Math Problem Statement
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
Solution
To calculate the mean value of from the given data, we follow these steps:
Step 1: Multiply each value of by its corresponding number of occurrences.
This gives us the total contribution of each group to the overall sum.
Step 2: Divide the total sum by the total number of groups (200) to get the mean value of .
So, the mean number of people wearing glasses in each group is .
Would you like more details, or do you have any questions?
Here are some related questions to deepen your understanding:
- How would you calculate the variance and standard deviation for this data?
- What is the mode of the number of people wearing glasses based on this data?
- What is the median number of people wearing glasses in these groups?
- How would you graph this data as a probability distribution?
- 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.
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Math Problem Analysis
Mathematical Concepts
Statistics
Mean
Data Distribution
Formulas
Mean = (Sum of x * occurrences) / Total number of occurrences
Theorems
-
Suitable Grade Level
Grades 8-10
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