If the mode of the following data is 31, find the value of \(p\).
34, 29, \(2p-3\), 31, 34, 27, 31, 36
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 17
The mode is the value that occurs most often. Without the unknown term, 31 and 34 each occur twice, so 31 becomes the only mode only if the unknown term is also 31.
For 31 to occur most often: \(2p-3=31\)
So \(p=17\)
Check: with \(p=17\), 31 occurs 3 times and every other value fewer times
The value of \(p\) is 17.
Why the other options are incorrect
Option (1) 18 — Incorrect. The term would be 33; then 31 and 34 each occur 2 times, so 31 would not be the only mode.
Option (2) 16 — Incorrect. The term would be 29; then 29 and 31 and 34 each occur 2 times, so 31 would not be the only mode.
Option (4) 19 — Incorrect. The term would be 35; then 31 and 34 each occur 2 times, so 31 would not be the only mode.