Answer:
d = 2
Explanation:
We have four unknown numbers a, b, c, d
It is given that the mode is 3,
Since the mode is 3 then at least two numbers are 3.
It is given that the median is 3,
Since the median is 3 which means the middle two values must be 3
a, 3, 3, d
It is given that the mean of the four numbers is 4,
Since the mean of the four number is 4 then
mean = (a + 3 + 3 + d)/4
4 = (a + 6 + d)/4
4*4 = a + 6 + d
16 = a + 6 + d eq. 1
It is given that the range is 6,
Since the range is 6 which is the difference between highest and lowest number that is
a - d = 6
a = 6 + d eq. 2
Substitute the eq. 2 into eq. 1
16 = a + 6 + d
16 = (6 + d) + 6 + d
16 = 12 + 2d
2d = 16 - 12
d = 4/2
d = 2
Substitute the value of d into eq. 2
a = 6 + d
a = 6 + 2
a = 8
so
a, b, c, d = 8, 3, 3, 2
Verification:
a ≤ b ≤ c ≤ d
8 ≤ 3 ≤ 3 ≤ 2
mean = (a + b + c + d)/4
mean = (8 + 3 + 3 + 2)/4
mean = 16/4
mean = 4
range = a - d
range = 8 - 2
range = 6