The mode of the following distribution is 66. What would be the median...
**Finding the Median:**
To find the median wage, we need to arrange the data in ascending order.
The given distribution is:
Daily wages (3) 30-40 40-50 50-60 60-70 70-80 80-90
No of workers: 8 16 22 28 12
Arranging the data in ascending order, we get:
30-40 40-50 50-60 60-70 70-80 80-90
**Calculating the Cumulative Frequency:**
Next, we need to calculate the cumulative frequency. The cumulative frequency is the sum of the frequencies up to a specific point in the data.
In this case, the cumulative frequency for each wage range is as follows:
30-40: 8
40-50: 8 + 16 = 24
50-60: 24 + 22 = 46
60-70: 46 + 28 = 74
70-80: 74 + 12 = 86
80-90: 86
**Finding the Median Class:**
The median class is the class interval that contains the median value. To find the median class, we need to determine the cumulative frequency just greater than the median.
In this case, the median value is (total number of workers + 1) / 2 = (86 + 1) / 2 = 43.5
The cumulative frequency just greater than 43.5 is 46, which corresponds to the class interval 50-60.
**Calculating the Median:**
The median can be calculated using the formula:
Median = Lower limit of median class + ((N/2) - CF) * (Width of class interval / Frequency of median class)
In this case, the lower limit of the median class is 50, the width of the class interval is 10, and the frequency of the median class is 22.
Plugging in the values, we get:
Median = 50 + ((43.5 - 46) * 10 / 22)
= 50 + (-2.5 * 10 / 22)
= 50 - 1.136
= 48.864
Therefore, the median wage is approximately 48.86.
**Answer: (b) 48.86**
However, none of the given answer choices match the calculated median. Therefore, none of the provided answer choices are correct.
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