

here we take p = 1 as it should be a positive integer

Answer 2

Answer:

p = 1

Step-by-step explanation:

Given : The sum of four observations is $p^2+31p$

And mean of observation is 8.

We have to find the value of p.

Mean is defined as sum of observation divided by number of observation.

Mathematically written as

$Mean=\frac{\text{sum of observation}}{\text{number of observation}}$

Given sum of observation is $p^2+31p$ and number of observation is 4.

and mean is 8.

Substitute, we get,

$8=\frac{p^2+31p}{4}$

Solving for p , cross multiply , we get

$32=p^2+31p$

$p^2+31p-32=0$

The above quadratic equation can be solved using middle term splitting method,

31p can be written as -p +32p , we get

$p^2-p+32p-32=0$

Solving, we get,

$p(p-1)+32(p-1)=0$

$(p+32)(p-1)=0$

This implies $(p+32)=0$ or $(p-1)=0$

thus, p = -32 or p = 1

Since given p is a positive integer so p has to be 1 .