Question

letter count number of words listed 4 letters 12 5 letters 49 6 letters 12 7 letters 9 8 letters 1 on a message board, participants listed words whose letters are all in alphabetical order, such as \almost\. the table lists the number of words they listed with each letter count. what was the median letter count of the words they listed?

Explanation:

Step1: Calculate the total number of words

Add up the number of words: \(12 + 49+12 + 0+1=74\)

Step2: Determine the position of the median

Since \(n = 74\) (even), the median is the average of the \(\frac{n}{2}=37\)th and \((\frac{n}{2}+ 1)=38\)th values.

Step3: Cumulative frequency

• For 4 - letter words: cumulative frequency \(=12\)
• For 5 - letter words: cumulative frequency \(=12 + 49=61\)

Since \(12<37\) and \(12<38<61\), both the 37th and 38th values correspond to 5 - letter words.

Answer:

5