Math Problem Statement
vGroup
10-under 20
20-under 30
30-under 40
40-under 50
Frequency
55
77
99
44 approxiamte mean
Solution
To calculate the approximate mean for grouped data, we use the formula:
Where:
- is the frequency for each group.
- is the midpoint of each group (also called the class mark).
Step 1: Find the midpoints of each group.
- For the group "10-under 20": midpoint
- For the group "20-under 30": midpoint
- For the group "30-under 40": midpoint
- For the group "40-under 50": midpoint
Step 2: Multiply each midpoint by its corresponding frequency.
Step 3: Sum up the products and frequencies.
- Sum of products:
- Sum of frequencies:
Step 4: Calculate the approximate mean.
So, the approximate mean is 29.8.
Would you like more details or explanations on any part of this?
Here are 5 questions for deeper understanding:
- How is the midpoint calculated for each group?
- What if the frequency distribution had more groups, how would it affect the mean?
- How does this method compare to calculating the mean for ungrouped data?
- What happens if the class intervals were unequal?
- Can this method be used for non-numerical data?
Tip: Always ensure the intervals are consistent and the frequencies cover all data points for accurate calculations!
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Math Problem Analysis
Mathematical Concepts
Statistics
Grouped Data
Mean Calculation
Formulas
Mean = (∑(f * x)) / ∑f
Theorems
-
Suitable Grade Level
Grades 8-10
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