Find median from the following data. Wage 5 15 15 25 25 35 35 45 45 55 55 65 65 75 : : : : : : : : No. of labour 4 5 7 10 4 3 4

To find the median from the given grouped data, follow these steps systematically:

Step 1: Compute the midpoint of each class interval

The midpoint (or class mark) is calculated using the formula: $$\text{Class mark}=\frac{\text{Lower limit}+\text{Upper limit}}{2}$$

Step 2: Compute cumulative frequency

The cumulative frequency helps locate the median class.

Total number of observations ($N$) = 37.

Step 3: Identify the median class

The median is the value corresponding to the $\frac{N}{2}$th term. $$\frac{37}{2}=18.5$$ The cumulative frequency just exceeding 18.5 is 26, which falls in the 35-45 wage class. Thus, the median class is 35-45.

Step 4: Apply the median formula for grouped data

The formula for the median in grouped data is: $$\text{Median}=L+\left(\frac{\frac{N}{2}-C}{f}\right)\times h$$ Where:

• $L$ = Lower limit of the median class = 35
• $N$ = Total frequency = 37
• $C$ = Cumulative frequency of the class preceding the median class = 16
• $f$ = Frequency of the median class = 10
• $h$ = Width of the median class = 10 (45 - 35)

Substitute the values: $$\text{Median}=35+\left(\frac{18.5-16}{10}\right)\times 10$$ $$=35+\left(\frac{2.5}{10}\right)\times 10$$ $$=35+2.5$$ $$=\text{37.5}$$

Thus, the median wage is ₹37.5.