Math Problem Statement

Determine the mean, median, and mode based on the given frequency distribution table.

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:

  1. Mean
  2. Median
  3. 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:

  1. Mean
  2. Median
  3. Mode

Steps to Solve:

1. Mean (Rata-rata):

We use the formula for the mean of grouped Mean=fixifi\text{Mean} = \frac{\sum f_i x_i}{\sum f_i} Where:

  • fif_i is the frequency for each group.
  • xix_i 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: Median=L+(n2CFf)×h\text{Median} = L + \left( \frac{\frac{n}{2} - CF}{f} \right) \times h Where:

  • LL is the lower boundary of the median class.
  • nn is the total number of observations.
  • CFCF is the cumulative frequency of the class preceding the median class.
  • ff is the frequency of the median class.
  • hh is the class width.

3. Mode (Modus):

For grouped data, the mode is calculated using the formula: Mode=L+(f1f0(f1f0)+(f1f2))×h\text{Mode} = L + \left( \frac{f_1 - f_0}{(f_1 - f_0) + (f_1 - f_2)} \right) \times h Where:

  • LL is the lower boundary of the modal class.
  • f1f_1 is the frequency of the modal class.
  • f0f_0 is the frequency of the class before the modal class.
  • f2f_2 is the frequency of the class after the modal class.
  • hh 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