Certainly! To find the median and the mode and their difference for the set of numbers: 14, 2, 1, 14, 21, 8, we will follow the steps below:
Step 1: Find the Median
The median is the middle number in a sorted list of numbers. If there's an odd number of numbers, it's the middle one; if there's an even number of numbers, it's the average of the two middle numbers.
First, let's order the numbers from smallest to largest:
1, 2, 8, 14, 14, 21
Since there are 6 numbers (an even amount), the median will be the average of the 3rd and 4th numbers.
The 3rd number is 8 and the 4th number is 14.
The median is:
(8 + 14) / 2 = 22 / 2 = 11
Step 2: Find the Mode
The mode is the number that appears most frequently in a set.
From our ordered list, we can see that:
1, 2, 8, 14, 14, 21
The number 14 appears twice, and all other numbers appear only once.
So, the mode is 14.
Step 3: Calculate the Difference
Finally, we calculate the difference between the median and the mode:
Difference = median - mode
Difference = 11 - 14
Difference = -3
Therefore, the difference between the median and the mode of the given numbers is -3.
