Question

The mean of X - 1, X + 1, X + 3 and X + 5 is

Answer 1

Answer:

The mean of a list of numbers is the sum of the numbers divided by the number of terms.

We know we have 1000 terms and each contain one x, so the sum of the variables is 1000x.

The sum of the integers could be hard, but we have a pattern of (x-y), (x+y+1), and we see this 500 times. The sum of these two terms is equal to 2x+1. Since this happens 500 times, we can multiply it to get 500(2x+1), or 1000x+500.

Lastly, we divide by the number of terms (1000), and get (1000x+500)/1000=x+0.5.

This is the mean.

Step-by-step explanation:

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Answer 2

The required mean = X + 2

Given :

The observations X - 1, X + 1, X + 3 and X + 5

To find :

The mean of the observations

Solution :

Step 1 of 3 :

Write down the given observations

Here the given observations are X - 1, X + 1, X + 3 and X + 5

Step 2 of 3 :

Calculate sum of the observations

Number of observations = 4

Sum of the observations

= X - 1 + X + 1 + X + 3 + X + 5

= 4X + 8

Step 3 of 3 :

Find the mean

The required mean

$\displaystyle \sf{ = \frac{Sum \: of \: the \: observations}{Number \: of \: observations} }$

$\displaystyle \sf{ = \frac{4X + 8}{4} }$

$\displaystyle \sf{ = \frac{4(X + 2)}{4} }$

$\displaystyle \sf{ = X + 2}$

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