Question
Download Solution PDFThe mean of three numbers is 15. The range of this data set is 8 while the difference between the two smallest numbers is 1. The greatest of the three numbers is:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
The mean of the three numbers is 15.
The range of this data set is 8 while the difference between the two smallest numbers is 1.
Concept used:
1. Mean = Sum of observations ÷ Number of observations
2. Range = Highest observation - Lowest observation
Calculation:
Let the numbers be P, Q, and R (in ascending order).
According to the question,
R - P = 8
⇒ R = 8 + P ....(1)
Q - P = 1
⇒ Q = P + 1 ....(2)
(P + Q + R) = 15 × 3
⇒ P + (P + 1) + (8 + P) = 45 (From 1, 2)
⇒ 3P + 9 = 45
⇒ P = 12
So, R = 8 + 12 = 20
∴ The greatest of the three numbers is 20.
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