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Back to Exercise: Summarize numerical data sets in relation to their context

Exercises: Summarizing Data Sets

Show your work. Always state units when interpreting your answers.

Grade 6·22 problems·~45 min·Common Core Math - Grade 6·standard·6-sp-b-5
Work through problems with immediate feedback
A

Warm-Up: Review What You Know

These problems review skills you need for data summaries.

1.

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

2.

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

3.

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?

B

Fluency Practice

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

1.

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

2.

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.
3.

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:
4.

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

5.

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?

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