Question

1.3 displaying numerical data: dotplots

1. magic words here are data on the lengths of the first 25 words on a randomly selected page from harry potter and the prisoner of azkaban.

2 3 4 10 2 11 2 8 4 3 7 2 7
5 3 6 4 4 2 5 8 2 3 4 4
a. make a dotplot of these data.
b. explain what the dot above 6 represents.
c. what percent of the words have more than 4 letters?

Explanation:

Step1: Count the number of words with more than 4 letters

We go through the data: 2, 3, 4, 10, 2, 11, 2, 8, 4, 3, 7, 2, 7, 5, 3, 6, 4, 4, 2, 5, 8, 2, 3, 4, 4.
Words with more than 4 letters are: 10, 11, 8, 7, 7, 5, 6, 5, 8. Count them: there are 9 such words.

Step2: Calculate the percentage

The formula for percentage is $\frac{\text{Number of favorable cases}}{\text{Total number of cases}}\times100\%$.
Here, the total number of words \(n = 25\), and the number of words with more than 4 letters \(m=9\).
So the percentage \(P=\frac{9}{25}\times 100\%=(9\times4)\% = 36\%\)

Answer:

36%