Describe in detail what you need | 72, 85, 91, 77, 65, 88. Whais the mean and median? |
How many pages | 1 |
In statistics, mean and median are two fundamental measures of central tendency. Let's calculate the mean and median for the given data set: 72, 85, 91, 77, 65, 88.
The data points provided are:
The mean is calculated by summing all the numbers in the data set and then dividing that sum by the count of numbers.
First, we add all the numbers together:
[ 72 + 85 + 91 + 77 + 65 + 88 = 478 ]
Next, we count how many numbers are in the data set. There are 6 numbers.
Now we divide the total sum by the count:
[ \text{Mean} = \frac{478}{6} \approx 79.67 ]
So, the mean of the data set is approximately 79.67.
The median is the middle number in a sorted list of numbers. If the list has an odd number of observations, it is the middle one; if even, it is the average of the two middle numbers.
First, we must sort the numbers in ascending order:
Since there are 6 numbers (an even count), the median will be the average of the two middle values (the 3rd and 4th numbers in the sorted list).
The two middle numbers are:
Now, we calculate the average of these two numbers:
[ \text{Median} = \frac{77 + 85}{2} = \frac{162}{2} = 81 ]
Therefore, the median of the data set is 81.
These calculations provide insights into the central tendency of the data set you provided, giving a sense of average performance based on the values presented. Understanding both mean and median is crucial when analyzing any set of numbers, as they can tell different stories about the data distribution depending on its characteristics.