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Calculate Measures of Center

Students compute the mean, median, and mode of a data set and understand when each measure is most appropriate to describe the center of a distribution. They recognize that the mean is affected by outliers while the median is resistant to them.

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Calculate Measures of Center

Grade 6 · Statistics and Data Analysis · question 1 of 3

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20 rungs. A star at the top.

The mean of 4, 5, 6, 7 is

How it is taught

0:00 of 4:24

The mode is the value that appears most often.

Order the data before you hunt a median.

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Read it: The center of a data set

The data 9, 3, 10 and 6 total 28. Shared evenly among the 4 values, that is a mean of 7. In order, 3, 6, 9, 10, the middle pair is 6 and 9: the median is 7.5.

  1. For the mean, add the values: 9 + 3 + 10 + 6 = 28.
  2. Divide the total by how many values there are: 28 ÷ 4 = 7.
  3. For the median, order the values and find the middle: halfway between 6 and 9 is 7.5.

The mean is what each value would be if the total were shared out evenly.

The median has as many values below it as above it.

With an even number of values, the median is halfway between the middle pair.

Mean: add, then divide by how many. Median: put them in order, then find the middle.

Taking the middle of the list as it is written: 3 and 10 sit in the middle of 9, 3, 10, 6, so the median is 6.5.

Put them in order first: 3, 6, 9, 10. The middle pair is 6 and 9, so the median is 7.5.

The mean of 25, 29, 33, 41 is ___ — 32. 25 + 29 + 33 + 41 = 128, and 128 ÷ 4 = 32.

Mean, Median, Mode of {4, 7, 3, 7, 9}

Five friends scored points in a game. Let's find the center of their scores three different ways.

Here are the scores: four, seven, three, seven, and nine.

First, the mean. The mean is the average — we add all the numbers, then divide.

Four plus seven plus three plus seven plus nine equals thirty.

Now divide thirty by five, because there are five scores. Thirty divided by five is six.

Measures of CenterMean · Median · ModeScores:47379MEAN = sum ÷ count4 + 7 + 3 + 7 + 9 = 3030 ÷ 5 = 6MEAN6average scoreMEDIAN = middle valueSorted:34779MEDIAN7middle valueMODE = most frequent34779MODE7appears twiceOutliers pull the MEAN, not the MEDIANIf 9 → 90: mean jumps to 22, median stays 7Three Measures of CenterMEAN6averageMEDIAN7middleMODE7most often
Grade 6 · Three ways to describe the middle of a data set

Next, the median. The median is the middle number — but first we have to put the data in order.

Sorted from least to greatest: three, four, seven, seven, nine.

The middle value is seven. That's our median.

Last, the mode. The mode is the number that appears most often.

Seven shows up twice — every other number shows up just once. So the mode is seven.

Quick tip: if one score were huge, like ninety, the mean would jump way up, but the median would barely move. The median resists outliers!

Mean six, median seven, mode seven. Three ways to describe the center of our data!

What you see

While they climb, your page writes one true line to ask about tonight, and a short note each Sunday.

MayaGrade 3 · Mathematics
Did you know?

A chessboard has 64 squares — share them out between the 8 rows and each row holds exactly 8.

Today’s goal
1 star — one skill mastered, every rung of its ladder climbed
Climbing now
Divide within 100

An example student.

MayaGrade 3 · Mathematics

Maya earned 2 stars this week — Interpret multiplication as equal groups, which took 6 answers over 3 days before its star landed 3 days ago and Multiply by 6, 7, 8 and 9. Next up: Divide within 100.

An example week.

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