OpenCyber AcademyLesson map
Lesson 01 published. Map, example, EX001.
flowchart TD
N0["Learning outcomes"]
N1["1.1 The case"]
N2["1.2 Percentages and ratios"]
N3["1.3 Common mistakes"]
N4["Synthesis"]
N0 --> N1 --> N2 --> N3 --> N4
N4 --> EX["Worked example"]
EX --> Q["Exercise EX001"]
Logical drawing
flowchart LR
N0["Learning outcomes"]
N1["1.1 The case"]
N2["1.2 Percentages and ratios"]
N3["1.3 Common mistakes"]
N4["Synthesis"]
N0 --> N1 --> N2 --> N3 --> N4 --> Q["EX001"]
[Learning outcomes]
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[1.1 The case]
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[1.2 Percentages and ratios]
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[1.3 Common mistakes]
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[Synthesis]
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[Worked example] --> [Exercise EX001]
Learning outcomes
You will (1) reason with percentages and ratios about accounts; (2) read simple tables of identity data; (3) avoid common numerical mistakes.
1.1 The case
Elena Petrova is a bachelor's student at the fictional Westmere University, supervised by Dr Kwame Asante. Her four-year project is with the fictional Greenhill Community Housing, a housing association with about 140 staff who use a cloud office suite, a housing management system and a finance system. Greenhill's small IT team worries that some former staff still have accounts, that not everyone uses multi-factor authentication and that a few accounts are shared between colleagues. Elena's job over the degree is to understand these problems, measure them carefully and help fix them, using only synthetic data in this book.
1.2 Percentages and ratios
Identity work is full of percentages: the share of staff with multi-factor authentication, the share of leavers disabled on time, the share of accounts never used. A percentage is only meaningful with its base. Saying ninety percent of administrators use multi-factor sounds good, but if there are ten administrators, the one without it may hold the most powerful account in the organisation. Elena learns to always report the count and the base alongside the percentage, such as nine of ten, so readers can judge both the proportion and its real-world size.
1.3 Common mistakes
Two mistakes appear often. The first is comparing percentages with different bases: a rise from 50 to 60 percent in a team of ten is one person, while the same rise across 140 staff is fourteen people. The second is confusing percentage points with percent: going from 50 to 60 percent is a rise of ten percentage points but a twenty percent relative increase. Elena writes both clearly in her reports, because managers make decisions from these numbers and an ambiguous figure can lead to the wrong priority.
Worked example
Of 140 synthetic staff, 108 use multi-factor authentication: 77.1 percent. Elena reports it as 108 of 140 (77.1%) and notes that the 32 without it are concentrated in one team.
Synthetic case. Elena Petrova, Westmere University, Greenhill Community Housing and all figures are synthetic.
Errors and limits
Reporting a percentage without its base hides whether a gap affects one person or many.
Exercises
- EX001 — Base matters. Why report nine of ten instead of only ninety percent?
Show marking criteria
Rubric: 3 = base shows the one missing may be critical;; 2 = base;; 1 = style;; 0 = none. - EX002 — Points versus percent. A rise from 50 to 60 percent is how many points and what relative increase?
Show marking criteria
Rubric: 3 = ten points, twenty percent;; 2 = ten points;; 1 = ten percent;; 0 = none. - EX003 — Greenhill size. About how many staff does Greenhill have?
Show marking criteria
Rubric: 3 = about 140;; 2 = 140;; 1 = 1,400;; 0 = none.
Synthesis
Percentages with their bases, and clear use of points versus percent, make identity figures honest and useful.