Comparing Populations Using Samples

5 min

Narrative

This Warm-up reminds students of the meanings of mean and MAD by comparing two sets of data with similar values and asking whether they will have the same means or MADs or both.

Launch

Explain to students that the pairs of data sets are the following: A and B, X and Y, and P and Q.

Student Task

Without calculating, tell whether each pair of data sets have the same mean and whether they have the same mean absolute deviation.

  1.  

    Set A

    1

    3

    3

    5

    6

    8

    10

    14

      

    Set B

    21

    23

    23

    25

    26

    28

    30

    34

  2.  

    Set X

    1

    2

    3

    4

    5

      

    Set Y

    1

    2

    3

    4

    5

    6

  3.  

    Set P

    47

    53

    58

    62

      

    Set Q

    37

    43

    68

    72

Sample Response

  1. Sets A and B have different means but the same MADs.
  2. Sets X and Y have different means and different MADs.
  3. Sets P and Q have the same means but different MADs.
Activity Synthesis (Teacher Notes)

The purpose of the discussion is to bring out methods students used to notice whether the pairs of data sets have the same mean or the same MAD or both.

Poll the class for each pair of data sets as to whether they had the same mean, the same MAD, both, or neither.

After students have had a chance to register their vote, ask some students to explain their reasoning for their answer.

Anticipated Misconceptions

For students who have a difficult time starting without calculating, help them to compare the values in the ones place for the first and third pairs of data.

Standards
Building On
  • 6.SP.5.c·Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.
  • 6.SP.B.5.c·Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.
Building Toward
  • 7.SP.B·Draw informal comparative inferences about two populations.
  • 7.SP.B·Draw informal comparative inferences about two populations.

10 min

15 min

15 min