Math Problem Statement
Solution
Based on the image, we have a frequency distribution table for grouped data. The intervals for the data are given along with their respective frequencies. The task is to determine:
- Mean
- Median
- Mode
Steps to Solve:
1. Mean (Rata-rata):
We use the formula for the mean of grouped dataBased on the image, we have a frequency distribution table for grouped data. The intervals for the data are given along with their respective frequencies. The task is to determine:
- Mean
- Median
- Mode
Steps to Solve:
1. Mean (Rata-rata):
We use the formula for the mean of grouped Where:
- is the frequency for each group.
- is the midpoint of each group (calculated as the average of the class boundaries).
2. Median (Median):
For grouped data, the formula for the median is: Where:
- is the lower boundary of the median class.
- is the total number of observations.
- is the cumulative frequency of the class preceding the median class.
- is the frequency of the median class.
- is the class width.
3. Mode (Modus):
For grouped data, the mode is calculated using the formula: Where:
- is the lower boundary of the modal class.
- is the frequency of the modal class.
- is the frequency of the class before the modal class.
- is the frequency of the class after the modal class.
- is the class width.
Let's first compute the class midpoints and proceed with the calculations. I'll do that now.
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Math Problem Analysis
Mathematical Concepts
Statistics
Frequency Distribution
Mean
Median
Mode
Formulas
Mean: (Σf_i * x_i) / Σf_i
Median: L + [(n/2 - CF) / f] * h
Mode: L + [(f_1 - f_0) / ((f_1 - f_0) + (f_1 - f_2))] * h
Theorems
Grouped Data Statistical Theorems
Suitable Grade Level
Grades 9-12