Subject: mean median and mode Name: rick
Question: Hi Rick,
Since the median is the middle number when they are sorted from smallest to largest, the middle number is zero. If zero appears twice in the list then, since the mode is larger than zero, the other three numbers must all have the same valus and be larger than zero. In this case the mean could not be zero. Thus zero must appear exactly once in the list of five numbers.
where k, m and n are positive integers (possibly all equal). Since the mean is zero
k + m + n = 4 Since the sum of the absolute values is 20
k + m + n = 16 This is clearly impossible so there must be exactly two of the numbers that are greater than zero, and since the mode is greater than zero these two numbers must have the same value. Hence the five numbers must be
where a, b, and c are positive integers.
a + b = 2c Since the sum of the absolute values is 20
But a + b = 2c so 4c = 20, that is c = 5. Also a + b = 10 and -b is 4 more than -a so the four numbers are
Cheers, |