Question

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

Answer 1

Step-by-step explanation:

a=2

b=3

c=3

d=8

As mode and median are 3. We can assume to find the answer.

Answer 2

a = 2, b = 3, c = 3, d = 8

Given

• a ≤ b ≤ c ≤ d, where a, b, c, d ∈ Z

• The mean of the four numbers is 4.
• The mode is 3.
• The median is 3.
• The range is 6

To Find

Value of a, b, c, and d

Solution

We know that mean = 4

Mean = (sum of the values)/ No. of terms

(a + b + c + d)/4 = 4

or, a + b + c + d = 16

The number of terms here is 4, which is even.

Hence, Median = (n/2th term + n/2th+1 term)/2

i.e (2nd + 3rd term)/2

Since a ≤ b ≤ c ≤ d

The median will be (b + c)/2 = 3

or, b + c = 6  

Using this in the previous result we get

a + 6 + d = 16

or, a + d = 10

Now Range = highest term - lowest term

Here d - a =6

Adding this and the previous equation we get

2d = 16

or, d =8

Therefore,

a = 10 - 8

= 2

a=2

Mode is the value that occurs the most number of times.

Here, since the mode is 3, it has to occur at least twice.

Therefore, b=c=3
Therefore,

a = 2, b = 3, c = 3, d = 8

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