Answer to Question #120420 in Statistics and Probability for Harriet

Question

Eric’s average income for the first 4 months of the year is $1,450.25, what must be his
average income for the remaining 8 months so that his average income for the year is
$1,780.75?

Answer 1

Let, $\overline{x}_1$ = Eric's average income for the first 4 months of the year = $1,450.25

$\overline{x}_2$ = Eric's average income for the remaining 8 months of the year

$\overline{x}$ = Eric's average income for the entire year = $1,780.75

n₁ = 4 months

n₂ = 8 months

Then by using the combined mean formula we have,

$\overline{x}=\frac{n_1\overline{x}_1+n_2\overline{x}_2}{n_1+n_2}$

i.e. 1780.75 = $\frac{4\times1450.25+8\overline{x}_2}{4+8}$

i.e. 5801 + 8$\overline{x}_2$ = 12 x 1780.75

i.e. 8$\overline{x}_2$ = 21369 - 5801 = 15568

i.e. $\overline{x}_2$ = $\frac{15568}{8}$ = 1946

Answer: Eric's average income for the remaining 8 months must be $1,946 so that his average income for the year will be $1,780.75.