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Statistics, STD2 2026 HSC 26

A dataset consists of four whole numbers: \(X,Y,34\) and \(Z\), where

  • \(X,Y,34\) and \(Z\) are in ascending order, and
  • \(Z=X+38\).

The median of this dataset is 26 and the mean is 28.

What is the value of \(X\)?   (3 marks)

Show Answers Only

\(X=11\)

Show Worked Solution

\(\text{Since the median = 26:}\)

\(\dfrac{Y+34}{2}\) \(=26\)  
\(Y+34\) \(=26 \times 2\)  
\(Y\) \(=54-34=18\)  

 
\(\text{Since the mean = 28 and }\ Z=X+38\):

\(\dfrac{X+18+34+(X+38)}{4}\) \(=28\)
\(2X+90\) \(=112\)
\(2X\) \(=112-90\)
\(X\) \(=11\)