Question

1. number of cavities in a dental survey of third - grade students, this distribution was obtained for the number of cavities found. find the average number of cavities for the class. use the weighted mean.

number of students number of cavities
12 0
8 1
5 2
5 3
8

Explanation:

Step1: Calculate the sum of products

The formula for the weighted mean is \(\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}f_{i}}{\sum_{i = 1}^{n}f_{i}}\). Here \(x_{i}\) represents the number of cavities and \(f_{i}\) represents the number of students.

$$
LATEXBLOCK0
$$

Step2: Calculate the total number of students

$$ \sum_{i = 1}^{n}f_{i}=12 + 8+5 + 5=30 $$

Step3: Calculate the weighted mean

$$ \bar{x}=\frac{\sum_{i = 1}^{n}x_{i}f_{i}}{\sum_{i = 1}^{n}f_{i}}=\frac{33}{30}=1.1 $$

Answer:

The average number of cavities for the class is \(1.1\)