Given the set of numbers (3, 5, 7, 11, 23), what number must be added to the set so that the median of the 6 numbers is 9? what number must be added to the set so that the mean of the 6 numbers is 9?

Easy

median is the number in the middle when they are arranged in increasing numerical order
example
1,2,3
median is 2 becaus it is in middle
1,4,6,7,8
6 is median

if you have an even amount then average the middle two
1,3,5,7
median is the mean of 3 and 5 which is 4

so

3,5,7,11,23
median is 7 right now
there are an odd amout of numbers
adding 1 will result in even
to find the median of even set of numbers, average the 2 middle ones
right now 7 is center
the mean of 5 and 7 is 6
the mean of 7 and 11 is 9
we want a mean of 9
so add any  number greater than or equal to 11
3,5,7,11,12,23 is one option
3,5,7,11,23,50 is another

mean is 9
mean is the average of them
x is the number to be added
6 numbers will be the set since there are 5 now and adding 1 will get 6
(3+5+7+11+23+x)/6=9
(49+x)/6=9
times both sides by 6
49+x=54
minus 49 both sides
x=5

the number added must be 5

to make the median of the 6 numbers 9, add any number greater than or equal to 11, such as 12 or 234

to make the mean 9, add 5 to the set