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Grade 6 Math WebQuest · Unit 8 · 6.SP.A.1–3 · 6.SP.B.4–5

The Cafeteria Comeback

The lunch line is a mess: kids wait too long, the food gets cold, and nobody can agree on what to fix. The principal is giving your Student Data Council one shot. Run a real survey, study the numbers with statistics, and walk into the meeting with a data-backed plan to win our cafeteria back.

⏱ 2–3 class periods 📋 Statistical questions 📊 Mean · Median · Mode · MAD 📈 Box plots & histograms

Your Council Gets the Case

Anybody can complain about lunch. A data scientist measures it. In this WebQuest you become a student data analyst: you will collect a set of numbers, find out what is typical, find out how spread out the data is, and picture the whole story with graphs — then recommend the one change that helps the most students.

The Driving Question

How can one set of numbers be summarized by its center, its spread, and its shape to make a fair decision for a whole school?

Level 1 · Support A statistical question is one you expect to get different answers to. "How long did each 6th grader wait in line today?" is statistical — the answers vary. "How long did I wait today?" is not — it has one answer. En español: Una pregunta estadística espera respuestas que varían. "¿Cuánto esperó cada estudiante en la fila?" varía. "¿Cuánto esperé yo?" tiene una sola respuesta, así que no es estadística.
Level 2 · Enrichment A good analyst never reports just one number. The center (mean, median, mode) says what is typical, the spread (range, MAD, IQR) says how much it varies, and the shape (symmetric, skewed, clusters, gaps, peaks) warns you when a single average could mislead the whole school.

The Task

By the end of this WebQuest your council will submit a Cafeteria Data Report. To pass review, your report must:

  • Sort four survey questions into statistical vs. not statistical.
  • Find the mean, median, and mode of the wait-time data set.
  • Measure the spread with the range and the MAD (mean absolute deviation).
  • Read a box plot and a histogram and describe the shape of the data.
  • Recommend one change and back it with two numbers from your analysis.
  • Pass the Check Your Understanding self-check at the bottom.
Dot plot of lunch line wait times in minutes for twelve students. Lunch-line wait (minutes) 2 4 6 8 10 12 14 12 students surveyed · each dot = 1 student

Your data set (wait time in minutes for 12 students): 4, 5, 5, 6, 6, 6, 7, 7, 8, 9, 11, 14. Keep it handy — you will use it in almost every step.

The Process

Work the steps in order. Each step fills one section of your Cafeteria Data Report.

Step 1 — Decide what is worth measuring

Your council drafted four questions. Tap a chip to label each one. A question is statistical only if you expect the answers to vary from student to student.

A. "How many minutes did each 6th grader wait in line today?"
B. "How many minutes did Mr. Lopez's clock show at 12:05?"
C. "How many lunch items does each student usually buy?"
D. "What is today's date on the cafeteria calendar?"
Level 1 · Support Ask yourself: "If I asked 30 students, would I get different answers?" If yes → statistical. If everyone gives the same one answer → not statistical. En español: Pregúntate: "Si pregunto a 30 estudiantes, ¿obtendría respuestas diferentes?" Si sí → estadística.

Step 2 — Find the center (mean, median, mode)

The center tells the principal what a typical wait looks like. Use your 12-value data set.

Mean
add all ÷ how many

The balance point — the "fair share" if everyone waited equally.

Median
middle of the sorted list

With 12 values, average the 6th and 7th numbers.

Mode
value that appears most

The most common single wait time.

Worked example — the mean:

Sum = 4+5+5+6+6+6+7+7+8+9+11+14 = 88. Mean = 88 ÷ 12 = 7.33 min (about 7⅓).

Level 2 · Enrichment The mean (7.33) is larger than the median (6.5). When the mean is pulled above the median, an unusually large value is stretching the data to the right. Which student's wait is doing that?

Step 3 — Measure the spread (range and MAD)

Two cafeterias can have the same mean but feel totally different — one steady, one wild. Spread captures that. The range is max − min. The MAD (mean absolute deviation) is the average distance of each value from the mean.

How to find the MAD (3 moves):

1) Distance of each value from the mean (7.33).
2) Add up all 12 distances.
3) Divide that total by 12. A larger MAD means a more inconsistent lunch line.

Level 1 · Support "Absolute" just means distance is never negative. Whether a value is above or below the mean, write the gap as a positive number, then average those gaps. En español: "Absoluto" significa que la distancia nunca es negativa. Escribe cada diferencia como número positivo y luego saca el promedio.

Step 4 — Picture the data (box plot & histogram)

A graph reveals the shape at a glance. Study the box plot and histogram below — they show the same 12 wait times two ways.

Box plot of wait times: minimum 4, lower quartile 5.5, median 6.5, upper quartile 8.5, maximum 14. Box plot · wait (min) 2 6 10 14 Q1 5.5 Med 6.5 Q3 8.5 min 4 max 14
Histogram of wait times in 3-minute bins: 3 to 5 has 3 students, 6 to 8 has 6 students, 9 to 11 has 2 students, 12 to 14 has 1 student. Histogram · 3-min bins 3 6 2 1 3–5 6–8 9–11 12–14

Both graphs show most students bunched around 6–8 minutes, with a thin tail stretching right toward 11 and 14. That makes this distribution skewed right.

Level 2 · Enrichment Because the data is skewed right, the median (6.5) describes a typical student better than the mean (7.33), which the 14-minute wait pulls upward. In your report, argue which "average" the principal should trust — and why.

Step 5 — Make the call

Write one clear recommendation and support it with two numbers from your analysis (for example: "median wait 6.5 min" and "MAD shows lines vary"). Decide whether a single average is enough, or whether the principal needs the spread and shape too.

Level 1 · Support Sentence frame: "The data shows ______. Because the ______ is ______, our council recommends ______." En español: "Los datos muestran ______. Como el/la ______ es ______, nuestro consejo recomienda ______."

Resources

Use these Neft Teacher tools as you work. They open in the same window — use your back button to return.

Unit 8 · 3D Data LabDrop data points and watch the mean, median, and graphs update live. Statistics ActivityPractice MAD, box plots, and histograms step by step. Reveal Evidence StudioBuild the Claim–Evidence–Reasoning for your recommendation. Math Writing Help · EN/ESSentence frames and bilingual vocabulary support.

Key vocabulary · Vocabulario clave

Evaluation

Your Cafeteria Data Report will be scored on this rubric.

Criteria 4 · Lead Analyst 3 · Analyst 2 · Apprentice 1 · Getting started
Statistical questions All 4 questions sorted correctly with a reason. 3 of 4 sorted correctly. 2 of 4 sorted correctly. 0–1 sorted correctly.
Center Mean, median, and mode all correct. Two of three correct. One correct. None correct.
Spread (range & MAD) Range and MAD both correct and labeled. One of two correct. Attempts MAD with errors. No spread shown.
Graphs & shape Reads box plot & histogram; names the shape. Reads one graph; shape unclear. Partial graph reading. No graph interpretation.
Recommendation Clear call backed by two numbers. Call with one number. Call with no data. No recommendation.
Teacher Notes & Answer Key (not printed)

Cafeteria Comeback · Data Report — pairs with the Evaluation rubric above.

Sample Answers — Cafeteria Data Report

  • Statistical vs not: "How long did each 6th grader wait?" is statistical (answers vary); "What time is lunch?" is not (one answer).
  • Data set 4,5,5,6,6,6,7,7,8,9,11,14 (12 values): Mean = 88 ÷ 12 = 7.33 min; Median = average of 6th & 7th = (6+7)/2 = 6.5; Mode = 6.
  • Spread: Range = 14 − 4 = 10; compute MAD as the mean distance of each value from 7.33.
  • Shape: mean (7.33) > median (6.5) → a large value (14) pulls the mean up; distribution is skewed right.

Facilitation

  • "Would 30 students give different answers?" → yes means statistical.
  • Order the data before finding the median; the mode can be read from the histogram's tallest bar.

Standard

CCSS 6.SP.A.1–B.5.

Check Your Understanding

Answer all six using the data set 4, 5, 5, 6, 6, 6, 7, 7, 8, 9, 11, 14. Click Check My Answers when you are done.

1.Which question is a statistical question?
2.The 12 wait times add up to 88. What is the mean? (Round to two decimal places.)
Hint / Pista: mean = sum ÷ how many = 88 ÷ 12.
3.The data is already in order. With 12 values, the median is the average of the 6th and 7th values (6 and 7). What is it?
Hint / Pista: median = (6 + 7) ÷ 2.
4.Which wait time appears most often (the mode)?
Hint / Pista: count how many times each value appears. Which shows up three times?
5.The longest wait is 14 min and the shortest is 4 min. What is the range?
Hint / Pista: range = maximum − minimum.
6.Most students wait 6–8 min, with a thin tail reaching out to 11 and 14. Look at the histogram below. Which best describes the shape?
3–5 6–8 9–11 12–14

Conclusion

You did what real data analysts do every day: you turned a noisy complaint into evidence. You measured the center, the spread, and the shape — and you saw why a single average like the mean (7.33) can hide the real story when one 14-minute wait stretches the data. Walk into that principal's meeting knowing your recommendation stands on numbers, not opinions.

Take it further · Level 2

Suppose a new express line removes the 14- and 11-minute waits. Recompute the mean and median. Did your recommendation get stronger?

Reflect · Reflexiona

Should the principal trust the mean or the median for this data, and why? Explain in 2–3 sentences. ¿Debería confiar en la media o en la mediana, y por qué?

Real careers · Carreras reales

Sports analysts, school nurses, and city planners all summarize messy data with center, spread, and shape — exactly the skills you just used.