Find the median wage of the following data. If the total frequency is 525, find the values of x and y.

Steps to Solve

1. Organize the Data

   From the table, extract the wage categories and the number of workers in each category. The data is as follows:

   Wage Category	No. of Workers
   Below 60	3
   60-69	27
   70-79	57
   80-89	75
   90-99	151
   100-109	104
   110-119	34
   120-129	10
   130-139	0
   140-149	29
   150-159	0
   160 and Above	60

2. Calculate the Cumulative Frequency

   Calculate the cumulative frequency for each wage category to determine how many workers are below each wage level. This helps identify the median wage category.

   Wage Category	Cumulative Frequency
   Below 60	3
   60-69	30
   70-79	87
   80-89	162
   90-99	313
   100-109	417
   110-119	451
   120-129	461
   130-139	461
   140-149	490
   150-159	490
   160 and Above	550

3. Find the Total Number of Workers

   Add up all the workers:

   $$ \text{Total Workers} = 3 + 27 + 57 + 75 + 151 + 104 + 34 + 10 + 0 + 29 + 0 + 60 = 550 $$

4. Determine the Median Position

   The median position is calculated by:

   $$ \text{Median Position} = \frac{\text{Total Workers}}{2} = \frac{550}{2} = 275 $$

5. Identify the Median Category

   Locate the cumulative frequency that first reaches or exceeds 275, which occurs in the "90-99" wage category.

   The cumulative frequency just before 275 is:

   • For "80-89": 162
   • For "90-99": 313 (this exceeds 275)

   Therefore, the median wage falls in the "90-99" category.

6. Estimate the Median Wage

   Since "90-99" is the median category, we can take the midpoint of this range to estimate the median wage:

   $$ \text{Median Wage} = \frac{90 + 99}{2} = 94.5 $$