Answer to Question #155421 in Statistics and Probability for Lauren

Question

Four numbers have a median of 30, a mode of 50 and a mean of 29. What are the numbers?

Answer 1

Four numbers: a, b, c, d.

A mode of 50, so at least two values will be 50.

Let a=50, b=50

A median of 30, so

$\frac{b+c}{2}=30 \\ b + c = 60 \\ 50 + c = 60 \\ c = 10$

A mean of 29, so

$\frac{a+b+c+d}{4}=29 \\ a+b+c+d = 116 \\ 50 + 50 + 10 + d = 116 \\ d = 6$

Answer: 50, 50, 10, 6.