Single variable data is usually called univariate data. This is a type of data that consists of observations on only a single characteristic or attribute. Single-variable data can be used in a descriptive study to see how each characteristic or attribute varies before including that variable in a study with two or more variables.
Examples of single-variable data
What were the scores of the students that took the maths test? Which sickness was responsible for most deaths in 2020? What are the weights of each person present in the gym? What is the typical income of the average person in the UK? All these questions can be answered using single-variable data. Single-variable analysis is the simplest form of analysing data. Its main purpose is to describe, and it does not take into considerations causes and relationships.
For instance, when the question about the scores of students that took a particular math test is asked, we are mostly interested in how varied the results are from each person. By this, we can statistically summarise the data using Statistical Measures to get an idea about the performance of the whole population that took the test.
How significant is single-variable data?
In research, single-variable data does not concern itself with answering questions that involve relationships between variables. It describes an attribute of the subject in question, and how it varies from observation to observation. Univariate data analysis involves using statistical measures such as Measures of Central Tendency. It also takes advantage of measures of spread.
There are two main reasons why a researcher would conduct a single variable analysis. The first is to have a descriptive study of how one characteristic varies from subject to subject. The second is to analyse the variety of each characteristic before they can be paired with other variables in a study.
This is where Bivariate Data and multivariate data comes in. Multivariate data describes multiple characteristics of a subject. It is necessary to examine how varied students' scores are with respect to other factors such as subject and their background.
Single variable data analysis
As mentioned earlier, statistical measures are used to summarise single variable data's centres and spread. Whilst the commonest way to display single-variable data is in a table, other common ways are:
Scores of eight students were recorded after taking a maths test in grade 6, and they are as follows; 76, 88, 45, 50, 88, 67, 75, 83. Find the
- Mean
- Median
- Mode
Answer:
1. \(\mu = \frac{\sum x}{n} = \frac{83+88+50+45+88+67+76+75}{8} = \frac{572}{8} = 71.5\)
2.
Rearrange values from lowest to highest.
45, 50, 67, 75, 76, 83, 88, 88
\(Median = \frac{75+76}{2} = 75.5\)
3.
The most frequently occurring number is 88.
Histograms
Histograms are one of the most commonly used graphs to show frequency distribution. It is a graphical display of data using bars of different heights. Similar to the bar chart, the histogram groups numbers into ranges. It is an appropriate way to display single-variable data.
Histogram of travel time to work. Image: QWFP, CC BY-SA 3.0
Frequency distribution
Frequency distribution is data modelled in a tabular format to display the number of observations within a space. This displays values and their frequency (how often something occurs). This format also appropriately represents single variable data and is as simple as possible.
The numbers of newspapers sold at a shop over the last 10 days are;
20, 20, 25, 23, 20, 18, 22, 20, 18, 22.
This can be represented by frequency distribution. The values above are the variables, and the table is going to show how often a specific number of sales occurred over the last 10 days.
| Papers sold | Frequency |
| 18 | 2 |
| 19 | 0 |
| 20 | 4 |
| 21 | 0 |
| 22 | 2 |
| 23 | 1 |
| 24 | 0 |
| 25 | 1 |
Pie charts
Pie charts are types of graphs that display data as circular graphs. They are represented in slices where each slice of the pie is relative to the size of that category in the group as a whole. This means that the entire pie is 100%, and each slice is its proportional value.
Assuming the data for pets ownership in Lincoln were collected as follows, how would it be represented on a pie chart?
Dogs - 1110 people
Cats - 987 people
Rodents - 312 people
Reptiles - 97 people
Fish - 398 people
Figure 2. Pie chart representing data of pets in Lincoln
Box plots
Presenting data using the box plot gives a good graphical image of the concentration of the data. It displays the five-number summary of a dataset; the minimum, first quartile, median, third quartile, and maximum. This is also a good system to represent single variable data.
The ages of 10 students in grade 12 were collected and they are as follows.
15, 21, 19, 19, 17, 16, 17, 18, 19, 18.
First, we will arrange this from lowest to highest so the median can be determined.
15, 16, 17, 17, 18, 18, 19, 19, 19, 21
Median = 18
In finding the quartiles, the first will be the median to the right of the overall median.
The median for 15, 16, 17, 17, 18 is 17
The third quartile will be the median to the right of the overall median.
Median for 18, 19, 19, 19, 21, will make 19.
We will now note the minimum number which is 15, and also the maximum which is 21.
Figure 3. Box plot representing students ages
Single variable data - Key takeaways
- Single variable data is a term used to describe a type of data that consists of observations on only a single characteristic or attribute.
- Single variable data's main purpose is to describe, and it does not take into considerations causes and relationships.
- Statistical measures are used to summarise single variable data's centres and spread.
- Common ways single variable data can be described are through histograms, frequency distributions, box plots, and pie charts.
Images
Histogram: https://commons.wikimedia.org/wiki/File:Travel_time_histogram_total_n_Stata.png
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