Back to Tutor Intake Assessment: Summarize numerical data sets in relation to their context

6.SP.B.5 Tutor Intake -- Summarizing Data in Context

This short check helps your tutor see where to start. Work on your own,
without a calculator. If you're unsure, give your best try — the goal is
to find what to work on together, not to grade you.

Grade 6·6 problems·~9 min·Common Core Math - Grade 6·standard·6-sp-b-5

Work through problems with immediate feedback

Concepts

A report says only: "The average is 57.84." What is missing for
this to be a complete, interpretable summary?

The number of observations (n), what attribute was measured and in what units — without these, "57.84" can't be connected to anything.

Nothing — a single computed number is always a complete summary.

A second decimal place, for more precision.

A graph, since numbers alone are never meaningful.

When computing the mean absolute deviation (MAD), why do we take
the ABSOLUTE VALUE of each deviation from the mean, instead of
just averaging the deviations directly?

Signed deviations from the mean always sum to zero, so their average would always be zero — useless as a variation measure. Absolute value prevents that cancellation.

Absolute value makes the numbers bigger, which is more useful.

It's just a convention with no mathematical reason.

Absolute value is needed only when some data values are negative.

Procedures

A data set has quartiles Q1 = 4 and Q3 = 10. Find the
INTERQUARTILE RANGE (IQR).
(Note: this data set also has a minimum of 2 and a maximum of
12 — make sure you compute IQR, not range.)

Find the MEAN ABSOLUTE DEVIATION (MAD) for this data set: 6, 8,
10. Enter your answer as a decimal or fraction.

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