Restaurant Customer Frequency Table: A Step-by-Step Guide

Hey guys! Let's break down how to complete a frequency table, specifically one related to the number of siblings restaurant customers have. It's a common concept in statistics and is super helpful for understanding data distribution. We will analyze the data provided and fill in the missing values. It's like a puzzle, and we'll solve it together. We will start with a provided table and fill in the missing values. The table includes columns for the number of siblings (N.º de hermano), the absolute frequency (f_i), the cumulative frequency (F_i), and the relative frequency (h_i). Let's dive in! This is important for analyzing customer behavior and understanding the demographics of the restaurant's clientele. Understanding frequency tables is a fundamental skill in statistics, and it's applicable in many real-world scenarios, not just in restaurants, such as marketing strategies and inventory management. This exercise is perfect for learning the basics! It will help you grasp the meaning of each column and how they relate to each other. Get ready to flex those math muscles and analyze that data! So grab a pen and paper, and let's get started. We will learn how to calculate cumulative frequencies, missing absolute frequencies, and relative frequencies to build a complete table. The process involves simple arithmetic operations, making it easy to understand. We will go through each step in detail so that it becomes second nature for you. By completing this table, you'll gain valuable insights into the distribution of the number of siblings among restaurant customers.

Understanding the Frequency Table Components

Alright, before we get started, let's make sure we're all on the same page regarding the parts of our frequency table. Each column in the frequency table provides different information about the data. Let's briefly define each term to ensure we understand the table's structure. Understanding these components is critical to complete the table accurately and interpret the results correctly. These columns are essential for organizing, summarizing, and interpreting data effectively. So, let's explore them in detail.

• N.º de hermano (Number of Siblings): This column represents the number of siblings each customer has. It's the variable we're analyzing. This is our independent variable, which categorizes how many siblings each customer reports.

• f_i (Absolute Frequency): This column indicates how many customers have a specific number of siblings. It's the count of occurrences for each value in the 'Number of Siblings' column. Also known as the frequency, represents the raw counts or the number of times each value appears in the dataset. This tells us how many customers fall into each sibling category.

• F_i (Cumulative Frequency): This column shows the running total of the absolute frequencies. It represents the number of customers with that number of siblings or fewer. It's calculated by adding up the frequencies of all previous categories. We can understand the progressive totals by observing the cumulative frequency column. This gives us a better sense of the distribution of our data.

• h_i (Relative Frequency): This column represents the proportion or percentage of customers in each sibling category. It's calculated by dividing the absolute frequency (f_i) by the total number of customers. The relative frequency expresses each group's size relative to the entire sample size. It's useful for comparing the distribution across different datasets. This is essential for comparing the distribution across different datasets and provides insights into the proportional distribution of the data.

So there you have it! Those are the essential elements of our frequency table. We're now ready to use this understanding to fill in the missing information in our table!

Filling in the Missing Values

Okay, let's get down to the business of actually completing the table. We've got some missing values, represented by letters (a, b, and c). Our goal is to calculate these and fill in the blanks. We will start with what we know, and the table provided will be our guide. We need to use the relationships between absolute frequency, cumulative frequency, and relative frequency to figure out those missing numbers. Let's do this step by step. We'll start by filling in the 'a', 'b', and 'c' values in the provided table using our knowledge of frequency distributions. It's not as hard as it might seem! The values will be calculated using simple formulas and logic.

Step 1: Finding 'b' (Cumulative Frequency)

We know that F_i for the '1 sibling' row is 'b', and that the F_i for the '2 siblings' row is 28. Remember that the cumulative frequency is the running total of the absolute frequencies. If we work backward, we can find b. We also know the absolute frequency (f_i) for '1 sibling' is 9. Also, we know that the cumulative frequency (F_i) for '0 siblings' is 6. The cumulative frequency for the '1 sibling' category can be calculated by adding the absolute frequencies of '0 siblings' and '1 sibling':

• b = 6 + 9
• b = 15

So, 'b' is 15. The cumulative frequency for the customers with one or fewer siblings is 15.

Step 2: Finding 'a' (Absolute Frequency)

We know that the cumulative frequency for the '2 siblings' row is 28, and the cumulative frequency for the '3 siblings' row is 45. The absolute frequency for the '3 siblings' row ('a') can be calculated by subtracting the cumulative frequency for the '2 siblings' row from the cumulative frequency for the '3 siblings' row:

• a = 45 - 28
• a = 17

So, 'a' is 17. This means that 17 customers have 3 siblings.

Step 3: Finding 'c' (Cumulative Frequency)

We have the absolute frequency for the '4 siblings' row is 5. We also know that the cumulative frequency is 45 for the '3 siblings' row. To calculate 'c', we'll add the absolute frequency for '4 siblings' to the cumulative frequency for the '3 siblings' row. We can calculate 'c' by adding the absolute frequency for the '4 siblings' row to the cumulative frequency for the '3 siblings' row:

• c = 45 + 5
• c = 50

So, 'c' is 50. This means that 50 customers have 5 or fewer siblings. In other words, this gives us the total number of customers.

Step 4: Finding 'f_i' for 5 Siblings

We know that c is 50. Therefore the total number of customers is 50. The sum of all absolute frequencies must equal the total number of customers. Then we can calculate 'f_i' for the '5 siblings' row. The sum of the absolute frequencies (f_i) for 0, 1, 2, 3, and 4 siblings is 6 + 9 + 13 + 17 + 5 = 50, which is equal to the total number of customers, which is 50. The sum of all the f_i values must equal the total number of customers. So, we'll calculate the absolute frequency for the '5 siblings' row by using:

• 50 - (6+9+13+17+5) = 0

So, the absolute frequency for the '5 siblings' row is 0. This means that there are no customers with 5 siblings in this dataset.

Step 5: Finding 'h_i' (Relative Frequency)

To find the relative frequency (h_i), we'll need to divide each absolute frequency (f_i) by the total number of customers (50). The relative frequency is often expressed as a percentage. It is crucial for comparing the distribution across different datasets or samples.

• For 0 siblings: h_i = 6 / 50 = 0.12 or 12%
• For 1 sibling: h_i = 9 / 50 = 0.18 or 18%
• For 2 siblings: h_i = 13 / 50 = 0.26 or 26%
• For 3 siblings: h_i = 17 / 50 = 0.34 or 34%
• For 4 siblings: h_i = 5 / 50 = 0.10 or 10%
• For 5 siblings: h_i = 0 / 50 = 0.0 or 0%

Now, let's put all the results into the table. Here's our completed frequency table!

The Completed Frequency Table

Here's the completed table with all the values filled in:

There you have it! We've successfully completed the frequency table. Great job!

Conclusion: Understanding and Using Frequency Tables

Alright, we've reached the finish line! Guys, we've walked through the entire process of completing a frequency table. Now, you understand how to calculate missing values for absolute, cumulative, and relative frequencies. The restaurant now has a clearer picture of its customer's demographics. By using these tables, you can gather information about your customer base! Remember, frequency tables are not only for restaurants! They're used in various fields to analyze the distribution of data. They're valuable for various types of data analysis. I hope that this comprehensive guide helps you understand how to create and interpret frequency tables. Keep practicing, and you'll become a pro in no time! So, keep an eye out for opportunities to use these valuable skills.