Organizing Data A Guide to Frequency Tables

organizing data will help us make sense of information and draw meanings.

When tabulating qualitative data, we only deal with non-measurable values. And for quantitative data, it is numerical and measurable.

1. Types of Data and Frequency Tables Qualitative Data Qualitative data focuses on descriptions, categories, and attributes that can't be measured numerically. Think of it as describing qualities rather than quantities. For example, colors, types of fruits, or opinions. Quantitative Data Quantitative data involves numerical measurements and values, providing quantifiable information. Examples include heights, weights, temperatures, or test scores.

2. Qualitative Frequency Table Purpose Summarize qualitative data, displaying categories and their frequencies. This makes it easy to see how often each category appears in a dataset.

3. Construction Create a table with two columns: one for categories and one for frequencies. Use tally marks to count occurrences of each category, then convert these tallies into numerical frequencies. Example Consider a survey on favorite ice cream flavors. A qualitative frequency table would list the flavors and the number of times each flavor was chosen.

4. Quantitative Frequency Tables 1 Ungrouped Data Each data point is listed individually, providing a detailed view of the raw data. 2 Grouped Data Data is organized into intervals , with each interval containing a range of values. Useful for large datasets or when focusing on trends. For the second type table that uses quantitative data is called the Frequency Distribution Table .  is a way of summarizing a set of data. One labelled with categories, and the other with the corresponding frequency.

5. Ungrouped Frequency Distribution Table Small Datasets Suitable for datasets with n < 30 data points, and individual data points are important. Detailed View Best for datasets with n>30 and it provides a precise overview of each data point's frequency, allowing for detailed analysis. Example The number of candies sold everyday is 5, 12, 13, 8, 17, 20 Example of Table

6. Grouped Frequency Tables 1 Large Datasets Ideal for datasets with many data points, making analysis more manageable. 2 Identifying Trends Helps visualize patterns and trends in the data, revealing distributions and outliers. 3 Example Interval Frequency 0 – 10 5 11 – 20 8 21 – 30 12 31 – 40 2 41 – 50 17

7. Choosing the Right Type of Frequency Table Data Type Dataset Size Analytical Goals

8. Example #1 Qualitative Data we interviewed 15 students of the University in the Cordilleras. Student Gender Year Major 1 Male 1 st English 2 Male 2 nd Pol-Sci 3 Female 1 st Psych 4 Female 1 st Art 5 Female 3 rd Biology 6 Male 2 nd Math 7 Female 3 rd Crim 8 Female 4 th Psych 9 Male 4 th English 10 Male 1 st Pol-Sci 11 Female 3 rd Art 12 Female 3 rd Biology 13 Male 2 nd English 14 Female 3 rd Math 15 Male 2 nd Crim

9. Example #2 Below are the results of a survey about the favorite colors of 10 students in a Grade-7 class. What color is the most favorite and least favorite color of the students? Green Purple Yellow Purple Blue Red Green Red Red Yellow Colors Tally Frequency Green II 2 Orange I 1 Yellow II 2 Red III 3 Purple II 2 TOTAL 10

10. In creating a Frequency Distribution Table, the first that we need to do is: 1) Make a table with suitable number of rows and columns 2) Fill the suitable headings in the 1st column and the 1st row 3) Lastly, fill the collected data in the box. Age Age Tally Frequency Age Tally Frequency 18 IIII 5 20 IIII - III 8 21 IIII – IIII – II 12 24 II 2 46 IIII – IIII – IIII - II 17

11. Let’s try quantitative data Example #3 Let say that we have data of the scores of Grade-6 students. 59 13 28 39 25 46 63 62 22 68 23 34 45 46 38 13 23 25 28 28 39 39 39 39 45 46 46 49 52 53  We can sort them if the data is manageable

12. Example #2 13 23 25 28 28 39 39 39 39 45 46 46 49 52 53 Scores Tally Frequency 13 I 1 23 II 1 25 I 1 28 II 2 39 IIII 4 45 I 1 46 II 2 49 I 1 52 I 1 53 I 1 Total 15 What does it mean? What do you think the data is interpreting?

13. Example #4 We have a gathered 45 people, and their ages are 28, 31, 50, 14, 44, 46, 33, 47, 41, 30, 23, 48, 36, 30, 28, 19, 28, 13, 35, 16, 43, 17, 16, 30, 12, 17, 20, 27, 35, 48, 32, 11, 15, 19, 16, 28, 49, 50, 47, 42, 12, 39, 15, 32, 33. To make a grouped Frequency Distribution Table, we first need to do the following: Identify the lowest and highest data Find the interval of each category Tally and get the frequency Interval = Range = highest – lowest

14. 28, 31, 50, 14, 44, 46, 33, 47, 41, 30, 23, 48, 36, 30, 28, 19, 28, 13, 35, 16, 43, 17, 16, 30, 12, 17, 20, 27, 35, 48, 32, 11, 15, 19, 16, 28, 49, 50, 47, 42, 12, 39, 15, 32, 33. Interval = Range = highest – lowest What is our lowest data? What is our highest data? Range = 50 – 11 Range = 39 Interval = Interval =5.81 Interval =6

15. 28, 31, 50, 14, 44, 46, 33, 47, 41, 30, 23, 48, 36, 30, 28, 19, 28, 13, 35, 16, 43, 17, 16, 30, 12, 17, 20, 27, 35, 48, 32, 11, 15, 19, 16, 28, 49, 50, 47, 42, 12, 39, 15, 32, 33. The interval of our data is 6. Age Tally Frequency 11 – 16 IIII - IIII 10 17 – 22 IIII 5 23 – 28 IIII - I 6 29 – 34 IIII - III 8 35 – 40 IIII 4 41 – 46 IIII 5 47 – 52 IIII - II 7 Total 45

16. I have interviewed 50 students and asked how many minutes they study each day. These are what I have gathered, 87, 100, 22, 96, 89, 51, 49, 23, 58, 84, 73, 22, 94, 37, 63, 35, 67, 70, 66, 80, 34, 61, 64, 53, 67, 88, 73, 50, 55, 77, 30, 91, 43, 46, 63, 76, 24, 79, 95, 56, 84, 71, 90, 95, 77, 73, 73, 84, 48, 62. Minutes Tally Frequency 22 - 32 IIII 5 33 – 43 IIII 4 44 – 54 IIII – I 6 55 – 65 IIII – III 8 66 – 76 IIII – IIII 10 77 – 87 IIII – III 8 88 – 98 IIII – III 8 99 – 100 I 1 TOTAL 50

17. Let us try and make a qualitative data

18. Key Takeaways 1 Organization Frequency tables provide a structured way to organize data, making it more understandable and interpretable. 2 Visualization They offer a visual representation of data, making it easier to identify patterns and trends. 3 Interpretation They help draw conclusions and gain insights from data, supporting informed decision-making.