Grade 6 Math · Topic 66

Median and Mode

The median is the middle value when the data are in order. The mode is the value that appears most often. Both are useful measures of center, and they are easier on data sets with outliers than the mean.

Lesson alignment: 6.SP.A.3 · Take your time. You can return to this lesson whenever you need it.

Explore visually

Find the median and mode

Sort the data to locate the middle value; compare frequencies to find the mode.

Think first: Which value will be in the middle after sorting, and which value occurs most often?

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Follow the worked examples

Read each step, then cover the explanation and see if you can explain why it works.

Worked example 1

Find median and mode of 3, 7, 5, 7, 9, 7, 4.

Sort the data first so the middle and repeated values are easier to see. Sort: 3, 4, 5, 7, 7, 7, 9. Median (middle of 7 values) = 7. Mode = 7 (appears three times).

Answer: Median = 7, Mode = 7

Worked example 2

Find the median of 2, 4, 6, 8, 10, 12.

Even count. Two middle values are 6 and 8. Median = (6+8)/2 = 7.

Answer: 7

Try a few on your own

Work these on paper first. Open “Check” when you are ready to compare your answer.

  1. Median: 1, 3, 5, 7, 9
    Check

    5

  2. Median: 2, 4, 6, 8
    Check

    5

  3. Mode: 5, 7, 5, 9, 5, 7
    Check

    5

  4. Median: 10, 12, 14, 16, 18
    Check

    14

  5. Mode: 1, 2, 3, 4, 5
    Check

    No mode

  6. Median: 3, 8, 1, 7, 5
    Check

    5

  7. Median: 6, 10, 4, 8, 2, 12
    Check

    7

  8. Mode: 4, 4, 6, 6, 8, 4, 6, 6
    Check

    6

Try this situation 1

Quiz scores: 85, 90, 78, 92, 88, 90, 75. Find the median and mode.

Show a worked solution

Answer: Median = 88, Mode = 90.

Sorted: 75, 78, 85, 88, 90, 90, 92. Mode is 90 (appears twice).

Try this situation 2

Shoe sizes in a group: 6, 7, 7, 8, 8, 8, 9, 10. Find the median and mode.

Show a worked solution

Answer: Median = 8, Mode = 8.

Two middle values: 8 and 8, so median = 8. The most frequent value is 8.

Fresh questions · saved on this device

Practice this skill

50 question pool

Try a fresh set each time. Answer one question, check your thinking, and read the explanation. If you miss one, return to the visual model and try another round.

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Check what you learned

Answer these five questions on your own. You can review the explanations after you submit and try again whenever you like. This short check is for practice, not a grade.

1. The daily high temperatures (in degrees Fahrenheit) over two weeks are: 72, 75, 72, 78, 75, 72, 80, 73, 78, 75, 82, 74, 78, 78. What is the mode?

2. The heights of basketball players (in inches) are: 72, 75, 68, 71, 74, 69, 73. What is the median height?

3. The number of books read by students in a month: 3, 5, 7, 5, 9, 4, 5, 8, 6. What is the mode?

4. Find the median of 4, 8, 6, 10, 12.

5. What is the mode of 2, 3, 3, 5, 6?

Practice and finish

Try the linked topic quiz for more practice. If something is tricky, return to the example and look for the step that changes the numbers or representation.

Open the practice quiz

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More Grade 6 resources

Use these free materials if you want another explanation, extra paper practice, or a broader review.

Browse free Grade 6 topic lessons ↗Print Grade 6 worksheets ↗Review Grade 6 flashcards ↗Open the formula review ↗Try the Statistics & Data quiz ↗Try a full practice test ↗