Free Printable WorksheetMathGrade 6Math Curriculum6.104

6.104 Find Interquartile Range and Mean Absolute Deviation and Interpret Variability Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Grade 6 Math worksheet provides structured practice on 6.104 Find Interquartile Range and Mean Absolute Deviation and Interpret Variability. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

Which answer choice correctly calculates interquartile range or mean absolute deviation and interprets what it means about variability? (CCSS 6.SP.B.5d; CA 6.SP.B.5d; MA 6.SP.B.5d; NY NY-6.SP.5d; FL MA.6.DP.1.3; TX 19 TAC §111.26(b)(12)(C))

Whether you are an educator preparing classroom handouts, a tutor reinforcing weekly topics, or a parent supporting homeschool learning, this printable resource gives students the deliberate practice required to achieve subject fluency and master state standards.

Grade

Grade 6

Subject

Math

Domain

Math Curriculum

Formats

PDF & DOCX

Sample Practice Problems

Preview the types of problems and questions covered in this worksheet

Below are sample questions representative of the exercises included on this worksheet and related 6.104 Find Interquartile Range and Mean Absolute Deviation and Interpret Variability skill assessments:

Problem 1Difficulty: Mastery

During the volleyball tryouts, the songs practiced by a group of students were recorded. Set 1: 10.5, 11, 13.5, 14.5, 19.5, 20, 23.5, 24, 25 Set 2: 10.5, 11, 13.5, 14.5, 19.5, 20, 23.5, 24, 25, 56 Set 2 is the same as Set 1 but with one extreme value added. Which statement about variability using MAD is correct? Round MAD to the nearest tenth if you calculate it.

AThe MAD stays the same because only the maximum changed.

BSet 1 has a larger MAD because it has fewer data values.

CSet 2 has a smaller MAD because the outlier pulls the mean toward it.

DSet 2 has a larger MAD because the extreme value is far from the mean, increasing the average distance from the mean.

Solution & Explanation:MAD is the average distance from the mean. Adding an extreme value adds a very large deviation, usually increasing MAD. Here, MAD(Set 1) ≈ 5.0 songs and MAD(Set 2) ≈ 8.3 songs, so Set 2 is more variable by MAD.

Problem 2Difficulty: Mastery

During the STEM night, the water samples tested by a group of students were recorded. Set 1: 10, 14, 15, 16, 20, 21, 26, 27, 28 Set 2: 10, 14, 15, 16, 20, 21, 26, 27, 28, 64 Set 2 is the same as Set 1 but with one extreme value added. Which statement about variability using IQR is correct?

ASet 2 has a larger IQR because it has a larger maximum value.

BSet 1 has a larger IQR because its range is smaller.

CThe IQRs are equal (12 samples), so the spread of the middle 50% is the same even though Set 2 has a much larger range.

DSet 2 must have a larger IQR because it has one more data value.

Solution & Explanation:IQR uses Q1 and Q3 (middle 50%). An extreme value at the end usually changes the range a lot but may not change Q1 or Q3. Here, both IQRs are 12 samples, so the middle 50% has the same spread in both sets.

Problem 3Difficulty: Mastery

During the math game tournament, the cards sold by a group of students were recorded. A data set has MAD = 5.1 cards. After a change, each data value is decreased by 4 cards. Which answer choice gives the new MAD and the correct reason?

AMAD = 9.1 cards; MAD increases by 4.

BMAD = 5.1 cards; shifting all values does not change how far they are from the mean.

CMAD = 5.1 cards; shifting changes the mean so MAD must change too.

DMAD = 4.0 cards; MAD becomes 4.

Solution & Explanation:MAD is an average distance from the mean. Shifting all values by the same amount does not change distances, but scaling multiplies distances.

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Frequently Asked Questions

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QWhat grade level and standards does this worksheet align with?

This worksheet is designed specifically for Grade 6 Math students. It aligns with educational standard 6.104 (Find Interquartile Range and Mean Absolute Deviation and Interpret Variability).