6.SP.B.5: Summarize numerical data sets in relation to their context — Practice

Warm-Up: Review What You Know

These problems review skills you need for data summaries.

A measure of center summarizes data with a single representative number. Which of these is a measure of center?

Range

IQR

MAD

Median

A student collects 5 test scores: 12, 7, 15, 4, 9. What is the sum of all five scores?

Five students scored 70, 80, 90, 85, and 75 on a quiz. A classmate says 'the typical score is about 80.' Which operation would let you check this claim by finding the exact average?

Add all five scores together, then divide by 5.

Multiply all five scores together, then divide by 5.

Subtract the smallest score from the largest score.

List the scores in order and pick the middle one.

Fluency Practice

Compute each summary statistic. Show your work step by step.

Data set: {8, 10, 12, 14, 16}. Find the mean.

Data set (sorted): {5, 8, 11, 14, 17, 20}. This data set has ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ values (even count). The two middle values are ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ and ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ . The median = average of these two = ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ .

number of values:

lower middle value:

upper middle value:

median:

$MAD computation table with column 'Value' and column 'Absolute Deviation from Mean (7)'. Values 3, 5, 7, 9, 11 listed. Deviation column has question marks to fill in.$

Data set: {3, 5, 7, 9, 11}. Mean = 7.

Compute MAD step by step. Fill in the absolute deviations from the mean:
|3 − 7| = ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ , |5 − 7| = ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ , |7 − 7| = ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ , |9 − 7| = ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ , |11 − 7| = ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ .
Sum of absolute deviations = ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ . MAD = sum ÷ 5 = ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ .

|3 - 7|:

|5 - 7|:

|7 - 7|:

|9 - 7|:

|11 - 7|:

sum:

MAD:

Data set (sorted): {12, 15, 18, 21, 24, 27, 30, 33, 36}. Find the IQR.

A student computes the 'average deviation' by finding each value's distance from the mean but forgets absolute values. She adds the signed deviations: (3−7) + (5−7) + (7−7) + (9−7) + (11−7) = (−4)+(−2)+0+2+4 = 0. She concludes 'the average deviation is 0, meaning the data has no variation.' What went wrong?

She should have divided by n−1 instead of n, applying a formula meant for a different statistic.

She computed the mean incorrectly, so every deviation that followed was based on a wrong reference point.

She is correct — the data has no variation, since her signed deviations summed to exactly zero.

She forgot to take the absolute value of each deviation. Signed deviations always sum to zero, so she needs |value − mean| before averaging.

Exercises: Summarizing Data Sets

Warm-Up: Review What You Know

Fluency Practice