Math Coach Lesson index ↗
Unit 09 · Statistics and Data DisplaysLesson

Day 124Medians and Unusual Values

LearnClassworkAnswer keyPDF packet ↗
Standards 6.SP.B.5c
LEARNING TARGET

I can find a median and compare it with the mean.

01 · LEARN

Build the idea

Order the data first. For an odd count, choose the middle value. For an even count, average the two middle values. The median often resists an unusually high or low value better than the mean.

WORKED EXAMPLE 1

Reading times in minutes are 4, 5, 5, 6, 6, 7. Find the median. Show the middle positions.

Median 11/2 min

6 ordered values: average positions 3 and 4: (5 + 6) ÷ 2 = 11/2.

WORKED EXAMPLE 2

Reading times in minutes are 8, 9, 9, 10, 11, 20. Find the median and mean. Explain the difference in this set.

Median 19/2 min; mean 67/6 min; the high value pulls the mean upward

6 ordered values: average positions 3 and 4: (9 + 10) ÷ 2 = 19/2.

02 · PRACTICE

Your turn

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

  1. Reading times in minutes are 4, 5, 5, 6, 6, 7. Find the median. Show the middle positions.

  2. Reading times in minutes are 3, 4, 4, 5, 5, 6. Find the median. Show the middle positions.

  3. Reading times in minutes are 2, 3, 3, 4, 4, 5. Find the median. Show the middle positions.

  4. Reading times in minutes are 8, 10, 10, 12, 12, 14. Find the median. Show the middle positions.

  5. Reading times in minutes are 4, 8, 8, 12, 12, 16. Find the median. Show the middle positions.

  6. Reading times in minutes are 2, 7, 7, 12, 12, 17. Find the median. Show the middle positions.

  7. Reading times in minutes are 6, 7, 7, 8, 9, 18. Find the median and mean. Explain the difference in this set.

  8. Reading times in minutes are 4, 5, 5, 6, 7, 16. Find the median and mean. Explain the difference in this set.

  9. Reading times in minutes are 3, 4, 4, 5, 6, 15. Find the median and mean. Explain the difference in this set.

  10. Reading times in minutes are 8, 9, 9, 10, 11, 20. Find the median and mean. Explain the difference in this set.

03 · CHECK

Answers and reasoning

Reveal the teacher answer key
  1. Median 11/2 min

    6 ordered values: average positions 3 and 4: (5 + 6) ÷ 2 = 11/2.

  2. Median 9/2 min

    6 ordered values: average positions 3 and 4: (4 + 5) ÷ 2 = 9/2.

  3. Median 7/2 min

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

  4. Median 11 min

    6 ordered values: average positions 3 and 4: (10 + 12) ÷ 2 = 11.

  5. Median 10 min

    6 ordered values: average positions 3 and 4: (8 + 12) ÷ 2 = 10.

  6. Median 19/2 min

    6 ordered values: average positions 3 and 4: (7 + 12) ÷ 2 = 19/2.

  7. Median 15/2 min; mean 55/6 min; the high value pulls the mean upward

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

  8. Median 11/2 min; mean 43/6 min; the high value pulls the mean upward

    6 ordered values: average positions 3 and 4: (5 + 6) ÷ 2 = 11/2.

  9. Median 9/2 min; mean 37/6 min; the high value pulls the mean upward

    6 ordered values: average positions 3 and 4: (4 + 5) ÷ 2 = 9/2.

  10. Median 19/2 min; mean 67/6 min; the high value pulls the mean upward

    6 ordered values: average positions 3 and 4: (9 + 10) ÷ 2 = 19/2.

← Lesson indexBack to top ↑Day 125 →