You are a junior data scientist at the City Environmental Agency. Air-quality sensors across two neighborhoods send a stream of daily AQI readings. Your job: turn that raw data into trustworthy statistics, build the right graphs, and write a report that tells the city where the air is cleaner — and which neighborhood is more consistent.
The agency sends you one week of daily readings from each neighborhood's sensor. The number is the Air Quality Index (AQI) — lower is cleaner air. Every task below uses this same field data set.
AQI scale 0–50 = Good (green) · 51–100 = Moderate (yellow) · lower = cleaner air
Greenfield Park · 7 days
Riverside Flats · 7 days
A data set is just a list of numbers collected by asking the same question many times. The center tells you a typical value; the spread tells you how much the values bounce around.
Español: Un conjunto de datos es una lista de números. El centro indica un valor típico; la dispersión indica cuánto varían los datos.A statistical question is one you expect to get many different answers to — its data varies. Before you collect AQI data, decide which of these field questions are statistical. Select all that are statistical, then press Check.
Ask yourself: "Would this question get one answer or many different answers?" One answer = not statistical. Many varying answers = statistical.
Español: ¿La pregunta tiene una respuesta o muchas respuestas diferentes? Muchas respuestas que varían = pregunta estadística.Start with Greenfield Park. The dot plot below shows the seven daily readings. Find the three measures of center, then read the dotted mean line to check yourself.
Q2.1 — Mean of Greenfield (round to the tenth)
Q2.2 — Median of Greenfield
Mean = add all 7 numbers, then divide by 7. Median = put the numbers in order and find the middle one. With 7 values, the middle is the 4th.
Español: Media = suma los 7 números y divide entre 7. Mediana = ordena los números y toma el del medio (el 4.º).The mode is "no mode" here — every reading appears once. When would a city analyst actually care about the mode instead of the mean? (Hint: think about the most common alert color, not a typical number.)
Build your own data set. Grab any dot and slide it along the AQI axis. Watch the dashed mean line and the live readout move with it — the mean is the balance point of all seven readings.
Drag one dot to the right (a higher AQI). The dashed mean line slides right too — one big reading pulls the mean up. Drag it back and the mean drops.
Español: Arrastra un punto a la derecha (AQI más alto). La línea de la media se mueve con él. Un valor grande sube la media.Drag dots until the mean reads exactly 50 but the range stays 12 or less. Is more than one data set possible? Explain why the mean can match while the dots differ.
The mean alone hides how much the air bounces around day to day. Measure Greenfield's variability. The MAD worktable below walks you through it: each |deviation| is the distance of a reading from the mean (42.857).
Q3.1 — Range of Greenfield (max − min)
| Day AQI | Mean | |deviation| |
|---|---|---|
| 42 | 42.857 | 0.857 |
| 38 | 42.857 | 4.857 |
| 45 | 42.857 | 2.143 |
| 40 | 42.857 | 2.857 |
| 50 | 42.857 | 7.143 |
| 41 | 42.857 | 1.857 |
| 44 | 42.857 | 1.143 |
| Sum of |deviations| | 20.857 |
Q3.2 — MAD of Greenfield = sum of |deviations| ÷ 7 (round to the tenth)
Read it like an analyst: "Greenfield's AQI is about 43, give or take 3." You will compare this MAD against Riverside's spread in your final report.
MAD = mean absolute deviation. Step 1: find each reading's distance from the mean (already done in the table). Step 2: average those distances (add the |deviations|, divide by 7).
Español: MAD = desviación media absoluta. Suma las distancias a la media y divide entre 7.A small MAD means a consistent sensor; a big MAD means the air swings a lot. Predict: will Riverside's MAD be larger or smaller than Greenfield's, and why? (Look at that 98 reading.)
Now look at Riverside Flats: 35, 38, 40, 37, 39, 41, 98. One sensor day spiked to 98 (a nearby brush fire). The histogram below bins the seven readings into AQI ranges so you can see the distribution's shape.
Q4.1 — Median of Riverside (order all 7, take the middle)
Q4.2 — Mean of Riverside (round to the tenth)
Analyst's insight: the median is 39 but the mean jumps to 46.9 — that one fire-day reading of 98 drags the mean upward. When a distribution has an outlier, the median describes the typical day more honestly.
The histogram has most readings in the 30s–40s, then a gap and a single bar way out at 90s. That makes the distribution right-skewed. Explain in one sentence why the mean ends up greater than the median for a right-skewed shape.
For the city dashboard you need a box plot of Greenfield's week. The five-number summary is drawn below from the ordered data 38, 40, 41, 42, 44, 45, 50. Read the plot and confirm the key values.
Q5.1 — Interquartile range = Q3 − Q1 (the box width)
A box plot shows five points: min, Q1, median, Q3, max. The box holds the middle half of the data. Its width is Q3 − Q1. The whiskers stretch to the smallest and largest readings.
Español: La caja contiene la mitad central de los datos. Su ancho es Q3 − Q1. Los bigotes llegan al mínimo y al máximo.Greenfield's box plot is short and centered (IQR = 5). Riverside's would have a tiny box but a whisker stretched all the way to 98. What does the length of a whisker tell a city planner about that neighborhood's air?
Bring your statistics together in the city report card. Enter the two missing values; the comparison verdict updates live so you can see which neighborhood the data supports.
| Statistic | Greenfield | Riverside |
|---|---|---|
| Median (typical day) | 42 | 39 |
| Mean | 42.9 | 46.9 |
| Range (max − min) | 63 | |
| MAD (consistency) | 3.0 |
Greenfield range = 50 − 38. Compute it and enter it to confirm you can pull spread from raw data.
Riverside has the lower median (39 vs 42) — its typical day is cleaner. But its MAD is 14.6 vs Greenfield's 3.0, so its air is far less consistent. Write your recommendation: which neighborhood would you call "reliably good air," and which statistic settles it — center or spread?
Lower median = cleaner typical day. Smaller MAD = steadier, more consistent air. Compare the two columns to fill the verdict.
Español: Mediana más baja = aire más limpio típico. MAD más pequeño = aire más constante.When every analysis checks out, file your report with the city. Enter your name in the field below, then press Submit report & grade to save your score as a PDF or DOC.
| Level | Score | Descriptor |
|---|---|---|
| 4 — Exceeds | 8 / 8 | Sorts statistical questions correctly and computes mean, median, range, MAD, and IQR accurately for both data sets. Reads the histogram and box plot, explains why the outlier makes the median the better measure, and writes a data-driven recommendation using both center and spread. |
| 3 — Meets | 6–7 / 8 | Computes most measures of center and spread with at most one arithmetic slip. Reads the graphs and reaches a reasonable recommendation. |
| 2 — Approaching | 4–5 / 8 | Finds simple measures (mean, median, range) but struggles with MAD or with interpreting the outlier and distribution shape. Partial report. |
| 1 — Beginning | 0–3 / 8 | Few correct statistics. Confuses mean with median, or cannot order data to find the median. Needs reteaching on measures of center, spread, and reading data displays. |