Question

a stage supervisor was trying to determine the most accurate quote for a time estimate for a kind of project only undertaken 7 times prior. he decided an average of prior times would be best. what should he quote based on the following data? project 1: $4\frac{1}{2}$ hours project 2: $4\frac{3}{4}$ hours project 3: $4\frac{1}{3}$ hours project 4: $3\frac{2}{3}$ hours project 5: $2\frac{1}{5}$ hours project 6: $2\frac{3}{5}$ hours project 7: $3\frac{4}{5}$ hours find the answer in decimal form and round the answer to the nearest tenth if needed. (you do not need to include the units. you only need to enter your answer as a number.)

Explanation:

Step1: Convert mixed - numbers to improper fractions

$4\frac{1}{2}=\frac{4\times2 + 1}{2}=\frac{9}{2}$, $4\frac{3}{4}=\frac{4\times4+3}{4}=\frac{19}{4}$, $4\frac{1}{3}=\frac{4\times3 + 1}{3}=\frac{13}{3}$, $3\frac{2}{3}=\frac{3\times3+2}{3}=\frac{11}{3}$, $2\frac{1}{5}=\frac{2\times5 + 1}{5}=\frac{11}{5}$, $2\frac{3}{5}=\frac{2\times5+3}{5}=\frac{13}{5}$, $3\frac{4}{5}=\frac{3\times5 + 4}{5}=\frac{19}{5}$

Step2: Find a common denominator

The common denominator of 2, 4, 3, 5 is 60.
$\frac{9}{2}=\frac{9\times30}{2\times30}=\frac{270}{60}$, $\frac{19}{4}=\frac{19\times15}{4\times15}=\frac{285}{60}$, $\frac{13}{3}=\frac{13\times20}{3\times20}=\frac{260}{60}$, $\frac{11}{3}=\frac{11\times20}{3\times20}=\frac{220}{60}$, $\frac{11}{5}=\frac{11\times12}{5\times12}=\frac{132}{60}$, $\frac{13}{5}=\frac{13\times12}{5\times12}=\frac{156}{60}$, $\frac{19}{5}=\frac{19\times12}{5\times12}=\frac{228}{60}$

Step3: Sum the fractions

$\frac{270 + 285+260+220+132+156+228}{60}=\frac{1551}{60}$

Step4: Calculate the average

The average is $\frac{\frac{1551}{60}}{7}=\frac{1551}{60\times7}=\frac{1551}{420}$

Step5: Convert to decimal

$\frac{1551}{420}=3.692857\cdots\approx3.7$

Answer:

3.7