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