Sure, let's solve the given problem step-by-step.
### Step 1: Arrange the Data in Ascending Order
We are given the number of rooms in 25 houses in the locality. The data set is:
4, 3, 2, 6, 4, 3, 2, 1, 5, 3, 2, 3, 4, 3, 5, 1, 6, 1, 3, 4, 2, 3, 4, 3, 5
To arrange this data in ascending order, we need to list all the numbers from smallest to largest. Here is the arranged data:
1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 6, 6
### Step 2: Find the Range of the Data
The range of a data set is the difference between the maximum value and the minimum value in that data set.
From the arranged data:
- The minimum number of rooms is 1.
- The maximum number of rooms is 6.
To find the range, we subtract the minimum value from the maximum value:
[tex]\[ \text{Range} = \text{Maximum} - \text{Minimum} \][/tex]
[tex]\[ \text{Range} = 6 - 1 \][/tex]
[tex]\[ \text{Range} = 5 \][/tex]
### Summary
So for the problem, we have:
(i) The data arranged in ascending order:
[tex]\[ 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 6, 6 \][/tex]
(ii) The range of the data is 5.
