Groups of six people are chosen at random and the number,
x
, of people in each group who normally wear glasses is recorded. The table gives the results from 200 groups.
Number wearing glasses,
x
0	  1	  2	  3	  4	5	6
Number of occurrences
17	53	65	45	18	2	0
a.
Calculate, from the above data, the mean value of
x

To calculate the mean value of \( x \) from the given data, we follow these steps:

### Step 1: Multiply each value of \( x \) by its corresponding number of occurrences.
This gives us the total contribution of each group to the overall sum.

\[
\text{Sum of } x = (0 \times 17) + (1 \times 53) + (2 \times 65) + (3 \times 45) + (4 \times 18) + (5 \times 2) + (6 \times 0)
\]

\[
= 0 + 53 + 130 + 135 + 72 + 10 + 0
\]

\[
= 400
\]

### Step 2: Divide the total sum by the total number of groups (200) to get the mean value of \( x \).

\[
\text{Mean value of } x = \frac{400}{200} = 2
\]

So, the mean number of people wearing glasses in each group is \( \boxed{2} \).

Would you like more details, or do you have any questions?

Here are some related questions to deepen your understanding:

1. How would you calculate the variance and standard deviation for this data?
2. What is the mode of the number of people wearing glasses based on this data?
3. What is the median number of people wearing glasses in these groups?
4. How would you graph this data as a probability distribution?
5. How could this data be modeled using a binomial distribution?

**Tip:** The mean of a data set gives a measure of the central tendency, but other statistics like variance or standard deviation provide insights into the spread of the data.

Groups of six people are chosen at random and the number, x, of people in each group who normally wear glasses is recorded. The table gives the results from 200 groups.
Number wearing glasses, x: 0  1  2  3  4  5  6
Number of occurrences: 17  53  65  45  18  2  0

Calculate, from the above data, the mean value of x.

This page provides a detailed solution to calculate the mean number of people who wear glasses in randomly selected groups of six. Based on a dataset from 200 groups, the solution demonstrates how to compute the mean value using a statistical approach. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation