Question

1. Suppose you are given the average pay of all working people in each of the 50 states of the United States. Explain what other information would be needed to determine the average for the entire country given the 50 state-wide averages, and explain how you would use that information.

Answer 1

We are given the average pay of people in all 50 states, let us represent them as :

( x1 , x2 , x3 ..... x50)

For calculating the average which is the sum of all the observation divided by the total number of observations.

So in this particular case we observing the pay of the population.

so we would also need the population of all these 50 states, let us represent them as :

(n1 , n2 , n3 ......n50)

Now let us consider state 1 :

average#1 = sum of pay of all people in #1 /Population of #1

x1*n1 = sum of pay of all people in #1

so sum of pay all the 50 states would be :

( x1*n1 + x2*n2 + x3*n3 ........... x50*n50 )

Population of 50 states we know is

(n1 +n2 +n3 ............n50 )

Average of the country = ( x1*n1 + x2*n2 + x3*n3 ........... x50*n50 ) / (n1 +n2 +n3 ............n50 )