This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Answer
30-39
Let's calculate the modal class and the median using the provided data.
First, here is the data table again:
| Age Group | Frequency () | Class Midpoint () | Cumulative Frequency () | | :-------- | :-------------- | :------------------- | :-------------------------- | | 10-19 | 6 | 14.5 | 6 | | 20-29 | 12 | 24.5 | 18 | | 30-39 | 15 | 34.5 | 33 | | 40-49 | 9 | 44.5 | 42 | | 50-59 | 5 | 54.5 | 47 | | 60-69 | 2 | 64.5 | 49 | | Total | | | |
2) Calculate the modal class.
Step 1: Identify the highest frequency in the table. The highest frequency is 15.
Step 2: Determine the class interval corresponding to the highest frequency. The frequency of 15 corresponds to the age group 30-39.
The modal class is .
3) Calculate the median.
Step 1: Find the total number of observations ().
Step 2: Determine the position of the median.
Step 3: Identify the median class. The median class is the first class whose cumulative frequency () is greater than or equal to the median position (24.5). From the table, the for 20-29 is 18, and for 30-39 is 33. Since 33 is the first greater than or equal to 24.5, the median class is 30-39.
Step 4: Identify the values for the median formula. • Lower boundary of the median class (): • Total frequency (): • Cumulative frequency of the class before the median class (): (for 20-29) • Frequency of the median class (): (for 30-39) • Class width (): (or )
Step 5: Apply the median formula for grouped data.
Step 6: Substitute the values and calculate.
The median is .
3 done, 2 left today. You're making progress.
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5 | 6 | | 20-29 | 12 | 24.5 | 18 | | 30-39 | 15 | 34.5 | 33 | | 40-49 | 9 | 44.5 | 42 | | 50-59 | 5 | 54.5 | 47 | | 60-69 | 2 | 64.5 | 49 | | Total | f = 49 | | | 2) Calculate the modal class.
This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.