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Use Measures of Center and Variability to Compare Data

Students use measures of center (mean, median) and measures of variability (mean absolute deviation, interquartile range) to draw comparative inferences about two populations from random samples. They explain what the numerical measures reveal about similarities and differences between groups.

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Use Measures of Center and Variability to Compare Data

Grade 7 · Statistics and Probability · question 1 of 3

0 of 20

20 rungs. A star at the top.

The MAD of 18, 20, 22, 24, 26 is

How it is taught

0:00 of 4:20

Range is highest minus lowest.

Spread matters when you compare two groups.

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Read it: Mean and median

The data 11, 4, 13 and 8 total 36. Shared evenly among the 4 values, that is a mean of 9. In order, 4, 8, 11, 13, the middle pair is 8 and 11: the median is 9.5.

  1. For the mean, add the values and divide by how many there are.
  2. For the median, order the values and find the middle.
  3. With an even count, the median is halfway between the middle pair.

The mean shares the total evenly: 36 ÷ 4 = 9 for each of the 4 values.

The median has as many values below it as above it, once the values are in order.

A missing value runs the mean backwards: the mean times the count is the total.

Mean = the total ÷ the count; median = the middle value in order.

Taking the middle of the list as written: 4 and 13 make 8.5.

Order the values first: 4, 8, 11, 13, so the median is 9.5.

The mean of 24, 28, 32, 40 is ___ — 31. 24 + 28 + 32 + 40 = 124, and 124 ÷ 4 = 31.

Class A vs Class B: pull-ups

Two PE classes had a pull-up contest. Let's compare how the two groups did.

Class A scored three, five, six, seven, and nine pull-ups.

Class B scored one, four, six, eight, and eleven pull-ups.

The mean of Class A is six pull-ups — that's the average.

The mean of Class B is also six. Same center!

The medians match too — both classes balance right at six.

Same average — but really the same?Comparing two classes' pull-up scoresClass A012Class B012Mean of A = 6Mean of B = 6Same center — medians match tooMAD of A = 1.6MAD of B = 2.8Class B's scores swing farther from 6Same mean, different spread.MAD reveals who is consistent.TAKEAWAYMADmeasures spread
Grade 7 · Two classes, same average — but are they really alike?

But how spread out are the scores? For Class A, the average distance from six is one point six.

For Class B, the average distance from six is two point eight — almost double!

Same center, but Class B has more variability — its scores swing farther from the average.

When two groups share a mean, the MAD tells us who is consistent. Class A is tight; Class B is spread out.

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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