Consider the four numbers a, b, c, d with a ≤ b ≤ c ≤ d, where a, b, c, d are integers. The mean of the four numbers is 4. The mode is 3. The median is 3. The range is 6. Find d

d = 2

Step-by-step 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