Lesson 2.92.1 · 2.3 · 2.9 Catch-Up
Start hereWords, worked example, and sentence starters
Learning target I can show I am caught up on Lessons 2.1 · 2.3 · 2.9 by using each lesson's big idea in mixed practice.
Start hereWords for this lesson
Read each word before you begin. Say it out loud.
| Word | What it means | Example |
|---|---|---|
| Statistical Questions and DataSpanish: Preguntas estadísticas y datos | A statistical question expects varied answers that can be collected as data. | How many minutes do students in our class read each night? |
| Statistical QuestionSpanish: Pregunta estadística | A question where the answers will be different for different people. | “How tall are the players on the team?” → answers vary: 60 in, 63 in, 58 in, 65 in |
| Non-statistical QuestionSpanish: Pregunta no estadística | A question that has just one fixed answer that is the same no matter who you ask, so there is no data to collect. | “How tall am I?” → one answer: 60 in. Everyone who measures gets the same number. |
| DataSpanish: Datos | Facts and numbers you collect, like answers to a survey. | Player heights: 60 in, 63 in, 58 in, 65 in — four different measurements |
| VariabilitySpanish: Variabilidad | How spread out the numbers are. | Scores 10, 12, 11 are close together (low variability); scores 2, 15, 30 are far apart (high variability) |
| SurveySpanish: Encuesta | Collecting facts by asking people questions. | Asking 50 students 'What is your favorite sport?' and recording the answers |
How it worksWorked examplefinding the mean absolute deviation
These numbers are not on your problems. The steps are. Follow them with your own numbers.
Five snack prices in cents are 80, 90, 100, 110, 120. Find the mean absolute deviation.
- Find the mean: the five prices total 500, and sharing that evenly gives 100.
- Measure each price's distance from 100: 20, 10, 0, 10, 20.
- Add the distances. They come to 60.
- Share that total distance among the five prices.
Answer: The MAD is 12 cents — a typical price sits about 12 cents away from the mean.
Now you trySame steps, your turn
The steps are the same as the worked example. The numbers are yours. Do the work.
Five backpack weights in ounces are 33, 36, 37, 38, 41. Find the MAD.
- Add the five weights: Mean:
- Distance of each weight from the mean: , , , ,
- Total of the distances:
- Share that total among the number of values. MAD: ounces
Say it and write itSentence starters
Finish each sentence out loud with a partner. Then use them in your writing.
- The mean of this set is .
- The distance from to the mean is .
- The distances total , and there are values.
- The MAD is , which means .
Word bank mean absolute deviationdeviationdistanceabsolute valuemeanspreadaveragetotaldividetypicalconsistentvariation
Watch outA common mistake
A common mistake in Mean Absolute Deviation is adding the signed deviations (value − mean) instead of their absolute values, so the positives and negatives cancel out to 0. For 6, 8, 10, 12 (mean = 9), the deviations are −3, −1, 1, 3 — they sum to 0, but that is NOT the MAD. Before averaging, take the absolute value of every deviation so each becomes a positive distance: |−3| = 3, |−1| = 1, |1| = 1, |3| = 3. Sum = 8, so MAD = 8 ÷ 4 = 2. A MAD of exactly 0 is a warning sign — it only happens if every value in the data set equals the mean.
Lesson 2.92.1 · 2.3 · 2.9 Catch-Up
Catch-UpSkill bridge
Learning target I can show I am caught up on Lessons 2.1 · 2.3 · 2.9 by using each lesson's big idea in mixed practice.
-
1Circle the letter of the best answer. Show how you know.
(Lesson 2.1) Which of the following is a statistical question?
- AHow many points did each player score this season?
- BHow many points are scored for a free throw?
- CWhat sport does this team play?
- DHow many halves are in a soccer game?
Hint Re-read each question and ask: would different people or games give different answers, or is there just one fixed answer?
Show your work -
2Circle the letter of the best answer. Show how you know.
(Lesson 2.1) Which question is NOT a statistical question?
- AHow many home runs did each player hit this year?
- BHow many miles does each runner train per week?
- CHow many innings are in a baseball game?
- DHow tall is each player on the basketball team?
Hint Careful — this asks for the question that is NOT statistical: the one with a single fixed answer instead of varying data.
Show your work -
3Circle the letter of the best answer. Show how you know.
(Lesson 2.3) Find the mean of: 10, 14, 8, 12, 16
- A10
- B12
- C14
- D60
Hint Mean means the average of all five numbers — you'll need both a total and how many numbers there are.
Put the data in orderWork- 1OrderSmallest to largest.
- 2CountHow many values?
- 3LocateMiddle, or add and divide.
- 4AnswerSay which measure it is.
-
4Circle the letter of the best answer. Show how you know.
(Lesson 2.3) Find the median of: 3, 7, 2, 9, 5
- A3
- B5
- C5.2
- D7
Hint Median = the middle number, but only AFTER the list is in order. Don't pick the middle of the unsorted list.
Put the data in orderWork- 1OrderSmallest to largest.
- 2CountHow many values?
- 3LocateMiddle, or add and divide.
- 4AnswerSay which measure it is.
-
5Circle the letter of the best answer. Show how you know.
(Lesson 2.9) The mean of a data set is 15. One value is 11. What is the absolute deviation of that value from the mean?
- A4
- B−4
- C11
- D26
Hint Absolute deviation asks: how FAR is the value 11 from the mean of 15? A distance is always a positive number.
Show your work
Explain your thinkingPlayer A's MAD is 2.4 points. If Player B's MAD is 7.2 points, what does that tell you about their consistency?
Sentence starter Player A has a ___ MAD, which means their scores are ___ to the mean. Player B has a ___ MAD, which means their scores are ___ from the mean. The more consistent player is ___ because ___.