Math Problem Statement
Class Interva2.docx
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solve for the mean, ungrouped and grouped data
Solution
The mean (or average) is a measure of central tendency that represents the sum of all values divided by the number of values. The method of calculating the mean differs for ungrouped and grouped data.
1. Mean for Ungrouped Data
For ungrouped data (raw data), the mean is calculated using the formula:
Where:
- = mean
- = each individual data value
- = number of values in the dataset
Example 1:
Find the mean of the numbers: 5, 8, 12, 10, 15.
The mean is 10.
2. Mean for Grouped Data
For grouped data, the mean is calculated using:
Where:
- = frequency of each class
- = midpoint of each class (found by )
Example 2:
Find the mean for the following frequency distribution:
Class Interval | Frequency () |
---|---|
1 - 5 | 3 |
6 - 10 | 5 |
11 - 15 | 4 |
-
Find the midpoints ():
Class Interval Frequency () Midpoint () 1 - 5 3 3 × 3 = 9 6 - 10 5 5 × 8 = 40 11 - 15 4 4 × 13 = 52 -
Compute the mean:
The mean is 8.42.
Do you need further details or have any questions?
Here are some related questions to deepen your understanding:
- How is the mean different from the median and mode?
- How do you handle missing values when calculating the mean?
- What are the advantages and disadvantages of using the mean?
- How do you calculate the mean from a histogram?
- What happens to the mean if an outlier is added to the data?
Tip: In grouped data, always ensure midpoints are correctly calculated before computing the mean.
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Math Problem Analysis
Mathematical Concepts
Statistics
Measures of Central Tendency
Mean Calculation
Formulas
Mean for Ungrouped Data: x̄ = (Σxi) / n
Mean for Grouped Data: x̄ = (Σfx) / (Σf)
Theorems
-
Suitable Grade Level
Grades 6-10
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