Ask Question
25 February, 10:37

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

+1
Answers (1)
  1. 25 February, 10:58
    0
    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
Know the Answer?
Not Sure About the Answer?
Get an answer to your question ✅ “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. ...” in 📙 Mathematics if there is no answer or all answers are wrong, use a search bar and try to find the answer among similar questions.
Search for Other Answers