Task Sets: Use measures of center and measures of variability to draw informal comparative inferences about two populations - Common Core Math - Grade 7

Recall / Warm-Up

A data set is: 4, 5, 6, 6, 7, 7, 8, 9, 42. Which measure of center best represents a typical value in this data set?

Mean, because it uses every value.

Median, because the outlier 42 pulls the mean far above most values.

Mean, because the data set has an even number of values.

Median, because the data set has values in the single digits.

You decide to use the median to describe the center of a data set. Which measure of variability is the best match for your choice?

MAD (Mean Absolute Deviation)

IQR (Interquartile Range)

Range

Mean

Compute the IQR of this data set: 3, 4, 5, 6, 7, 8, 9.

Fluency

Compute the mean of the following data set: 3, 4, 4, 5, 5, 5, 6, 6, 7, 8.

Data set: 4, 5, 6, 6, 7, 7, 8, 9, 10, 13. The mean of this data set is 7.5. Compute the MAD.

A data set has one extremely large outlier. Which measure of variability is more resistant to the outlier's effect?

MAD, because it uses every value in the data set.

IQR, because it is computed from the middle 50% of values and the outlier falls in the upper tail.

Both are equally resistant to outliers.

Neither — both are affected the same way by outliers.

Compute the IQR of the following data set: 4, 5, 6, 6, 7, 7, 8, 9, 10, 13.

A random sample of word lengths from two science textbooks produced these results: 4th-grade — median = 5 letters, IQR = 2 letters; 7th-grade — median = 7 letters, IQR = 3 letters. Which statement best compares the two samples?

Words in the 7th-grade text are exactly 2 letters longer than words in the 4th-grade text.

Words in the 7th-grade text tend to be about 2 letters longer than words in the 4th-grade text; the 7th-grade text also has slightly more variability in word length (IQR = 3 vs. 2).

The 7th-grade text has a higher median, so all of its words are longer than 4th-grade words.

The two samples cannot be compared because the IQR values are different.

Comparing Two Populations: Center, Variability, and Informal Inference

Recall / Warm-Up

Fluency