Solution:

Given, mode of the distribution is 66.

We are given the frequency distribution of daily wages and the number of workers in each group.

To find the median wage, we need to find the middle value of the data set.

Step 1: Find the total number of workers

Total number of workers = 8 + 16 + 22 + 28 + 12 = 86

Step 2: Find the cumulative frequency

Cumulative frequency is the running total of frequencies.

Class interval | Frequency | Cumulative Frequency
--------------|-----------|---------------------
30-40 | 8 | 8
40-50 | 16 | 24
50-60 | 22 | 46
60-70 | 28 | 74
70-80 | 12 | 86

Step 3: Find the median class interval

Median class interval is the interval that contains the middle value of the data set.

Median class interval = (n/2)th term = 86/2 = 43rd term

From the cumulative frequency table, we can see that the 43rd term lies in the interval 60-70.

Step 4: Find the median wage

To find the median wage, we need to use the formula:

Median wage = Lower limit of median class + ((n/2) - cumulative frequency of previous class) * width of class interval / frequency of median class

Lower limit of median class = 60

Width of class interval = 10

Frequency of median class = 28

Cumulative frequency of previous class = 24

n/2 = 43

Median wage = 60 + ((43 - 24) * 10 / 28)

Median wage = 60 + 6.43

Median wage ≈ 66.43

Therefore, the median wage is approximately 66.43.

Conclusion:

The median wage can be found by finding the middle value of the data set. We can use the formula of median wage to find the median wage of the given frequency distribution. In this case, the median wage is approximately 66.43.