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Last updated: October 22, 2026 · Written by the Math Made Easy math teachers
Standards: 7.SP.B.3, 7.SP.B.4 · Level: Grade 7
Problem 2 Median and range
In order: 17, 18, 20, 22, 25, 28, 30. The middle value is 22. Range: 30 − 17 = 13.
median 22 miles; range 13 miles
Problem 3 Mean absolute deviation
Mean: 28 ÷ 4 = 7. Distances: 2, 2, 0, 0. Sum: 4. MAD: 4 ÷ 4 = 1.
MAD = 1
Problem 4 Read a box plot
Median: 23. IQR: 27 − 18 = 9. Range: 35 − 14 = 21.
median 23; IQR 9; range 21
Problem 5 Compare two means
84 − 78 = 6, and Class B is higher.
Class B, by 6 points
Problem 6 Which set is more spread out
Range of P: 7 − 3 = 4. Range of Q: 9 − 1 = 8.
Set Q is more spread out (range 8 versus 4)
Problem 7 Gap in MADs
Difference: 21 − 15 = 6. 6 ÷ 2 = 3.
3 times the MAD
Problem 8 MAD of eight values
Sum: 96, so mean = 96 ÷ 8 = 12.
Distances: 0, 3, 3, 2, 2, 0, 4, 4. Sum: 18. MAD: 18 ÷ 8 = 2.25.
mean 12; MAD 2.25
Problem 9 Seedling heights
Mean P: 230 ÷ 10 = 23 cm. Mean Q: 300 ÷ 10 = 30 cm.
Distances for P: 4, 2, 1, 0, 0, 0, 0, 1, 2, 4. Sum 14, so MAD = 1.4 cm.
Difference: 30 − 23 = 7. 7 ÷ 1.4 = 5.
means 23 cm and 30 cm; MAD 1.4 cm; the difference is 5 MADs
Problem 10 Two classes in box plots
Class A: median 72, IQR 80 − 65 = 15. Class B: median 78, IQR 85 − 70 = 15.
Difference of medians: 78 − 72 = 6. 6 ÷ 15 = 0.4.
medians 72 and 78; both IQR 15; difference is 0.4 of the IQR
Problem 11 Small gap
Difference: 52 − 48 = 4 minutes. 4 ÷ 6 ≈ 0.67.
The centers are less than 1 MAD apart, so the data overlap a lot.
about 0.67 MAD; the difference is small
Problem 12 Quartiles from a list
There are 11 values; the median is the 6th: 12.
Lower half: 5, 7, 8, 8, 10, so Q1 = 8. Upper half: 13, 15, 16, 20, 21, so Q3 = 16.
IQR: 16 − 8 = 8.
median 12; Q1 8; Q3 16; IQR 8
Problem 13 Build a box plot
Mark 3, 6, 9, 12 and 18 on a number line. Draw a box from 6 to 12 with a line at 9, and whiskers to 3 and 18.
Range: 18 − 3 = 15. IQR: 12 − 6 = 6.
range 15; IQR 6
Problem 14 Check a statement
Difference of the means: 36 − 30 = 6. 6 ÷ 4 = 1.5.
Yes: the means are 1.5 MADs apart
Problem 15 Pizza delivery times
Mean X: 280 ÷ 10 = 28. Mean Y: 400 ÷ 10 = 40.
Distances for X: 6, 3, 3, 0, 0, 0, 0, 3, 3, 6. Sum 24, so MAD = 2.4.
Difference: 40 − 28 = 12. 12 ÷ 2.4 = 5.
means 28 and 40 minutes; MAD 2.4; 5 MADs apart; Shop X is faster
Problem 16 Swim times
Lena: median 62, IQR 65 − 60 = 5. Omar: median 61, IQR 63 − 59 = 4.
Difference of medians: 1 second. 1 ÷ 5 = 0.2 of the larger IQR.
medians 62 and 61; IQR 5 and 4; the gap is only 0.2 IQR, so neither swimmer is clearly faster
Problem 17 Two weeks of weather
Week 1: sum 420, mean 70. Distances: 4, 0, 2, 2, 4, 0. Sum 12, MAD = 2.
Week 2: sum 456, mean 76. Distances: 4, 0, 2, 2, 4, 0. Sum 12, MAD = 2.
Difference: 76 − 70 = 6. 6 ÷ 2 = 3.
means 70°F and 76°F; both MAD 2°F; the means differ by 3 MADs
Problem 18 Quiz scores of two classes
P: sum 42, mean 7. Distances: 2, 1, 0, 0, 1, 2, sum 6, MAD = 1.
Q: sum 48, mean 8. Distances: 2, 1, 0, 0, 1, 2, sum 6, MAD = 1.
Difference: 1 point, which is 1 MAD.
means 7 and 8; both MAD 1; the difference is only 1 MAD, so the classes overlap a lot
Problem 19 Medians and spread
IQR of Group 1: 46 − 34 = 12. IQR of Group 2: 64 − 50 = 14. The spreads are similar.
Difference of medians: 58 − 40 = 18. 18 ÷ 12 = 1.5.
IQRs 12 and 14; the medians differ by 1.5 times the IQR of Group 1
Problem 20 Tomato plots
Plot 1: sum 56, mean 7. Distances: 2, 1, 1, 0, 0, 1, 1, 2. Sum 8, MAD = 1.
Plot 2: sum 72, mean 9, and the same MAD of 1.
Difference: 9 − 7 = 2 ounces, or 2 MADs.
means 7 oz and 9 oz; MAD 1 oz for both; a difference of 2 MADs, so the plots overlap but Plot 2 is clearly heavier on average