Calculate the value of median from the following data:Income 1,200 1,800 5,000 2,500 3,000 1,600 3,500No. OfPersons12 16 2 10 3 15 7

To calculate the median from the given data, we first need to arrange the data in ascending order and then find the middle value. However, in this case, we have grouped data, so we need to use a slightly different approach. Here are the steps:

1. Arrange the data in ascending order:

Income: 1,200, 1,600, 1,800, 2,500, 3,000, 3,500, 5,000 No. of Persons: 12, 15, 16, 10, 3, 7, 2

2. Calculate the cumulative frequency (the running total of frequencies):

Income: 1,200, 1,600, 1,800, 2,500, 3,000, 3,500, 5,000 No. of Persons: 12, 27, 43, 53, 56, 63, 65 Cumulative Frequency: 12, 27, 43, 53, 56, 63, 65

3. Find the median group (the group where the cumulative frequency surpasses half of the total frequency). The total number of persons is 65, so half would be 32.5. The median group is the one that contains the 33rd person, which is the group with income 1,800.

4. Use the formula for the median of grouped data:

Median = L + [(N/2 - CF) / f] * c

where: L = lower boundary of the median group = 1,800 N = total number of data = 65 CF = cumulative frequency of the group before the median group = 27 f = frequency of the median group = 16 c = width of the interval = 200 (since the income is in hundreds)

Substituting the values into the formula:

Median = 1,800 + [(65/2 - 27) / 16] * 200 Median = 1,800 + [(32.5 - 27) / 16] * 200 Median = 1,800 + (5.5 / 16) * 200 Median = 1,800 + 68.75 Median = 1,868.75

So, the median income is approximately 1,868.75.