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:

Step 1: Determine the Median Class

The median is the value that divides the data into two equal parts. For grouped data, the median class is the class where the cumulative frequency reaches or exceeds half of the total frequency.

First, calculate the total frequency (N): $$N=4+5+7+10+4+3+4=37$$

The median position is given by: $$\frac{N}{2}=\frac{37}{2}=18.5$$

Now, find the cumulative frequencies:

The cumulative frequency reaches 18.5 in the 35-45 class (since 16 < 18.5 ≤ 26). Thus, the median class is 35-45.

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Step 2: Apply the Median Formula

The formula for the median in grouped data is:

$$\text{Median}=L+\left(\frac{\frac{N}{2}-cf}{f}\right)\times w$$

Where:

• $L$ = Lower limit of the median class = 35
• $N$ = Total frequency = 37
• $cf$ = Cumulative frequency of the class preceding the median class = 16
• $f$ = Frequency of the median class = 10
• $w$ = Class width = 10 (since 45 - 35 = 10)

Substitute the values:

$$\text{Median}=35+\left(\frac{18.5-16}{10}\right)\times 10$$

$$=35+\left(\frac{2.5}{10}\right)\times 10$$

$$=35+2.5$$

$$=37.5$$

Final Answer:

The median wage is 37.5.