Consider the following data set: 3, 4, 6, 7, 9, 9, 11.
Identify a number you could add to the set to keep the mean equal to the median.
Please help me out. I have no idea how to find this and my lesson doesn't explain how to do it either. I already know that the mean and median for the set given is 7.
Try adding one.
To find a number that can be added to the data set to keep the mean equal to the median, we need to understand the relationship between mean and median.
In a set of numbers arranged in ascending order, the median is the middle value. If there are an odd number of data points, the median is the middle number. If there are an even number of data points, the median is the average of the two middle numbers.
The mean of a set of numbers is the sum of all the numbers divided by the total number of data points.
In this case, the given data set is: 3, 4, 6, 7, 9, 9, 11.
The mean is 7, and the median is also 7 because there are seven data points in the set, with 3 numbers below 7 and 3 numbers above 7.
To keep the mean equal to the median, we need to add a number such that the resulting set still has a median of 7.
Since the median is the middle value, we need to add a number between the existing 3 numbers below 7 and the existing 3 numbers above 7. This means the number we add should be greater than or equal to 6 and less than or equal to 9.
There are multiple numbers that can be added to the set to achieve this. For example, you could add the number 7, or any number between 6 and 9 (inclusive), such as 6, 8, or 9.
By adding any of these numbers to the set, the median will still be 7, and the mean will remain equal to 7 as well.