Statistika Bagian 2 - Menghitung Mean Data Tunggal dan Data Kelompok Matematika Wajib Kelas 12

Introduction

In this tutorial, we will learn how to calculate the mean (average) of both single data sets and grouped data using various methods. Understanding how to compute the mean is essential in statistics, especially for students in grade 12. This guide will cover the following methods: the ordinary method, the average deviation method, and the coding method.

Step 1: Calculate the Mean Using the Ordinary Method

1. Gather Your Data: Collect all the data points you want to analyze.
2. Sum the Data Points: Add all the values together.
   • Example: If your data set is 4, 5, 8, the sum is ( 4 + 5 + 8 = 17 ).
3. Count the Data Points: Determine how many data points are in your set.
   • In the example above, there are 3 data points.
4. Divide the Total by the Count: Calculate the mean by dividing the total sum by the number of data points.
   • Formula: Mean = Total Sum / Number of Data Points
   • Using our example: Mean = ( 17 / 3 \approx 5.67 ).

Step 2: Calculate the Mean Using the Average Deviation Method

1. Calculate the Mean: First, find the mean using the ordinary method as described above.
2. Find the Deviation: Subtract the mean from each data point to find the deviation.
   • Example: For the mean 5.67, deviations are ( 4 - 5.67 = -1.67 ), ( 5 - 5.67 = -0.67 ), and ( 8 - 5.67 = 2.33 ).
3. Sum the Absolute Deviations: Add the absolute values of the deviations.
   • Sum = ( |-1.67| + |-0.67| + |2.33| = 1.67 + 0.67 + 2.33 = 4.67 ).
4. Calculate the Average Deviation: Divide the total absolute deviation by the number of data points.
   • Average Deviation = Total Absolute Deviation / Number of Data Points
   • Example: ( 4.67 / 3 \approx 1.56 ).

Step 3: Calculate the Mean Using the Coding Method

1. Select a Base Value: Choose a convenient base value (often the mean value of the data set).
2. Calculate Deviations from the Base: For each data point, subtract the base value to find the deviation.
3. Transform the Data: Add a constant to each deviation if necessary.
4. Calculate the Mean of Deviated Values: Use the formula:
   • Mean = Base Value + (Sum of Deviations / Number of Data Points)
5. Example: If the base value is 5 and deviations are -1, 0, +3:
   • Sum of Deviations = -1 + 0 + 3 = 2.
   • Mean = 5 + (2 / 3) ≈ 5.67.

Conclusion

In this tutorial, we discussed three methods to calculate the mean of data sets: the ordinary method, the average deviation method, and the coding method. Each method has its own application and can be useful depending on the data set you are dealing with. Practice these methods using different data sets to become proficient in calculating means. For further study, consider exploring additional statistical concepts such as median, mode, and standard deviation, which are crucial for a comprehensive understanding of statistics.