Data Display
Various fields like finance, science and politics rely heavily on the interpretation of large amounts of numerical data. Because many people find this difficult, tables and graphs are used to display the information in an understandable manner. While there are many different kinds of tables and graphs, if you remember some basic guidelines, you can interpret them all.
Tables are the most basic form of data representation. A table divides the information into columns and rows for easy reading.
For example, the number of different dogs from different breeds available for ownership is given in the table below.
Dog breed | Number of dogs available in pet store |
|---|---|
Pug | 6 |
Beagle | 2 |
German shepherd | 8 |
What are Two way Tables?
Data collected can often come from multiple categories. For example, gender may be one category in data collected on students at a primary school, while year and group are another. Two-way tables are a type of data sorting tool that helps you to collect and represent the data from two different variables.
How to make a Two way table?
We can make a two way table as follows:
Step 1: Determine which variables are of interest.
Step 2: Determine the possible values of the variables.
- Step 3: Choose one variable to represent the rows and another to represent the columns.
- Step 4: Fill in the frequencies in the table.
We can represent the comparison of two variables using two-way tables and frequency tables. This can be used to make important decisions through data visualization and analysis.
Joint frequency: It refers to the number or the value of entries in the two way table.
Marginal frequency: The entries in the ‘total’ of the column and the ‘total’ of the row in the two-way frequency table are called marginal frequencies. The sum of the joint relative frequencies in a row or column is called marginal relative frequency.
Interpretation of a Two-way table
Let us take an example to understand how a two way table can be interpreted.
The table below depicts the various activities on which men and women can take part in. Interpret the two-way table to determine the total number of competitors in both competitions.
Dance competition | Music competition | |
|---|---|---|
Men | 31 | 21 |
Women | 11 | 41 |
Reading the two way table:
31 men performed in the dance competition.
21 men performed in the music competition.
11 women performed in the dance competition.
41 women performed in the music competition
Let us take an example to understand how to find marginal frequencies
For the same table, create a new column and row for sum and then add the entries.
Dance competition | Music competition | Total | |
|---|---|---|---|
Men | 31 | 21 | 31 + 21 = 52 |
Women | 11 | 41 | 11 + 41 = 52 |
Total | 31 + 11 = 42 | 21 + 41 = 62 |
The total number of participants in the dance competition = 42.
The total number of participants in the music competition = 62.
The total number of men in the dance and music competition = 52.
The total number of women in the dance and music competition = 52.
Therefore, the marginal frequencies are 42, 62, 52, and 52.
Types of Data display
Before knowing how to choose a data display, Let’s see what are the types of data displays.
Choosing a Data display
If you want to visualize data, make sure you use the appropriate charts. While your data may work with a variety of chart types, it’s up to you to choose the one that ensures a clear and accurate result.
Following are the conditions representing which data type can be represented with which chart or display.
Type of chart | Data type |
|---|---|
Bar chart | Many items |
Column chart | Few items |
Circular area chart | Cyclical data |
Line chart | Non cyclical data |
Column chart | Single or few categories |
Line chart | Many categories |
Scatter chart | Two variables |
Bubble chart | Three variables |
Stacked 100% column chart | Only relative differences matter |
Stacked column chart | Relative and absolute differences matter |
Stacked 100% area chart | Only relative differences matter |
Stacked area chart | Relative and absolute differences matter |
Pie chart | Simple share of total |
Waterfall chart | Accumulation or subtraction to total |
Stacked 100% column chart with subcomponents | Components of components |
Column histogram | Few data points |
Line histogram | Many data points |
Scatter chart | Two variables |
3D area chart | Three variables |
Identifying misleading Data display
The most common types of misleading graphs are those in which:
- The vertical scale is too large or small, skips numbers and does not begin at zero.
- The graph is incorrectly labeled.
- Data is missing.
Solved Examples
Example 1:
The table below shows which activities Grade 1 and Grade 2 students participated in for lunch. Calculate the number of students who ate lunch using the two-way table.
Eaten lunch | Not yet eaten their lunch | |
|---|---|---|
Grade 1 students | 27 | 13 |
Grade 2 students | 34 | 41 |
Solution:
We can determine the number of students who ate lunch by calculating the marginal frequency.
For this, create a new column and row for sum and then add the entries in the column for eaten lunch..
Eaten lunch | Not yet eaten their lunch | |
|---|---|---|
Grade 1 students | 27 | 13 |
Grade 2 students | 34 | 41 |
Total | 27 + 34 = 61 |
Marginal frequency = 61
Hence, the Total number of students who ate lunch is 61.
Example 2:
Select a way to display data that is appropriate for the situation. Justify your decision.
- The number of students who performed in a powerpoint presentation each year.
- Comparison of people’s heights and their age.
- Compare the total area of the continents to the area of each continent.
Solution:
- The number of students who performed in a powerpoint presentation each year is represented by a line graph because it depicts the evolution of data over time. As a result, a line graph is a suitable data display.
- Comparison of people’s heights and their age is represented by the scatter plot because you’d like to compare two sets of data. As a result, a scatter plot is a suitable data display.
- We can compare the total area of the continents to the area of each continent using the pie chart because data is represented as parts of a whole in a circle graph or pie chart. As a result, a pie chart is an appropriate way to present the data.
Example 3:
Identify whether the following data displayed is misleading or not. Give the reason for your answer.
Solution:
The vertical axis of the right-hand bar graph has a break (ל) and starts at 60. This graph makes it appear that the total vitamin C in green pepper and orange juice is much greater than in broccoli or papaya. The graph on the left hand has an unbroken axis and correctly represents there is no substantial difference in the vitamin C content of the 4 food items. As a result, the graph on the right is misrepresenting the data.
A two way table is used when we want to represent 2 categorical variables. 1 category is represented by a row and the another by a column.
A line Graph depicts the evolution of data over time. So, to represent the weekly variation in temperature over a year, a line graph is a suitable way to display data.