Back to Tutor Intake Assessment: Use measures of center and measures of variability to draw informal comparative inferences about two populations

7.SP.B.4 Tutor Intake -- Comparing Two Populations with Center and Variability

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Grade 7·8 problems·~12 min·Common Core Math - Grade 7·standard·7-sp-b-4

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Concepts

Data Set A: 5, 6, 6, 7, 7, 7, 8, 8, 9, 10
Data Set B: 5, 6, 6, 7, 7, 7, 8, 8, 9, 27

Data Set B has one unusually large value (27) that Data Set A
does not have. Which measure of center should you use to
describe Data Set B's typical value, and why?

Median — it is not pulled toward the outlier the way the mean is

Mean — it is the most commonly used measure, so it should always be reported

Median — because the mean cannot be computed when an outlier is present

Mean — because it uses every data value, so it is always more accurate

A data set's median word length is used to describe its center.
Which measure of variability should be paired with the median,
and why?

IQR — both the median and IQR are based on the position of values, not their arithmetic average

MAD — a higher MAD always means the data is less trustworthy

Range — range and median were introduced in the same grade

It doesn't matter which variability measure is used with the median

Procedures

Find the median of this data set: 3, 4, 4, 5, 5, 5, 6, 6, 7, 8.

Find the Interquartile Range (IQR) of this data set:
4, 5, 6, 6, 7, 7, 8, 9, 10, 13.

A data set has mean 7.5. The absolute deviations of its 4 values
from the mean are 3.5, 1.5, 0.5, and 2.5. What is the Mean
Absolute Deviation (MAD) of this data set?

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