If the mode of the following data is 13, find the value of \(p\).
13, 7, 11, \(2p-1\), 13, 12, 12, 18, 14, 16
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 7
The mode is the value that occurs most often. Without the unknown term, 13 and 12 each occur twice, so 13 becomes the only mode only if the unknown term is also 13.
Known values: 13 twice, 12 twice, every other value once
For 13 to occur most often: \(2p-1=13\)
\(2p=14\), so \(p=7\)
Check: with \(p=7\), 13 occurs three times and 12 only twice
The value of \(p\) is 7.