**Finding the Median Number of Persons in a House in the Village**

To find the median number of persons in a house in the village, we need to arrange the given data in ascending order and then find the middle value. If the number of data points is odd, the middle value will be the median, and if the number of data points is even, the median will be the average of the two middle values.

Let's arrange the given data in ascending order:

Number of persons in houses: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10
Number of houses: 26, 113, 120, 95, 60, 42, 21, 14, 5, 4

Now, let's calculate the cumulative frequency for the number of houses:

Cumulative Frequency: 26, 26+113=139, 139+120=259, 259+95=354, 354+60=414, 414+42=456, 456+21=477, 477+14=491, 491+5=496, 496+4=500

**Calculating the Median:**

Since the total number of houses is 500, the median will be the value that corresponds to the cumulative frequency of 500/2 = 250.

Looking at the cumulative frequency, we can see that the median falls in the third category (259). Therefore, the median number of persons in a house is 3.

**Explanation:**

The median is a measure of central tendency that represents the middle value of a dataset when arranged in ascending or descending order. In this case, we arranged the data in ascending order and used the cumulative frequency to identify the category that corresponds to the middle value.

By finding the cumulative frequency, we can determine the number of houses that fall into each category. This helps us identify the category that contains the median value. In this case, the cumulative frequency of 259 indicates that the median falls within the third category, which represents the number of houses with 3 persons.

Therefore, the median number of persons in a house in the village is 3.

NOTE: The given data suggests that there are no houses with more than 10 persons, so the median cannot be higher than 10.