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6th grade · Math · Unit 21 of 21

Center, Spread & Shape

Describe a set of data

What your child practices

Telling statistical questions (answers that vary) from questions with one answer, and describing data by its center (mean, median), its spread (range, IQR) and its shape (clusters, outliers, symmetric or skewed), and knowing that each measure sums up the data in one number.

New York State Learning Standards learning standard: NY-6.SP.1a; NY-6.SP.2; NY-6.SP.3 · recognizing statistical questions, describing a data distribution by its center, spread and overall shape, and telling measures of center from measures of variation

How we explain it

Children can open this short lesson before they practice.

  1. Describe data by its typical value, its spread and its shape.
  2. The mean and the median sum up all the values in one typical number.
  3. The range and the IQR sum up in one number how much the values vary.

Example: Find the median and the range of 3, 5, 6, 8, 13. The middle value is 6, so the median is 6. 13 − 3 = 10, so the range is 10. Answer: Median 6, range 10

Center, Spread & Shape in New York

In the New York State Learning Standards, this is unit 21 of 21 in 6th grade Math, after Perfect Squares & Cubes.

Gradelings describes a child's practice on this unit as Beginning, Approaching, Meeting or Exceeding (Four practice steps). That reflects practice, not a report-card mark: the teacher decides the mark.

Source: New York State Education Department (NYSED)

Sample questions

A taste of this unit. In the app, questions change every time and get easier or harder to match your child.

  1. Question 1

    Which number tells how spread out the data is in one number?

    • the least value
    • the number of values
    • the mean
    • the mean absolute deviation (MAD)

  2. Question 2

    Two classes both have a mean of 6 books read. Class A has a range of 2; Class B has a range of 8. What does this tell you?

    • Both are typically the same, but Class B's values are more spread out
    • The classes read exactly the same numbers of books
    • Class A's values are more spread out
    • Class B read more books in all

  3. Question 3

    Find the mean, a measure of center.

    Pets per family (pets): 1, 2, 2, 7, 9, 13, 15

    • 9
    • 7
    • 14
    • 8

  4. Question 4

    Why is “How many hours do students in our class sleep on school nights?” a statistical question?

    • it uses a number
    • it asks about one person or thing
    • it has one exact answer
    • the answers are expected to vary

  5. Question 5

    What three things describe a distribution of data?

    • the number of questions asked
    • only its greatest value
    • its first value, last value and title
    • its center, its spread and its overall shape

  6. Question 6

    Find the mean, a measure of center.

    Hours of sleep (hours): 4, 7, 10, 10, 14

    • 9
    • 7
    • 10
    • 6

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