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Unit 10 · Final Applications and ReviewLesson

Day 138Reporting Class Reading Data

LearnClassworkAnswer keyPDF packet ↗
Standards 6.SP.A.16.SP.B.5a6.SP.B.5b6.SP.B.5c6.SP.A.36.SP.B.46.SP.B.5d
LEARNING TARGET

I can represent and summarize a collection of reading data.

01 · LEARN

Build the idea

Read the requested quantity first and identify the relevant model. A statistical question anticipates different answers in a collection of data. Name the group, the measured attribute, and the expected variation. A question about one fixed fact is not statistical. Explain why the units and the final value fit the situation.

WORKED EXAMPLE 1

Reading times in minutes are 5, 6, 6, 7, 7, 8. Report n, units, and mean.

n = 6; minutes; mean 13/2 min

Sum = 39; mean = 39 ÷ 6 = 13/2.

WORKED EXAMPLE 2

Reading times in minutes are 6, 7, 7, 8, 9, 18. Find the five-number summary and draw a labeled box plot. State the IQR.

(6, 7, 15/2, 9, 18); IQR 2 min

Box runs from 7 to 9, median line at 15/2, whiskers to 6 and 18.

02 · PRACTICE

Your turn

Work in order. Start with the foundations, then build toward explanation and application.

  1. Is “How many pages did each student read last night?” statistical? Explain.

  2. Reading times in minutes are 6, 7, 7, 8, 8, 9. Report n, units, and mean.

  3. Reading times in minutes are 6, 7, 7, 8, 8, 9. Find the median. Show the middle positions.

  4. Reading times in minutes are 2, 8, 8, 14, 14, 20. Find Q1, Q3, IQR, and range.

  5. Reading times in minutes are 3, 8, 8, 13, 13, 18. Calculate the mean and MAD. Show all absolute deviations.

  6. Reading times in minutes are 5, 10, 10, 15, 15, 20. Draw a labeled dot plot. Check the number of dots.

  7. Daily reading times in minutes: 3, 8, 3, 12, 11, 3, 18, 13, 7, 13. Draw a histogram using bins 0–4, 5–9, 10–14, and 15–19. Label axes. Which interval has the greatest frequency? Include ties.

  8. Reading times in minutes are 4, 5, 5, 6, 7, 16. Find the five-number summary and draw a labeled box plot. State the IQR.

  9. Reading times in minutes are 8, 9, 9, 10, 11, 20. Write a summary with count, attribute, units, center, variability, shape, and a justified choice of measures.

  10. Critique: “A question is statistical whenever it contains numbers.” Give a counterexample and a corrected rule.

03 · CHECK

Answers and reasoning

Reveal the teacher answer key
  1. Yes; pages read vary across students.

    Look for a collection of data and anticipated variation; identify the population and variable.

  2. n = 6; minutes; mean 15/2 min

    Sum = 45; mean = 45 ÷ 6 = 15/2.

  3. Median 15/2 min

    6 ordered values: average positions 3 and 4: (7 + 8) ÷ 2 = 15/2.

  4. Q1 8, Q3 14; IQR 6 min; range 18 min

    Lower half [2, 8, 8] has median 8; upper half [14, 14, 20] has median 14. Subtract Q1 from Q3.

  5. Mean 21/2 min; MAD 25/6 min

    Distances: 15/2, 5/2, 5/2, 5/2, 5/2, 15/2; sum 25; divide by 6 = 25/6.

  6. 5: 1 dot; 10: 2 dots; 15: 2 dots; 20: 1 dot; n = 6

    Each observation contributes one dot; stack repeated values at their number-line position.

  7. Frequencies 3, 2, 4, 1; greatest: 10–14

    Count every value once. Bars touch and have equal width; horizontal axis is minutes, vertical axis is frequency.

  8. (4, 5, 11/2, 7, 16); IQR 2 min

    Box runs from 5 to 7, median line at 11/2, whiskers to 4 and 16.

  9. 6 observations of reading time in minutes. Median 19/2 min, IQR 2 min; right-skewed with a high value 20 min, so median/IQR resist that value.

    Calculate the center and spread before interpreting them in context. Other accurate, justified summaries are acceptable.

  10. Counterexample: How many sides does a triangle have? It has a fixed answer. A statistical question anticipates variability in a collection of data.

    Look for a collection of data and anticipated variation; identify the population and variable.

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