Calculating Median from Data of Wages and Number of Workers

To calculate the median from the given data, we need to determine the middle value of the data set. Since the data is already sorted, we can easily determine the median.

Step 1: Determine the total number of workers

15 + 34 + 85 + 160 + 185 = 479

Step 2: Determine the cumulative frequency of the data set

Less than 10: 15 workers

Less than 20: 15 + 34 = 49 workers

Less than 30: 15 + 34 + 85 = 134 workers

Less than 40: 15 + 34 + 85 + 160 = 294 workers

Less than 50: 15 + 34 + 85 + 160 + 185 = 479 workers

Step 3: Determine the median value

Since the total number of workers is odd (479), the median is the middle value of the data set. To determine the median, we need to find the value that has a cumulative frequency of 239.5 (which is half of 479).

From the cumulative frequency, we can see that the median falls between the wages of 30 and 40 because the cumulative frequency of wages less than 30 is 134, and the cumulative frequency of wages less than 40 is 294.

To determine the exact value of the median, we can use the following formula:

Median = L + ((n/2 - CF)/f) x w

Where:
L = Lower class limit of the median class (30)
n = Total number of workers (479)
CF = Cumulative frequency of the class before the median class (134)
f = Frequency of the median class (160 - 85 = 75)
w = Width of the median class (40 - 30 = 10)

Plugging in the values, we get:

Median = 30 + ((239.5 - 134)/75) x 10
Median = 30 + (105.5/75) x 10
Median = 30 + 1.407 x 10
Median = 43.07

Therefore, the median wage is 43.07.

Conclusion: In summary, we have calculated the median wage from the given data of wages less than and number of workers. By using the cumulative frequency and appropriate formulas, we determined that the median wage is 43.07.