Correct Answer - Option 4 : 28
Given:
The mean of three numbers = 21.
Range = 12
Difference between the two smallest numbers = 3
Formula used:
Mean = (sum of observations)/(number of observations)
Range = (Highest observation) - (lowest observation)
Calculation:
Let the three numbers be x, y and z.
Where x be the smallest number and z be the greatest number.
According to the question,
Mean = (sum of observations)/(number of observations)
⇒ 21 = (x + y + z)/3
⇒ x + y + z = 63 .....(1)
The range of this data set is 12,
Range = Highest observation - lowest observation
z – x = 12
⇒ z = 12 + x .....(2)
Difference between the two smallest numbers = 3
y – x = 3
⇒ y = 3 + x ....(3)
Using Equation(2) and (3) in (1) we get
x + (3 + x) + (12 + x) = 63
⇒ 3x + 15 = 63
⇒ 3x = 63 – 15
⇒ 3x = 48
⇒ x = 16
Putting the value of x in (3),
y = 3 + 16 = 19
Putting the value of x in (2),
z = 12 + 16 = 28
∴The greatest of three numbers is 28.
