Community medicine chapters
Data, presentation and summary measures
The types of data and scales of measurement, which table or graph suits each, and how to summarise data with the mean, median, mode, range, variance and standard deviation.
- Data are qualitative (nominal or ordinal) or quantitative (discrete or continuous; interval or ratio).
- Bar and pie charts suit qualitative data; histograms and frequency polygons suit continuous data; scatter diagrams show the relation of two variables.
- Summarise with a measure of central tendency (mean, median, mode) and a measure of dispersion (range, variance, standard deviation); use the median for skewed data.
On this page
Overview
Biostatistics is the science of collecting, presenting, summarising and interpreting health data.
Descriptive statistics describe the data you have: what kind of data it is, how to show it in a table or graph, and how to sum it up in a few numbers. Inferential statistics (see hypothesis testing) draw conclusions about a whole population from a sample.
Types of data
| Type | Subtype | Meaning | Examples |
|---|---|---|---|
| Qualitative (categorical) | Nominal | Named categories with no order | Sex, blood group, religion, district |
| Ordinal | Categories with a natural order, but unequal gaps | Pain mild/moderate/severe; cancer stage; socioeconomic class | |
| Quantitative (numerical) | Discrete | Counts; whole numbers only | Number of children, number of attacks |
| Continuous | Any value within a range | Height, weight, blood pressure, haemoglobin |
Quantitative data are also measured on:
- Interval scale: equal gaps but no true zero; ratios are meaningless. Example: temperature in °C (20°C is not "twice as hot" as 10°C).
- Ratio scale: equal gaps and a true zero. Example: weight, height, pulse rate.
Blood group is nominal; stage of cancer is ordinal; temperature in °C is interval; weight is ratio.
An ordinal scale is still qualitative, even when its categories are given numbers (stage 1, 2, 3). You cannot add or average them meaningfully.
Presenting data
Tables
The simplest way to show data. A good table has a clear title, labelled rows and columns, units, and the source. A frequency distribution table shows how many times each value or class occurs.
Graphs for qualitative data
- Bar chart: separate bars with gaps between them; the length shows the frequency. Can be simple, multiple (side by side) or component (stacked).
- Pie chart: a circle divided into sectors; each angle = (frequency ÷ total) × 360°. Best for showing parts of a whole.
- Pictogram: small pictures for the public.
Graphs for quantitative data
- Histogram: for continuous data in class intervals. Bars touch (no gaps); the area of each bar shows the frequency.
- Frequency polygon: a line joining the midpoints of the tops of the histogram bars.
- Cumulative frequency curve (ogive): shows how many observations fall below each value; used to find the median and percentiles.
- Line graph: shows a trend over time (for example monthly cases).
- Scatter diagram: shows the relationship between two quantitative variables (for example height and weight); used before calculating correlation.
- Box-and-whisker plot: shows the median, quartiles and range; good for comparing groups and spotting skew.
- Stem-and-leaf plot: shows the shape of the data while keeping the actual values.
Histogram = continuous data, no gaps. Bar chart = categorical data, with gaps.
A line graph shows change over time; a scatter diagram shows the relation between two variables.
Measures of central tendency
| Measure | Definition | Strengths and weaknesses |
|---|---|---|
| Mean (arithmetic) | Sum of all values ÷ number of values | Uses all the data; affected by extreme values (outliers) |
| Median | The middle value when data are put in order | Not affected by extremes; best for skewed data |
| Mode | The most frequent value | Can be used for nominal data; there may be no mode or more than one |
Example: the incubation periods (days) 2, 3, 3, 4, 13. Mean = 25 ÷ 5 = 5; median = 3; mode = 3. The one long value (13) pulls the mean up but not the median.
Incubation periods (days): 2, 3, 3, 4, 13
Mean = (2 + 3 + 3 + 4 + 13) ÷ 5 = 25 ÷ 5 = 5 days
Median = middle value of 2, 3, 3, 4, 13 = 3 days
Mode = most frequent value = 3 days
The one long value (13) pulls the mean up, not the median.
For skewed data (incubation periods, income, hospital stay), the median is the best summary.
Skewness
- Symmetrical (normal) data: mean = median = mode.
- Positive (right) skew: a long tail to the right: mean > median > mode.
- Negative (left) skew: a long tail to the left: mean < median < mode.
Measures of dispersion
These describe how spread out the data are.
- Range: highest − lowest value. Simple but depends only on the two extremes.
- Interquartile range: the spread of the middle 50% (third quartile − first quartile). Used with the median for skewed data.
- Mean deviation: the average of the absolute differences from the mean.
- Variance: the average of the squared differences from the mean. For a sample, divide by (n − 1).
- Standard deviation (SD): the square root of the variance. It is in the same units as the data and is the most widely used measure of spread.
- Coefficient of variation (CV) = (SD ÷ mean) × 100. It has no units, so it compares spread between variables measured in different units (for example height in cm and weight in kg).
Same data: 2, 3, 3, 4, 13 (mean = 5)
Deviations from mean: −3, −2, −2, −1, +8
Squared: 9, 4, 4, 1, 64 → sum = 82
Sample variance = 82 ÷ (n − 1) = 82 ÷ 4 = 20.5
SD = √20.5 = 4.53 days
CV = (SD ÷ mean) × 100 = (4.53 ÷ 5) × 100 = 90.6%
SD = √variance. Use the CV to compare variability of two different measurements.
Standard deviation describes the spread of individual values. Standard error describes how precisely the sample mean estimates the population mean (SE = SD ÷ √n).
Percentiles
A percentile shows the value below which a given percentage of observations fall. The 50th percentile is the median. Growth charts use percentiles to compare a child with others of the same age.
Expect: identify the scale of a variable (nominal, ordinal, interval, ratio), choose the right diagram (histogram vs bar chart vs pie vs scatter vs line), calculate mean, median and mode from a small set, choose the median for skewed data, the order of mean, median and mode in skewed data, and SD vs variance vs CV.
Quick revision
- Nominal (no order), ordinal (order), interval (no true zero), ratio (true zero).
- Bar chart and pie chart: categorical. Histogram (no gaps) and frequency polygon: continuous.
- Line graph: trends over time. Scatter: relation of two variables.
- Mean (affected by outliers), median (best for skew), mode (most frequent).
- Right skew: mean > median > mode.
- SD = √variance; CV = SD ÷ mean × 100.
Written by The House Job from Excel Community Medicine and Park's Textbook of Preventive and Social Medicine (named in the UHS PGET syllabus).
FAQ
What type of data is blood group?
Qualitative nominal data, because the categories have no natural order.
Which measure of central tendency is best for skewed data?
The median, because it is not affected by extreme values.
What is the difference between a histogram and a bar chart?
A histogram shows continuous data with no gaps between bars; a bar chart shows categorical data with gaps between bars.
How is standard deviation related to variance?
The standard deviation is the square root of the variance.