Exam practice

• DataFrame: pandas’s table, with named columns and numbered rows. Example: pd.read_csv("districts.csv") gives a DataFrame of 77 rows and 6 columns.
• Outlier: a value far from the others. Example: Kathmandu’s 4,936 people per km², among hill districts mostly between 100 and 250.
• Multivariate chart: a chart that shows three or more variables at once. Example: a scatter chart of the districts’ height and rain, with dots colored by belt.
• Simulation: a program that acts out a real system with made-up data that behaves like the real thing, to answer “what if?” questions. Example: the ticket counter’s mornings with one or two counters.
• Parameter: a number that sets how simulated data is made. Example: 25 people an hour, or service taking 1 to 3 minutes; the 48 and 12 in random.gauss(48, 12).

• 15 years: a number with words attached. Take the number out (for example, the digits only) and put the unit in the column’s name.
• fifteen: a number written as a word. Convert it, with a small dictionary of words, or mark it for a person to check.
• The empty cell: a missing value. Leave it missing (None/<NA>), never 0, and report how many answered.
• 150: an impossible value for a student (probably 15 typed with an extra 0). Check it with the person if you can; otherwise mark it missing and say so. A range check (say, 5 to 25) finds such values.

Then convert the column to numbers on purpose and check dtypes. Keep the original file, and write down every change and why.

A merge matches the key values exactly. If one table has “ Kathmandu” (with a space) or “Kavre”, and the other has “Kathmandu” and “Kavrepalanchok”, those rows find no match. A plain merge then drops them without any error, so their numbers silently vanish from every total; a left merge keeps them but with empty values. In this unit, before cleaning, the merge left out six of Bagmati’s 13 districts, about four million people. Cleaning the keys to one spelling first makes every row match, and checking for unmatched rows after the merge (isna().sum()) proves it.

A log scale is an axis on which each equal step is a multiplication, usually by 10 (1, 10, 100, 1,000), instead of an addition. Use it when the values run over several powers of ten, such as people per km² of Nepal’s districts (2 to 4,936) or the populations of countries, so that small values aren’t squashed into a line at the bottom. It must be named (“log scale”) and its ticks labeled, because equal gaps no longer mean equal differences.

import randomimport statistics random.seed(1)heights = []for i in range(30):    h = round(random.gauss(155, 7))    h = max(130, min(185, h))    heights.append(h) print("Mean:", round(statistics.mean(heights), 1))print("Spread:", round(statistics.stdev(heights), 1))

Mean: 155.8Spread: 6.3

The mean and spread are close to 155 and 7 but not exactly, as with any 30 real students: a different seed gives slightly different numbers.

• start = max(now, free_at[k]): the person is served at whichever is later, the moment they arrive (now) or the moment counter k is free. If the counter is free already, they start at once (no wait); if it is busy, they wait until it is free. Without it the program couldn’t work out waits at all.
• free_at[k] = start + random.uniform(1, 3): counter k will be busy with this person from start for a random time between 1 and 3 minutes, so it is next free then. This is how one person’s service makes the next person wait.

One run is one made-up morning; another run, with other random numbers, can give 1 minute or 20. The simulation should be run many times (say 100 mornings), and the results reported as data: the typical (median) average wait, and the spread, including how bad the worst mornings are (a histogram shows it). And even then the result is only as good as the model: its parameters should come from real counts, and its results be checked against real waits.

Any three, such as:

• How many students were in the data, from where, and how were they chosen? (Is it one school or the whole country? Are the groups big enough?)
• How was phone use measured: by the students’ own guesses, or by the phones?
• Could a third thing explain both, such as students with less help at home or less time for study, or students who work in the evenings? Were the groups compared like with like (Simpson’s paradox)?
• “15% lower” than whom, and is the difference bigger than the usual spread of marks?
• “Ruining” claims a cause; the data only shows that the two go together. Was there an experiment?

Seriously ill patients recover less often wherever they are treated. The city hospital treats mostly seriously ill patients (400 of its 500), while the district hospital treats mostly mild cases (450 of its 500). So the city hospital’s overall rate is mostly its seriously-ill rate (80%), pulled down by who it treats, and the district hospital’s overall rate is mostly its mild rate (96%). In each group, comparing like with like, the city hospital does better (80% against 70%, and 98% against 96%).
A newspaper should report the comparison within each group, say that the city hospital treats far more seriously ill patients, and not rank the hospitals by their overall rates alone.

Claim. In Nepal’s districts, the lower belts tend to be much more crowded: Terai districts have the most people per km², Mountain districts the fewest.
Evidence. The median district has 551 people per km² in the Terai, about 146 in the Hill belt and about 40 in the Mountain belt (2021 census, divided by each district’s area). On a scatter chart of height and people, the Terai dots sit high and the Mountain dots low.
How sure. These are all 77 districts, not a sample, so the difference is not chance. But the Hill belt varies hugely: the Kathmandu valley’s three districts are more crowded than any Terai district, which is why the median is used.
Limits. A district’s average hides crowded towns and empty land inside it. People per km² of the whole district counts snow, rock and forest where nobody can live. The data says where people live, not why (flat land for farming, roads, jobs, history are all possible reasons).

Parameters: how many students come to the canteen during the break (and whether they all come in the first few minutes); how long serving one student takes (the shortest and longest, or the average and spread); how long the break is; how many people serve.

Finding them: on a few normal days, count the students arriving each minute of the break and time a sample of students being served, with a watch.

The simulation: like one_morning, with arrivals bunched at the start of the break, run for 100 breaks with one server and with two. Report the typical wait and the spread, the share of students who wait longer than, say, 5 minutes, and how many reach the counter before the bell rings, which matters most here.

Left out (any two): students who give up when they see a long line; friends who buy for each other; days when there is a special food; a server who is slower or faster; students who pay with a phone and take longer or shorter. Check the model by running it with today’s settings and comparing it with the real lines.