Chapter 2B Flashcards
(15 cards)
❓ Is a Frequency Table the Same as Grouped Data?
No, a frequency table and grouped data are not the same thing, although they are closely related.
* A frequency table is the actual structure or format used to record and organise data.
* Grouped data refers to data that has been arranged into classes or intervals, instead of being shown as individual values.
So, in short: Grouped data is the type of data, while a frequency table is the tool used to display it.
Give 5 Comparison Between Frequency Table and Grouped Data (in words)
- A frequency table is a chart or list that shows values (or value ranges) alongside the number of times (frequencies) they occur. It is a presentation method.
- Grouped data is data that has been sorted into categories or intervals (e.g. 0–10, 11–20), usually when there are too many distinct data values to list individually.
- You can have a frequency table of raw data (e.g. tallying how many people scored 5, 6, 7, etc. in a test), or a frequency table of grouped data (e.g. how many people scored between 0–10, 11–20, etc.).
- The frequency table often includes grouped data in real-life applications, but they are not identical terms. One refers to how data is displayed, the other to how it is organised before display.
- So: grouped data is a format of data; a frequency table is a method of organising either grouped or ungrouped data.
- f or F = frequency
- x = individual data value
- x̄ = mean of the data (if calculated from the table)
- Σf = sum of frequencies
- Σfx = sum of each value times its frequency
What does x mean?
- x = individual data value
What does x̄ mean?
- x̄ = mean of the data (if calculated from the table)
What does Σf mean?
- Σf = sum of frequencies
What does Σfx mean?
- Σfx = sum of each value times its frequency
Give 5 Examples of Situations Where Frequency Tables (or Grouped Data Tables) Are Used
Here are 5 unique, realistic examples — not one repeated — across different subjects and real-world contexts:
1. A teacher records the number of correct answers from students out of 20 and lists how many students scored each mark.
2. A shop tracks how many customers bought 0, 1, 2, 3, etc. items in a week.
3. A class survey shows how many people have 0, 1, 2, or more siblings.
4. A gym logs how many people attended each hour of the day.
5. A school collects shoe sizes and how many students wear each size.
Give three numerical examples of frequency tables which are ungrouped.
Here are three numerical examples of frequency tables which are ungrouped
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Example 1: Number of pets owned by students
Pets Owned (x) | Frequency (f)
0 | 3
1 | 5
2 | 7
3 | 4
4 | 1
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Example 2: Number of daily phone calls made by workers
Calls Made (x) | Frequency (f)
0 | 1
1 | 4
2 | 6
3 | 5
4 | 2
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Example 3: Number of books borrowed by each student
Books Borrowed (x) | Frequency (f)
1 | 4
2 | 6
3 | 8
4 | 3
5 | 2
Give Three Examples of Grouped Frequency Tables
10 Examples of Grouped Frequency Tables
In these, the data has been grouped into class intervals.
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Example 1: Heights of students (in cm)
Height (cm) | Frequency (f)
140 – 149 | 2
150 – 159 | 4
160 – 169 | 8
170 – 179 | 5
180 – 189 | 1
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Example 2: Time spent revising (in minutes)
Time (mins) | Frequency (f)
0 – 29 | 1
30 – 59 | 3
60 – 89 | 6
90 – 119 | 7
120 – 149 | 2
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Example 3: Daily screen time (in hours)
Screen Time (hrs) | Frequency (f)
0 – 1 | 2
1 – 2 | 5
2 – 3 | 8
3 – 4 | 4
4 – 5 | 1
Grouped Frequency Table
🔹 Grouped Frequency Table
A grouped frequency table is a table where the data values are placed into intervals, or groups, rather than listed individually. Each group shows how many values fall within a certain range, and this number is called the frequency (often written as f). Grouping data makes it easier to spot patterns, especially when you are working with large sets of numbers.
Data Value
🔹 Data Value
A data value is a single piece of information collected from a survey, experiment, or observation. It can be a number like 7, 150, or 21.3, or it can be a label like “green” or “cat”, depending on the type of data. When you collect many data values, you form a data set.
Class
🔹 Class
A class is a range or interval used to group data in a frequency table. Instead of listing every data value on its own, we group values into classes like “10–19” or “50–59”. Each class shows how many values fall within that specific range.
Class Boundary
🔹 Class Boundary
A class boundary is the exact point where one class ends and the next one begins. It is used when there are no gaps between the classes. For example, in the class “10–19”, the lower class boundary is 9.5 and the upper class boundary is 19.5. Class boundaries help when drawing histograms or dealing with continuous data.
Midpoint of a Class
🔹 Midpoint of a Class
The midpoint of a class is the value exactly in the middle of a class interval. You find it by adding the lower and upper class limits and dividing the total by 2. For example, the midpoint of the class 10–19 is (10 + 19) ÷ 2 = 14.5. It is used when estimating averages from grouped data.
