Solution:
The median is the middle score in a set of given numbers.
The mean is the arithmetic average of a set of given numbers.
The mode is the most frequently occurring score in a set of given numbers.
Median
The median is the middle score of a distribution. To calculate the median
* Arrange your numbers in numerical order.
* Count how many numbers you have.
* If you have an odd number, divide by 2 and round up to get the position of the median number.
* If you have an even number, divide by 2 . Go to the number in that position and average it with the number in the next higher position to get the median.
In the question above, there are 12 numbers. 12 is even and so to get the median position, divide 12 by 2 , which falls on the 6th number.
The numbers are not ordered so you have to order them from the lowest to the highest before determining the 6th position
⇒4,16,13,18,3,20,6,7,15,2,10,12=2,3,4,6,7,10,12,13,15,16,18,20
The 6th number from the ordered numbers is 10
Since the total number count (12) is even, the median is the average of the 6th and its next number(7th number)
Average simply means the sum of the two numbers divided by 2
So the median will be the 6th number + the 7 th number divided by 2
⇒ the median =(10+12)∕2=22∕2=11
If the total number count is odd, the median is simply the middle number in the ordered numbers
Mean
The mean, or average, is calculated by adding up the scores and dividing the total by the number of scores. Consider the following number set: 3,4,6,6,8,9,11.
The mean is calculated in the following manner:
3+4+6+6+8+9+11=47
number of scores is 7
⇒ The mean =47∕7=6.7
The mean (average) of the number set is 6.7 .
Mode
Since the mode is the most frequently occurring score in a distribution, simply select the most common score as your mode.
Consider the following number distribution of 2, 3, 6, 3, 7, 5, 1, 2, 3, 9 .
The mode of these numbers would be 3 since three(3) is the most frequently occurring number.
In some number sets, there may actually be two modes. This is known as bi-modal distribution and it occurs when there are two numbers that are tied in frequency.
For example, consider the following set of numbers: 13,17,20,20,21,23,23,26,29,30.
In this set, both 20 and 23 occur twice.
If no number in a set occurs more than once, then there is no mode for that set of data.
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