Math Problem Statement
Solution
The image contains a frequency distribution table with cumulative frequencies (C.F.) and the median calculation using the formula for grouped data. Here's a breakdown of the steps:
Given Data:
Age | No. of Persons | C.F. |
---|---|---|
0-10 | 5 | 5 |
10-20 | 25 | 30 |
20-30 | ||
30-40 | 18 | |
40-50 | 7 |
- Total .
- Median is 24, which corresponds to the class interval .
Formula for Median:
Where:
- (Lower boundary of the median class),
- (Total frequency),
- (Cumulative frequency before the median class),
- (Class width),
- (Frequency of the median class).
Median Calculation:
Using the formula:
Simplify and solve for .
Let me calculate that.The value of is 25. Therefore, the frequency of the 20-30 age group is 25.
Would you like further details on the steps or any clarifications?
Here are five related questions for further practice:
- What would happen to the median if the value of were different?
- How do you calculate the mean from a frequency distribution like this one?
- What if you were asked to calculate the mode instead of the median?
- How would you compute the quartiles from this data?
- How would you adjust the class intervals if the number of persons changed?
Tip: Always check if the total cumulative frequency is consistent with the sum of individual frequencies for accuracy.
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Math Problem Analysis
Mathematical Concepts
Statistics
Frequency Distribution
Median for Grouped Data
Formulas
Median = L + ((N / 2) - C.F.) * (h / f)
Theorems
Median for Grouped Data Theorem
Suitable Grade Level
Grades 11-12
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