To find the range and median of the first 20 odd natural numbers, let's follow a detailed, step-by-step approach.
### Step 1: List the First 20 Odd Natural Numbers
The first 20 odd natural numbers are:
1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39
### Step 2: Calculate the Range
The range of a set of numbers is the difference between the maximum and the minimum values in the set.
- Minimum value: The smallest number in the list is 1.
- Maximum value: The largest number in the list is 39.
Thus, the range is calculated as follows:
[tex]\[ \text{Range} = \text{Maximum value} - \text{Minimum value} \][/tex]
[tex]\[ \text{Range} = 39 - 1 \][/tex]
[tex]\[ \text{Range} = 38 \][/tex]
So, the range of the first 20 odd natural numbers is 38.
### Step 3: Calculate the Median
The median is the middle number in a sorted list of numbers. If there is an even number of observations, the median is the average of the two middle numbers.
Since we have 20 numbers (which is even), the median will be the average of the 10th and 11th numbers in the sorted list.
The sorted list of the first 20 odd natural numbers is the same as provided:
1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39
- The 10th number in this list is 19.
- The 11th number in this list is 21.
The median is calculated as follows:
[tex]\[ \text{Median} = \frac{\text{10th number} + \text{11th number}}{2} \][/tex]
[tex]\[ \text{Median} = \frac{19 + 21}{2} \][/tex]
[tex]\[ \text{Median} = \frac{40}{2} \][/tex]
[tex]\[ \text{Median} = 20.0 \][/tex]
So, the median of the first 20 odd natural numbers is 20.0.
### Summary
- The range of the first 20 odd natural numbers is 38.
- The median of the first 20 odd natural numbers is 20.0.
