Reading Data — Graphs, Histograms & Pie Charts
Data and Engineering
Engineering decisions rarely rest on a single measurement. A quality control team might test hundreds of components and need to see the spread of results at a glance. A production manager might track output over a six-month period to spot a downward trend. Presenting data as a visual graph makes patterns that are invisible in a column of numbers immediately obvious. Your exam may show you a graph based on an engineering scenario and ask you to read values from it, describe trends, or choose which type of graph is most appropriate for a given set of data.
Bar Charts — Comparing Discrete Categories
A bar chart uses separate rectangular bars to compare distinct categories. The bars do not touch each other because the categories are discrete — they are not part of a continuous scale. Each bar has equal width; only height varies. The vertical axis usually shows frequency, quantity or value; the horizontal axis lists the categories.
Bar charts are the right choice when the data falls into named, unordered groups. For example: the number of defective components produced by five different machines in a factory; the number of each type of engineering join used in a product (welded, brazed, bolted, riveted); or the frequency of failures by fault type recorded in a maintenance log.
In a bar chart the bars do not touch because the data is discrete (separate categories). All bars must be the same width. The height of each bar represents the value or frequency for that category.
Histograms — Showing Continuous Data Distributions
A histogram looks similar to a bar chart but there are two critical differences. First, the bars touch because the data is continuous — the intervals follow on from each other with no gap. Second, strictly speaking the area of each bar represents frequency (frequency = frequency density × class width); When all class widths are equal, bar height is proportional to frequency, so the tallest bar shows the most common interval. Use the vertical-axis label to decide whether a height is a frequency or a frequency density.
Histograms are suited to continuous data grouped into intervals. Engineering examples include: the distribution of shaft diameters measured across a production batch (e.g. 19.90–19.95 mm, 19.95–20.00 mm, 20.00–20.05 mm); the distribution of load-bearing test results grouped into force ranges; or the distribution of measured temperatures at different points in a manufacturing process.
Scenario: An engineering firm tests 200 turned components and records the diameter of each. The diameters (in mm) are grouped into 0.1 mm intervals and plotted as a histogram. The tallest bar, covering 19.95–20.05 mm, has a height corresponding to a frequency of 120. The neighbouring bars have frequencies of 40 and 30. The remaining components fall in the outermost bars.
Reading the histogram: To find how many components fell within tolerance (defined as 19.95–20.05 mm), read the height of the central bar. The answer is 120 components out of 200, which is 60%.
Interpreting the distribution: The tall central bar shows most components cluster near the target diameter of 20.00 mm. The short bars at either side show that only a small number are significantly over- or under-size. The pattern (tall in the middle, short at the edges) is a roughly symmetrical distribution — a sign the machining process is reasonably well controlled.
Line Graphs — Showing Trends Over Time
A line graph plots a series of data points and connects them with straight lines. It is ideal for showing how a quantity changes over time, or how one continuous variable responds to another. The horizontal axis (x-axis) typically shows the independent variable (for example, time or temperature); the vertical axis (y-axis) shows the dependent variable (for example, output, force or power).
Line graphs allow you to identify trends (general directions of change), peaks and troughs, and periods where values stay constant. A rising line indicates an increase; a falling line indicates a decrease; a flat line means no change. Engineering uses for line graphs include: machine output rate over a production shift; voltage across a capacitor charging over time; or temperature of a component being heat-treated in a furnace.
Scenario: A factory records the number of components produced each hour over an 8-hour shift. The y-axis shows components per hour (0 to 250). The data shows: hours 1–2 rising from 100 to 200; hours 3–5 staying constant at 200; hour 6 dropping to 150 (scheduled maintenance); hours 7–8 recovering to 200.
Describing the trend: “Output rose steadily during the first two hours as operators settled in, then remained constant at 200 components per hour for three hours. It fell to 150 during hour 6 due to scheduled maintenance, and then returned to full production for the final two hours.”
In your exam, describing a trend means using words like increases, decreases, remains constant, peaks, drops and giving the approximate values read from the graph. Describe what the data shows, then explain the likely engineering reason if you can.
Pie Charts — Showing Proportions of a Whole
A pie chart divides a circle into sectors. The full circle represents the whole data set (100%). Each sector’s angle is proportional to the percentage it represents. To find a sector angle:
$$\text{Sector angle} = \frac{\text{Percentage}}{100} \times 360°$$
Alternatively, if you have frequencies: $$\text{Sector angle} = \frac{\text{Frequency}}{\text{Total frequency}} \times 360°$$
Pie charts work well when you want to show the relative proportions of several categories that together make up a whole — for example, the breakdown of material costs in a product (steel 40%, aluminium 25%, plastics 20%, fixings 15%), or the distribution of defect types found during a quality inspection.
Problem: A quality control log records 80 defective components. The faults are: surface scratches 40, incorrect dimensions 20, cracks 16, other 4. Calculate the sector angle for each fault type.
Step 1 — Check total: 40 + 20 + 16 + 4 = 80 ✓
Step 2 — Calculate each angle:
Surface scratches: \(\frac{40}{80} \times 360 = 180°\)
Incorrect dimensions: \(\frac{20}{80} \times 360 = 90°\)
Cracks: \(\frac{16}{80} \times 360 = 72°\)
Other: \(\frac{4}{80} \times 360 = 18°\)
Step 3 — Check: 180 + 90 + 72 + 18 = 360° ✓ Always check your sector angles sum to exactly 360°.
Choosing the Right Graph Type
Selecting the wrong graph type is a straightforward way to lose marks. Use this guide:
Bar chart → Discrete (separate) categories you want to compare. E.g. number of components from five different suppliers.
Histogram → Continuous data grouped into intervals. E.g. distribution of component dimensions across a production run.
Line graph → Continuous data showing change over time or another variable. E.g. temperature of a furnace over two hours.
Pie chart → Proportions of a total. E.g. percentage breakdown of production costs.
Bar charts compare discrete categories (bars do not touch). Histograms show continuous data distributions (bars touch). Line graphs show trends or change over time. Pie charts show proportions of a whole (sector angle = percentage × 3.6).