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 larger than the median.
100
To determine a number that can be added to the data set to keep the mean larger than the median, let's first calculate the mean and median of the given data set.
1. Mean: To find the mean of a data set, add up all the numbers and then divide the sum by the total number of values.
Sum of data set = 3 + 4 + 6 + 7 + 9 + 9 + 11 = 49
Number of values = 7
Mean = Sum of data set / Number of values
Mean = 49 / 7
Mean = 7
2. Median: To find the median of a data set, first arrange the numbers in ascending order, then identify the number in the middle. If there is an odd number of values, the median is the middle number. If there is an even number of values, the median is the average of the two middle numbers.
Arranging the data set in ascending order: 3, 4, 6, 7, 9, 9, 11
Since the data set has an odd number of values, the median is the middle number.
Median = 7
Now, in order to keep the mean larger than the median, we need to add a number greater than 7 to the data set.
To choose a number, we can consider any value greater than 7. For example, let's add 10 to the data set:
New data set = 3, 4, 6, 7, 9, 9, 11, 10
Calculating the new mean:
Sum of new data set = 3 + 4 + 6 + 7 + 9 + 9 + 11 + 10 = 59
Number of values = 8
Mean = Sum of new data set / Number of values
Mean = 59 / 8
Mean ≈ 7.38
Comparing the new mean (approximately 7.38) with the median (7), we can see that the mean is now larger than the median.
Therefore, by adding a number greater than 7, such as 10, to the data set, we can keep the mean larger than the median.