Question

The following numerically ordered sequence of numbers has a mean of 19 and a median of 24.

3,a,10,13,22,b,27,27,28,30

Given this information, find the values of a and b.

a=?
b=?

Answer 1

a = 4

b = 26

Explanation:

median is the middle number(s)

middle numbers are 22 and b

if the median is 24 then

that means the average if 22 and b is 24

so do the math in reverse

22 and b are 2 numbers

24 * 2 = 48
22 + b = 48

48 - 22 = 26

b = 26

mean is average

so do the math in reverse

there are 10 numbers

the average or mean is 19

so all the numbers add up to 190

3+a+10+13+22+26+27+27+28+30 = 190

a + 186 = 190

a = 4