Calculating SMK Budi Murni 2 Students' Average Score

Hey guys! Let's dive into a math problem involving the scores of 40 students from SMK Budi Murni 2. We're going to calculate the average score based on the frequency distribution provided. This is a classic problem in statistics, and understanding how to solve it is super useful. Knowing how to find the average, or mean, of a grouped frequency distribution is a fundamental skill, and we'll break it down step by step so you can totally nail it. Ready to get started? Let's do this!

Understanding the Problem: Frequency Distribution

First off, let's understand what we're dealing with. We're given a frequency distribution table. This table shows us the interval of scores and the frequency (how many students) fall into each score range. Here’s the data again:

Each row tells us about a group of scores. For example, 3 students scored between 60 and 64. 8 students scored between 65 and 69, and so on. Our goal is to find the average score for all 40 students. To do this, we'll need to find the midpoint of each interval, multiply it by its frequency, and then calculate the weighted average. It's all about taking into account how many students achieved each score range. Don't worry; it's not as complicated as it sounds. We'll take it one step at a time. So, let's roll up our sleeves and get to work!

Step-by-Step Calculation of the Average Score

Alright, here's how we find the average score. We'll break it down into easy-to-follow steps. This way, we make sure we don't miss a beat:

1. Find the Midpoint of Each Interval: The midpoint is the average of the upper and lower limits of each interval. It represents the 'typical' score within that range. To calculate this, we add the lower and upper bounds of the interval and divide by 2. For example, for the interval 60-64, the midpoint is (60 + 64) / 2 = 62. We'll do this for each interval. This is an important step. Why? Because when working with grouped data, the midpoint helps us represent the data in a more manageable format.
2. Multiply Midpoint by Frequency: For each interval, multiply the midpoint by its frequency. This gives us a weighted score for that interval. For example, for the interval 60-64, the midpoint is 62 and the frequency is 3, so the weighted score is 62 * 3 = 186. This step essentially calculates the total contribution of each score range to the overall average. The greater the frequency, the more weight that interval has in the average.
3. Sum the Weighted Scores: Add up all the weighted scores you calculated in the previous step. This gives you the total score for all students. This aggregated value will be used in the final stage of the calculation, where we divide the total scores by the total number of students.
4. Sum the Frequencies: Add up all the frequencies. This should equal the total number of students, which is 40 in our case. This step is essential for verification. It ensures that the total number of data points considered in the calculation matches the total student count, providing a sanity check for accuracy.
5. Calculate the Average: Divide the sum of the weighted scores (from step 3) by the sum of the frequencies (from step 4). This gives you the average score.

Let's put it all together in a table to make it super clear. This will make the whole process organized. Let's get to it, shall we?

Detailed Calculation Table

Here is the breakdown in a handy table:

Here’s how we got each column:

• Interval: The score ranges given in the problem.
• Frequency (f): The number of students in each interval.
• Midpoint (x): Calculated as (lower bound + upper bound) / 2 for each interval.
• f * x: The product of the frequency and the midpoint, giving us the weighted score for each interval.

To find the average, we use the formula: Average = Σfx / Σf. In our case, Σfx (sum of f*x) is 2940, and Σf (sum of frequencies) is 40.

Therefore, Average = 2940 / 40 = 73.5.

So, the average score of the 40 students is 73.5. Awesome job, guys!

Conclusion: The Average Score Revealed

So, we did it! The average score for the 40 students of SMK Budi Murni 2 is 73.5. That means, on average, each student scored about 73.5 on the test. We've taken the frequency data, calculated the midpoints, multiplied them by the frequencies, found the sums, and finally, calculated the average. This is a perfect illustration of how to work with grouped frequency data to find an average. Remember, understanding how to calculate an average from grouped data is a fundamental statistical skill. Knowing how to do this is super important, not just for math class, but also for understanding data in real-world situations. Pretty cool, right?

This method is widely used in various fields, from education to market research, whenever data is presented in a summarized format. Keep practicing these types of problems, and you'll get the hang of it in no time. Keep in mind that accuracy in calculations is key. Triple-check your numbers, and you will be absolutely fine. Great job, everyone! You've successfully calculated the average score. Keep up the excellent work!

I hope this helps you guys. If you have any more questions or want to try another example, let me know. Happy learning!