Relative Frequency Of Score 18: Calculation Guide
Hey guys! Let's dive into calculating the relative frequency of a score, specifically the score 18, from a given set of final grades. This is a fundamental concept in statistics, and understanding it can help you interpret data in many real-world scenarios. So, let's break it down step-by-step!
Understanding Relative Frequency
First off, what exactly is relative frequency? Simply put, it's the proportion of times a specific value appears in a dataset compared to the total number of values. You can think of it as the probability of encountering that value within the dataset. In mathematical terms, relative frequency (often denoted as hn) is calculated using this formula:
hn = (Number of times the value appears) / (Total number of values)
This gives us a decimal value, which can also be expressed as a percentage if you multiply it by 100. Relative frequency is super useful because it gives us a sense of how common or rare a particular value is within a set of data. For example, in our case, calculating the relative frequency of the score 18 will tell us how often this score appeared compared to all the other scores in the final grades.
Knowing the relative frequency helps in various ways. In education, like our example, it can indicate how many students achieved a particular grade. In market research, it might show how many customers prefer a certain product. In weather forecasting, it could represent the likelihood of a specific temperature on a given day. The possibilities are endless, making relative frequency a powerful tool in data analysis. To really grasp the concept, it's essential to practice with different datasets and understand how the numbers translate into real-world insights. Remember, relative frequency bridges the gap between raw data and meaningful information, allowing us to make informed decisions based on evidence.
Identifying the Data Set and Target Value
Before we jump into the calculation, let's clearly identify our dataset and the specific value we're interested in. Our dataset consists of the final grades: |18|20|14|13|17|18|16|20|15|19|20|20|17|. These are the numbers we'll be working with. The target value, the one we want to find the relative frequency for, is 18. This is crucial because the entire calculation revolves around this value.
The first step in calculating any statistical measure is always to know your data. We need to be absolutely clear on what numbers we are dealing with and what specific piece of information we are trying to extract. In our case, the grades represent the performance of students in a class, and we are specifically interested in how frequently the score of 18 appears. This could be relevant for several reasons. Maybe the teacher wants to know how many students scored exactly 18, or perhaps they want to compare the frequency of this score with other scores like 20 or 15.
Understanding the context of the data is also incredibly important. Are these scores out of 20? Are they percentages? Knowing these details helps us interpret the results more accurately. For instance, if the scores are out of 20, then 18 is a pretty good score, but if they are percentages, then 18 might indicate a need for improvement. Data in isolation is just numbers; context transforms it into meaningful information. So, let's keep our focus sharp: we have our dataset of grades, and our mission is to find out how often the score 18 shows up relative to the rest of the scores.
Step-by-Step Calculation
Alright, let's get down to the nitty-gritty and calculate the relative frequency of the score 18. We'll break it down into simple steps so it's super easy to follow.
Step 1: Count the occurrences of the target value.
First, we need to count how many times the score 18 appears in our dataset. Looking at the grades |18|20|14|13|17|18|16|20|15|19|20|20|17|, we can see that 18 shows up twice. So, the number of times the value 18 appears is 2.
Step 2: Determine the total number of values in the dataset.
Next, we need to figure out the total number of grades in our dataset. We simply count all the numbers listed: |18|20|14|13|17|18|16|20|15|19|20|20|17|. There are 13 grades in total.
Step 3: Apply the formula for relative frequency.
Now, we use the formula we discussed earlier:
hn = (Number of times the value appears) / (Total number of values)
Plugging in our numbers, we get:
hn = 2 / 13
Step 4: Calculate the result and round to two decimal places.
Performing the division, 2 divided by 13, gives us approximately 0.1538. The question asks us to round the answer to a maximum of two decimal places. So, we round 0.1538 to 0.15.
And that's it! We've calculated the relative frequency. Each step is straightforward, but it's essential to understand the logic behind it. The key is to accurately count the occurrences and the total values and then apply the formula correctly. With practice, these calculations will become second nature, and you'll be a pro at understanding data in no time!
Final Answer
So, after all that calculating, we've arrived at our final answer. The relative frequency (hn) of the score 18 in the given dataset, rounded to two decimal places, is 0.15. This means that the score 18 appeared about 15% of the time in the final grades.
It's always a good idea to double-check your work, especially in statistics, where small errors can lead to significant misinterpretations. We've carefully counted the occurrences of 18, determined the total number of values, applied the formula, and rounded our result appropriately. We're confident in our answer!
Understanding what this number means in context is just as important as the calculation itself. A relative frequency of 0.15 for the score 18 gives us a sense of how common this score was compared to others. If we were to compare this with the relative frequencies of other scores, like 20 or 17, we could get a better picture of the overall distribution of grades in the class.
Interpreting the results in a meaningful way is the ultimate goal of any statistical calculation. Numbers are just numbers until we give them context and use them to understand the world around us. So, there you have it – the relative frequency of the score 18 is 0.15, and we know exactly what that means. Nice work, guys! You've nailed it!
