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Mean Median IQR and MAD Test Answer Key with Scoring – Grade 6

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Last updated: October 22, 2026 · Written by the Math Made Easy math teachers

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Looking for a mean median IQR and MAD test answer key? Then this answer key gives the solutions and the scoring guide of the Grade 6 test on Measuring Center and Variability in Data.

Award the points in each scoring line. Give credit for correct work carried through from an earlier slip. Accept answers written as fractions or decimals, and take off a point when a median is found without ordering the data.

Standards: 6.SP.A.3, 6.SP.B.5c, 6.SP.B.5d · Level: Grade 6

Question 1 Mean and median (2 points)

Mean: (14 + 9 + 21 + 12 + 24) ÷ 5 = 80 ÷ 5 = 16. Ordered: 9, 12, 14, 21, 24, so the median is 14.

mean 16; median 14

Scoring: 1 point for each measure.

Question 2 Median and range (2 points)

Ordered: 26, 28, 31, 35, 36, 40. The median is (31 + 35) ÷ 2 = 33. The range is 40 − 26 = 14.

median 33; range 14

Scoring: 1 point for each measure.

Question 3 Mean and MAD from a dot plot (3 points)

  1. The sum is 2 + 3 + 4 + 4 + 5 + 5 + 5 + 6 + 7 + 9 = 50, so the mean is 50 ÷ 10 = 5.
  2. The distances from 5 are 3, 2, 1, 1, 0, 0, 0, 1, 2, 4, with a total of 14. The MAD is 14 ÷ 10 = 1.4.

Scoring: 1 point for the mean; 2 points for the MAD (1 point for the distances, 1 point for the answer).

Question 4 Quartiles (3 points)

  1. The median is (18 + 22) ÷ 2 = 20.
  2. Q1 = (15 + 17) ÷ 2 = 16 and Q3 = (25 + 27) ÷ 2 = 26.
  3. IQR = 26 − 16 = 10.
101214161820222426283032Value
Box plot of the 8 values.

Scoring: 1 point for each part.

Question 5 Missing score (2 points)

The total is 4 × 84 = 336. The known scores total 80 + 92 + 78 = 250. The fourth score is 336 − 250 = 86.

86

Scoring: 1 point for the total of 336, 1 point for the answer.

Question 6 Adding an outlier (3 points)

  1. Mean: 375 ÷ 5 = 75. Median: 75. Both are 75.
  2. The sum is 390, so the mean is 390 ÷ 6 = 65. The ordered values 15, 70, 72, 75, 78, 80 have median (72 + 75) ÷ 2 = 73.5. Mean 65; median 73.5.
  3. The mean changed by 10 and the median by 1.5. The mean changed more.

Scoring: 1 point for each part.

Question 7 Choosing a measure (3 points)

  1. The sum is 300,000, so the mean is 300,000 ÷ 6 = $50,000.
  2. The middle values are $33,000 and $35,000, so the median is $34,000.
  3. The median is better: the $134,000 salary is an outlier that pulls the mean above five of the six salaries.

Scoring: 1 point for each part.

Question 8 Comparing two teams (2 points)

  1. Team 1 median is 55 and Team 2 median is 58, so Team 2.
  2. Team 1: 62 − 48 = 14. Team 2: 60 − 52 = 8. Team 1 has the greater IQR.

Scoring: 1 point for each part.

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