Statistika | Ukuran Pemusatan Data (Mean, Modus, Median) untuk Data Kelompok

Introduction

This tutorial will guide you through the methods of calculating central tendency measures—mean, median, and mode—specifically for grouped data. Understanding these concepts is essential for interpreting statistical data effectively, making it a crucial skill in fields such as research, business analytics, and social sciences.

Step 1: Create a Grouped Frequency Distribution Table

• Start by organizing your raw data into a frequency distribution table. This involves:
  • Defining intervals: Choose the range of values and decide on the class intervals (e.g., 0-10, 11-20).
  • Counting frequencies: Tally how many data points fall into each interval.

Example of a simple frequency table:

| Interval | Frequency |
|----------|-----------|
| 0-10    |     5     |
| 11-20   |     8     |
| 21-30   |     7     |

Step 2: Calculate the Mean of Grouped Data

• To find the mean, follow these steps:

  1. Determine midpoints: For each interval, calculate the midpoint (e.g., for 0-10, the midpoint is (0+10)/2 = 5).
  2. Multiply midpoints by frequencies: Create a new column for midpoint * frequency.
  3. Sum the products: Add up all the products from the previous step.
  4. Sum the frequencies: Add all the frequencies together.
  5. Apply the formula: Use the formula for the mean:

  [ \text{Mean} = \frac{\sum (midpoint \times frequency)}{\sum frequency} ]

Step 3: Calculate the Median of Grouped Data

• To find the median, you will need to:

  1. Find the cumulative frequency: Create a cumulative frequency column by adding the frequencies cumulatively.
  2. Locate the median class: Determine the median position using the formula:

  [ \text{Median position} = \frac{N}{2} \quad (N = \text{total frequency}) ] 3. Identify the median class: The median class is the first class where the cumulative frequency is greater than or equal to the median position. 4. Use the median formula:

  [ \text{Median} = L + \left(\frac{\frac{N}{2} - CF}{f}\right) \times c ] Where:

  • (L) = lower boundary of the median class
  • (CF) = cumulative frequency of the class before the median class
  • (f) = frequency of the median class
  • (c) = class width

Step 4: Calculate the Mode of Grouped Data

• To find the mode, follow these steps:

  1. Identify the modal class: Look for the class with the highest frequency.
  2. Use the mode formula:

  [ \text{Mode} = L + \left(\frac{f_1 - f_0}{(2f_1 - f_0 - f_2)}\right) \times c ] Where:

  • (L) = lower boundary of the modal class
  • (f_1) = frequency of the modal class
  • (f_0) = frequency of the class before the modal class
  • (f_2) = frequency of the class after the modal class
  • (c) = class width

Conclusion

In this tutorial, you learned how to create a grouped frequency distribution table and calculate the mean, median, and mode for grouped data. These statistical measures are fundamental in data analysis, helping summarize and interpret data sets. As a next step, practice applying these techniques to real-world data to strengthen your understanding.