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Unit 09 · Statistics and Data DisplaysLesson

Day 133Comparing Data Sets

LearnClassworkAnswer keyPDF packet ↗
Standards 6.SP.A.26.SP.B.5d
LEARNING TARGET

I can compare centers and variability in two data sets.

01 · LEARN

Build the idea

Compute comparable measures for both groups. Compare typical values and consistency using the same units. State what the data support without claiming that every member of one group exceeds every member of the other.

WORKED EXAMPLE 1

Reading times (min): Group A [2, 3, 3, 4, 4, 5], Group B [4, 5, 5, 6, 6, 7]. Compare median and IQR. Which group reads longer typically? Which is more consistent?

A median 7/2, B median 11/2 min; both IQR 1 min. B is typically 2 min higher; equal middle-half variability.

Adding 2 shifts all values and the median by 2, but does not change Q3 - Q1.

WORKED EXAMPLE 2

Reading times (min): Group A [6, 7, 7, 8, 9, 18], Group B [8, 9, 9, 10, 11, 20]. Compare median and IQR. Which group reads longer typically? Which is more consistent?

A median 15/2, B median 19/2 min; both IQR 2 min. B is typically 2 min higher; equal middle-half variability.

Adding 2 shifts all values and the median by 2, but does not change Q3 - Q1.

02 · PRACTICE

Your turn

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

  1. Reading times (min): Group A [2, 3, 3, 4, 4, 5], Group B [4, 5, 5, 6, 6, 7]. Compare median and IQR. Which group reads longer typically? Which is more consistent?

  2. Reading times (min): Group A [8, 9, 9, 10, 10, 11], Group B [10, 11, 11, 12, 12, 13]. Compare median and IQR. Which group reads longer typically? Which is more consistent?

  3. Reading times (min): Group A [4, 5, 5, 6, 6, 7], Group B [6, 7, 7, 8, 8, 9]. Compare median and IQR. Which group reads longer typically? Which is more consistent?

  4. Reading times (min): Group A [6, 8, 8, 10, 10, 12], Group B [8, 10, 10, 12, 12, 14]. Compare median and IQR. Which group reads longer typically? Which is more consistent?

  5. Reading times (min): Group A [2, 6, 6, 10, 10, 14], Group B [4, 8, 8, 12, 12, 16]. Compare median and IQR. Which group reads longer typically? Which is more consistent?

  6. Reading times (min): Group A [8, 11, 11, 14, 14, 17], Group B [10, 13, 13, 16, 16, 19]. Compare median and IQR. Which group reads longer typically? Which is more consistent?

  7. Reading times (min): Group A [7, 8, 8, 9, 10, 19], Group B [9, 10, 10, 11, 12, 21]. Compare median and IQR. Which group reads longer typically? Which is more consistent?

  8. Reading times (min): Group A [4, 5, 5, 6, 7, 16], Group B [6, 7, 7, 8, 9, 18]. Compare median and IQR. Which group reads longer typically? Which is more consistent?

  9. Reading times (min): Group A [5, 6, 6, 7, 8, 17], Group B [7, 8, 8, 9, 10, 19]. Compare median and IQR. Which group reads longer typically? Which is more consistent?

  10. Reading times (min): Group A [3, 4, 4, 5, 6, 15], Group B [5, 6, 6, 7, 8, 17]. Compare median and IQR. Which group reads longer typically? Which is more consistent?

03 · CHECK

Answers and reasoning

Reveal the teacher answer key
  1. A median 7/2, B median 11/2 min; both IQR 1 min. B is typically 2 min higher; equal middle-half variability.

    Adding 2 shifts all values and the median by 2, but does not change Q3 - Q1.

  2. A median 19/2, B median 23/2 min; both IQR 1 min. B is typically 2 min higher; equal middle-half variability.

    Adding 2 shifts all values and the median by 2, but does not change Q3 - Q1.

  3. A median 11/2, B median 15/2 min; both IQR 1 min. B is typically 2 min higher; equal middle-half variability.

    Adding 2 shifts all values and the median by 2, but does not change Q3 - Q1.

  4. A median 9, B median 11 min; both IQR 2 min. B is typically 2 min higher; equal middle-half variability.

    Adding 2 shifts all values and the median by 2, but does not change Q3 - Q1.

  5. A median 8, B median 10 min; both IQR 4 min. B is typically 2 min higher; equal middle-half variability.

    Adding 2 shifts all values and the median by 2, but does not change Q3 - Q1.

  6. A median 25/2, B median 29/2 min; both IQR 3 min. B is typically 2 min higher; equal middle-half variability.

    Adding 2 shifts all values and the median by 2, but does not change Q3 - Q1.

  7. A median 17/2, B median 21/2 min; both IQR 2 min. B is typically 2 min higher; equal middle-half variability.

    Adding 2 shifts all values and the median by 2, but does not change Q3 - Q1.

  8. A median 11/2, B median 15/2 min; both IQR 2 min. B is typically 2 min higher; equal middle-half variability.

    Adding 2 shifts all values and the median by 2, but does not change Q3 - Q1.

  9. A median 13/2, B median 17/2 min; both IQR 2 min. B is typically 2 min higher; equal middle-half variability.

    Adding 2 shifts all values and the median by 2, but does not change Q3 - Q1.

  10. A median 9/2, B median 13/2 min; both IQR 2 min. B is typically 2 min higher; equal middle-half variability.

    Adding 2 shifts all values and the median by 2, but does not change Q3 - Q1.

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