Final answer:
The value of x in the given data set must be 17 for the mean to be 1 greater than the median, which is 12.
Step-by-step explanation:
The student is asking to find the value of x in a data set so that the mean of the set is 1 more than its median. The data set includes numbers 5, 6, 10, 11, 12, 14, x, 20, and 22. To solve this, we first have to determine the median of the data set.
Since the data set has 9 values, the median will be the fifth number. In this set, the fifth number is 12, which means the median is 12. Since the mean needs to be 1 more than the median, the mean should be 12 + 1 = 13.
To find the mean, we add up all the data values including x, and divide by the total number of data values, which is 9:
(5 + 6 + 10 + 11 + 12 + 14 + x + 20 + 22) / 9 = 13.
By multiplying both sides by 9, the equation becomes:
5 + 6 + 10 + 11 + 12 + 14 + x + 20 + 22 = 117.
We then add up all known numbers:
100 + x = 117,
and by subtracting 100 from both sides, we find that x = 17.
Therefore, the value of x is 17, for the mean of the set to be 1 more than its median of 12.