Neft Teacher · Learn It

Unit 2 · Standard 6.DS.4

Describe the Data Using the Median

Lesson 2-3 · Learn It — how the math works

Why we're learning this

You're the stats analyst for the school basketball team. Coach needs a report on the team's scoring: in the last 7 games they scored 42, 38, 55, 41, 38, 44, and 40 points. Which average best represents the team's typical performance?

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What are mean, median, and mode?

Mean, median, and mode are three ways to find the center, or "typical" value, of a data set. The mean is the average, the median is the middle, and the mode is the most common value.

Picture itSee what the math looks like before you read about it

Some students surveyed the teachers at their school about their years of teaching experience. The data they collected is shown.
Where you see this in real lifeSome students surveyed the teachers at their school about their years of teaching experience. The data they collected is shown.

Watch me solve itI do — read one step at a time

The problem looks like this
Dot plot of 2, 4, 4, 6, 9. The 3rd of the 5 values is 4, so the median is 4.23456789Median is the middle value: 4
  1. My data set: 2, 4, 4, 6, 9 — five values, already in order. Ordering first is what makes a middle exist at all.
  2. With 5 values, the middle is the 3rd one. Counting in from both ends: 2 and 9 pair off, 4 and 6 pair off, and 4 is left alone.
  3. So the is 4. Half the values sit at or below it and half at or above it.
  4. Now an even set: 2, 4, 6, 9. There is no single middle, so I take the mean of the two middle values: (4 + 6) ÷ 2 = 5. The is 5, even though 5 is not in the data.(4 + 6) ÷ 2 = 5

Watch out — mistakes students make here

  • The largest value is the maximum, not the middle.
  • With an even count, take the average of the two middle values.
  • Don't add all values and divide—find the middle two values.

Try it with meWe do — you answer first, then check

Same steps, new numbers.

  1. New data set, out of order: 13, 3, 7, 10, 7. Put it in order first.
  2. In order: 3, 7, 7, 10, 13. Five values, so the middle is the 3rd.
  3. The is 7. Say what it means: a typical value in this set is about 7.
  4. Now change the 13 to 130. Does the move?
    Check this step
    It does not — still 7. That resistance is exactly why the is used.

On your ownYou do — solve this one by yourself

Before you start, remember:

  • Order the team's game scores from least to greatest.
  • Find the , and say whether the count is odd or even.
  • Decide what the tells you about a typical game.

Solve: Data set: 4, 6, 6, 8, 10, 12. What is the ?

My answer

Stuck? Open one hint at a time.

Hint 1

Count the values: there are 6, an even number — so no single value sits exactly in the middle.

Hint 2

With an even count, the median is the average of the TWO middle values. In an ordered list of 6, those are the 3rd and 4th.

Hint 3

The list is already ordered. Step 1: circle the 3rd and 4th values. Step 2: add them and divide by 2 — that result is the median.

Check my answer
✅ Answer: 7
With 6 values, the median is the average of the 3rd and 4th values: (6 + 8) ÷ 2 = 7.

Turn & TalkSay it out loud with a partner

The team scored 42, 38, 55, 41, 38, 44, 40 points over 7 games. Which 'average' would best tell the coach the team's typical scoring: mean, , or ?

Try starting with:

  • I would use the ___ because it best shows the typical score.Usaría la ___ porque muestra mejor el puntaje típico.
  • The ___ is the most common score, which is ___.La ___ es el puntaje más común, que es ___.
Use these wordsmeanmedianmodeaveragedata set