We need to find the mean of the following mixed numbers, rounded to two decimal places: $1\frac{1}{2}$, $2\frac{2}{3}$, $3\frac{3}{4}$, $4\frac{4}{5}$, and $5\frac{5}{6}$.

1. Problem Description

We need to find the mean of the following mixed numbers, rounded to two decimal places: $1\frac{1}{2}$, $2\frac{2}{3}$, $3\frac{3}{4}$, $4\frac{4}{5}$, and $5\frac{5}{6}$.

2. Solution Steps

First, convert the mixed numbers to improper fractions:

$1\frac{1}{2} = \frac{1 \times 2 + 1}{2} = \frac{3}{2}$

$2\frac{2}{3} = \frac{2 \times 3 + 2}{3} = \frac{8}{3}$

$3\frac{3}{4} = \frac{3 \times 4 + 3}{4} = \frac{15}{4}$

$4\frac{4}{5} = \frac{4 \times 5 + 4}{5} = \frac{24}{5}$

$5\frac{5}{6} = \frac{5 \times 6 + 5}{6} = \frac{35}{6}$

Next, find the mean by adding the fractions and dividing by the number of fractions (which is 5):

Mean = $\frac{\frac{3}{2} + \frac{8}{3} + \frac{15}{4} + \frac{24}{5} + \frac{35}{6}}{5}$

To add the fractions, find a common denominator. The least common multiple of 2, 3, 4, 5, and 6 is

6

0. Convert the fractions:

$\frac{3}{2} = \frac{3 \times 30}{2 \times 30} = \frac{90}{60}$

$\frac{8}{3} = \frac{8 \times 20}{3 \times 20} = \frac{160}{60}$

$\frac{15}{4} = \frac{15 \times 15}{4 \times 15} = \frac{225}{60}$

$\frac{24}{5} = \frac{24 \times 12}{5 \times 12} = \frac{288}{60}$

$\frac{35}{6} = \frac{35 \times 10}{6 \times 10} = \frac{350}{60}$

Now, add the fractions:

$\frac{90}{60} + \frac{160}{60} + \frac{225}{60} + \frac{288}{60} + \frac{350}{60} = \frac{90 + 160 + 225 + 288 + 350}{60} = \frac{1113}{60}$

Divide the sum by 5:

Mean = $\frac{\frac{1113}{60}}{5} = \frac{1113}{60 \times 5} = \frac{1113}{300}$

Now, convert the fraction to a decimal:

$\frac{1113}{300} = 3.71$

3. Final Answer

3. 71