Math Problem Statement
Solution
To find the median of a frequency distribution, we need to determine the cumulative frequency and then locate the median class.
Step-by-Step Solution:
1. Organize the Data
Given dataTo find the median of a frequency distribution, we need to determine the cumulative frequency and then locate the median class.
Step-by-Step Solution:
1. Organize the Data
Given
- Values (x): 2, 4, 6, 8, 10
- Frequencies (f): 12, 8, 5, 1, 2
2. Calculate the Total Frequency (N)
Sum of all frequencies:
3. Find the Cumulative Frequency (cf)
The cumulative frequency table is:
- For :
- For :
- For :
- For :
- For :
4. Determine the Median Position
The median position in the cumulative frequency is at .
5. Identify the Median Class
We look for the cumulative frequency that reaches or just exceeds 14. In this case:
- for
- for
Since 14 lies between 12 and 20, the median class corresponds to .
Answer
The median value is:
Would you like more details on the calculation steps or have further questions?
Related Questions
- How would you find the mode in a frequency distribution?
- How is the median different from the mean in a data set?
- What is the importance of cumulative frequency in statistics?
- How would you calculate the median if the data had an odd total frequency?
- Can the median be a non-integer in frequency distributions?
Tip
For frequency distributions, the median class is identified based on cumulative frequency, rather than raw frequency values.
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Math Problem Analysis
Mathematical Concepts
Statistics
Frequency Distribution
Cumulative Frequency
Median
Formulas
Median position = N/2
Cumulative frequency
Theorems
-
Suitable Grade Level
Grades 8-10