Last Updated on October 11, 2026 by Karl Thompson
Univariate analysis refers to the analysis of one variable at a time.
The most common approaches are:
- Frequency tables.
- Diagrams: bar charts, histograms, pie charts.
- Measures of central tendency: mean, median, mode.
- Measures of dispersion: range and standard deviation.
Frequency Tables
A frequency table provides the number of cases and the percentages belonging to each of the categories for a variable. Frequency tables can be used for all the different types of variable.
Below is a simple example of a frequency table showing the number of schools in three different categories of the ‘type of school’ variable in England for the 2022-2023 academic year. I rounded the percentages below.
| Type of school | Number of schools | Percent |
| Local Authority | 11858 | 48 |
| Academy | 10176 | 42 |
| Independent | 2408 | 10 |
| Total | 24442 | 100 |
Analysts usually clean raw data and turn it into frequency tables, so people can understand and visualise it more easily.
Frequency tables are the starting point for generating diagrams which put the data into visual form making trends stand out.
Diagrams
Diagrams represent quantitative data in visual form to make it easier to understand and interpret. Bar charts and pie charts are two of the most commonly used visual representations of quantitative data.
Bar charts
The chart below shows the same data as in the frequency table above. Each bar represents one of the three school types.
The bar chart below shows the largest category is Local Authority (LA) maintained schools with academies the second largest category. You can also see there are relatively few independent schools.
Pie Charts
The main advantage of a pie chart is that you can see the proportion of each category in relation to the total. A pie chart shows this sense of relation to the whole more clearly than a bar chart.
For example you can clearly see below that LA Maintained schools make up nearly 50% of the total. This doesn’t stand out as much in the bar chart.
You can also see that Independent schools represent around 10% of schools from the pie chart.
Frequency tables and diagrams: final thoughts
Diagrams are useful to make frequency tables easier to understand.
Bar charts are more useful when you want to look at proportions in relation to each other. Pie charts are more useful when you want to look at proportions in relation to the whole.
Keep in mind however that charts are only as useful as the data. For example, one limitation with the above data is that it tells you nothing about pupil numbers, only school numbers!
Sources
Department for Education (2023) Schools, Pupils and their Characteristics: Academic year 2022/23.
Measures of Central Tendency
Measures of central tendency encapsulate in one figure a value which is typical for a distribution of values. In effect, we are seeking out an average for a distribution.
Quantitative social research analysts recognise three different forms of average:
- mean
- median
- mode
Arithmetic mean
The mean is the sum of all values in a distribution divided by the number of values.
In diagram one above, we add ALL the ages together and divide by 20 which is the total number of ages in the sample. This gives us a mean of 51.6.
The mean should only be used with interval/ratio variables. It isn’t appropriate for ordinal variables, because the distances between the categories are not equal.
Median
The median is the mid-point in a distribution of values. We arrive at the median by lining up all the values smallest to largest and then finding the middle value.
The mean is vulnerable to outliers, which are extreme values at either end of the distribution. Outliers can greatly increase or decrease the mean, but they have much less of an effect on the median.
We see this in diagram one above, where the median point is 45.5, considerably lower than the mean of 51.6. In the case above the mean is higher because the oldest four people skew the mean average upwards. The four oldest are a lot older than the people in the middle, compared to the average ages of the rest of population.
The median can be used in relation to both interval/ratio and ordinal variables.
Mode
The mode is simply the value that occurs most frequently in a distribution. The mode can be applied to all types of variable.
In the diagram above, the mode is 28, because that is the only age which occurs twice.
Median more useful than the Mean?
With social data it is often more useful to know the median rather than the mean. This is especially true with wealth statistics in the UK.
Wealth and income distribution are of special interest to sociologists, because there is a lot of variation in distribution. Neither wealth nor income are equally distributed. Understanding how they are distributed has significant implications for life chances and social policy.
Visualising the total wealth in a bar chart looks like this:
Here you can clearly see a skew towards the top two deciles, especially the first decile. The richest 10% of households have an average of almost £2 million in wealth, which 8 times more than even the 4th decile.
In cases where there is a lot of variation in data, in terms of a large skew showing up at one end, as above, then get the mean and median being very different.
If you calculate the mean and median from the ten decile averages in the chart above, the mean is £489,000, pulled up by the huge relative wealth of the top 20%, while the median is only £280,000.
The ONS’s own figure for median household wealth, calculated from all households rather than decile averages, was £302,500 in April 2018 to March 2020. Half of all households had less than this. The ONS also found that the wealthiest 10% of households held 43% of all the wealth in Great Britain.
Mean wealth gives you a misleading picture of the amount of wealth most households in Great Britain have!
Sources
ONS: Household Wealth in the UK, 2018-2022.
Measures of Dispersion
Measures of dispersion show the variation in a distribution.
Two measures of dispersion include:
- the range (the simplest)
- the standard deviation.
Range
The range of data is the distance between minimum and maximum values in a distribution. Like the mean, outliers can greatly affect the range.
The range of household wealth (grouped by decile) in Great Britain is £1.9 million (see the chart above).
This is a very simple measure which doesn’t tell us vary much about how much wealth ordinary people.
For example it doesn’t tell us that the top decile of households are almost twice as wealthy as the next decile down.
Standard Deviation
We calculate the standard deviation in four steps: work out how far each value is from the mean, square each of these differences, find the average of the squared differences (this is called the variance), and then take the square root of that average.
In simple terms, the standard deviation tells you roughly how far a typical value is from the mean: a small standard deviation means the values are bunched closely around the mean, a large one means they are spread out.
For example, if you calculate it from the ten decile averages above, the standard deviation of household wealth in Great Britain is £575,211.
Unlike the range, the standard deviation uses every value in the distribution, not just the two most extreme ones, so it gives a fuller picture of the spread. However, because the differences are squared, it is still quite sensitive to outliers.
Box Plots
Box plots are popular for showing dispersion for interval/ratio variables.
The box plot provides an indication of both the central tendency (median) and dispersion (outliers).
The box plot of wealth below treats the top richest decile as an outlier. It clearly shows you the skew is the top.
The box shows you where the middle 50% of households sit: between about £50,000 and £800,000.
The line in the box shows you the median value of household wealth: £280 000.
The shape of a box plot will vary depending on whether cases tend to be high or low in relation to the median. They show us whether there is more or less variation above or below the median.
Sources
ONS: Household Wealth in the UK, 2018-2022.
Signposting and related posts
This material is most relevant to the Research Methods module. It might be a little advanced for A-level sociology. You are more likely to need this during a first year university statistical methods course.
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