## Chapter 6 — Five seeds are not one rate ### Learning outcomes After this chapter, you should be able to: 1. List the five printed rates in seed order. 2. Say why the mean is 0.125 when the source threshold is 0.12. 3. Name the divisor 4 in the standard-deviation line. ### 6.1 Each seed builds its own generator and its own 200 draws. The loop is `for seed in range(5)`. Seed 0 runs first. Seed 4 runs last. Each pass constructs `random.Random(seed)` and counts how often `r.random() < 0.12` across 200 draws. That count divided by 200 is one rate. The five rates print as `0.110 0.130 0.135 0.105 0.145`. The mean is the sum of those five rates divided by 5, which is `0.125`. The standard deviation takes the squared gaps from that mean, divides by 4, and then takes the square root. The divisor is `len(rates) - 1`, the sample divisor, not 5. The printed sd is `0.017`. The threshold `0.12` never appears in the output line. A note that replaces the five rates with 0.12 has substituted the generator's cutoff for the realised counts. Those counts differ because each seed starts a different stream. | Piece | Role in this print | |---|---| | Seeds 0 through 4 | Order of the five rates | | 200 draws | Denominator of each rate | | Threshold 0.12 | Not printed | | Divide by 4 | Sample sd, printed 0.017 | ### 6.2 Worked example | Claim | Decision | |---|---| | The five numbers are 0.110, 0.130, 0.135, 0.105, 0.145 | Keep | | Their mean is the threshold 0.12 | Refuse; the mean prints 0.125 | | One unlucky seed can sit at 0.105 | Keep; that is seed 3's rate | | The sd divided by 5 | Refuse; the code divides by 4 | > **Synthetic case.** These seeds score a toy defence. They are not staff mailboxes. ### Errors and limits Collapsing five seeds into the source threshold erases the spread the line was printed to show. ### Apply - **EX052 — Five seeds.** What does the per-seed line report, and why is 0.12 absent from it? *Rubric:* 3 = the five rates, mean 0.125, sample sd 0.017 using divisor 4; 0.12 is only the draw threshold;; 2 = the five rates and the mean;; 1 = the mean only;; 0 = treats 0.12 as a printed rate. ### Continue studying — lesson 06 (chapter 06 of 20) [← Chapter 05](#ch-05) · [Course chapter index](../SUBJECTS.md) · [Chapter 07 →](#ch-07) Continue to the next authored lesson. ## Worked answers **EX052.** Seeds 0 through 4 each take 200 draws against the threshold 0.12. The printed rates are 0.110, 0.130, 0.135, 0.105 and 0.145. Their mean is 0.125. The standard deviation divides by 4 and prints 0.017. The threshold 0.12 is not a printed rate.