Question

The highest score of a certain data exceeds the lowest score by 16 and the coefficient of range is \[\dfrac{1}{3}\]. The sum of the highest score and the lowest score is?

Answer 1

Hint: In this problem, we are given that the highest score of a certain data exceeds in lowest score by 16 and coefficient of range is \[\dfrac{1}{3}\]and we have to find the sum of highest score and the lowest score. We can now assume the highest score as h and the lowest score as l. We can now write the given condition. We can then substitute the given coefficient of range in its formula \[\dfrac{h-l}{h+l}\], we can then solve and find the value of h and l and add them to get the answer.

Complete step by step answer:
Here we are given that the highest score of a certain data exceeds the lowest score by 16 and the coefficient of range is \[\dfrac{1}{3}\]and we have to find the sum of the highest score and the lowest score.
We can now assume the highest score as h and the lowest score as l.
We can see that, the given condition is
\[\Rightarrow h=16+l\] ……. (1)
We know that coefficient of range formula is \[\dfrac{h-l}{h+l}\] and the given coefficient of range is \[\dfrac{1}{3}\], we can now write it as
\[\begin{align}
  & \Rightarrow \dfrac{h-l}{h+l}=\dfrac{1}{3} \\
 & \Rightarrow 3h-3l=h+l \\
 & \Rightarrow 2h-4l=0......(2) \\
\end{align}\]
We can now substitute (1) in (2), we get
\[\begin{align}
  & \Rightarrow 2\left( 16+l \right)-4l=0 \\
 & \Rightarrow 32+2l-4l=0 \\
 & \Rightarrow l=16..........(3) \\
\end{align}\]
We can now substitute (3) in (1), we get
\[\begin{align}
  & \Rightarrow h=16+16 \\
 & \Rightarrow h=32 \\
\end{align}\]
We can now add the value of h and l, we get
\[\Rightarrow h+l=32+16=48\]
Therefore, the sum of the highest score and the lowest score is 48.

Note: We should always remember that the coefficient of the range formula is \[\dfrac{h-l}{h+l}\]. We should know how and where to apply the given conditions to solve it step by step and to find the required answer. We should find the unknown variable values using the given condition and then we can solve for the required sum.