What is the distribution of wand lengths?

Based on the known wands in the Wizarding World we can come up with the following information:

• Max Length: 18"
• Min Length: 7"
• Average Length: 10.92" (not an actual wand length because wands lengths are in 1/4" increments)
• Median Length: 10.375" (not an actual wand length because wands lengths are in 1/4" increments)
• Mode Length: 9"

So with the mode length, which is most commonly occurring number, the answer to your question would be 9". However, when taking into account the distribution, you are probably going to get wand greater than 9".

A wizard is most likely to receive a wand between 9.00" and 11.50" which account for ~62% (26/42) of all wands. The most common range of wands is 10" or greater but less than 12" (10.00" to 11.75"), accounting for ~38% (16/42). This matches up nicely to Ollivanders own comments on the matter:

Most wands will be in the range of between nine and fourteen inches. While I have sold extremely short wands (eight inches and under) and very long wands (over fifteen inches), these are exceptionally rare.

^{Wand Lengths & Flexibility by J.K. Rowling on Wizarding World}

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There are 42 wands for which the length is mentioned at some point in the series.

_{*Note on lengths: Some of the lengths are derived directly from text of the books or similar written canon (interviews, games, etc.) but others are taken from the measurement of the props in the films. The prime example being Lucius' 18" wand.}

• 18.00" - 1 - Lucius Malfoy
• 16.00" - 1 - Rubeus Hagrid
• 15.00" - 1 - Albus Dumbledore (The Elder Wand)
• 14.00" - 2 - Ron Weasley (2nd wand), Player Choice in Hogwarts: Mystery
• 13.50" - 1 - Tom Riddle
• 12.75" - 2 - Bellatrix Lestrange, Garrick Ollivander
• 12.25" - 1 - Cedric Diggory
• 12.00" - 3 - Charlie Weasley (passed down as Ron's 1st), 2 Player Choices in Hogwarts: Mystery
• 11.50" - 1 - Silvanus Kettleburn
• 11.25" - 2 - Player Choices in Hogwarts: Mystery
• 11.00" - 4 - Harry Potter, James Potter, 2 Player Choices in Hogwarts: Mystery
• 10.75" - 1 - Hermione Granger
• 10.50" - 1 - Celestina Warbeck
• 10.25" - 4 - Horace Slughorn, Lily Potter nee Evans, Remus Lupin, Viktor Krum
• 10.00" - 3 - Draco Malfoy, Snatcher's Wand (used by Harry), Jacob (character from Hogwarts: Mystery)
• 9.50" - 3 - Fleur Delacour, Minerva McGonagall, Sybill Trelawney
• 9.25" - 2 - Peter Pettigrew, Ron Weasley (after he took it from Peter; note: this is the same wand... may need to take it out and recalculate)
• 9.00" - 5 - Gilderoy Lockhart, Quirinus Quirrell, Sir Cadogan, 2 wands made by Ollivander but never given to a character
• 8.75" - 1 - Mary Cattermole
• 8.50" - 1 - Made by Ollivander but never given to a character
• 8.00" - 1 - Dolores Umbridge
• 7.00" - 1 - Made by Ollivander but never given to a character