6th Grade Mean, Median, Spread and Box Plots Worksheet Solutions (PDF)

6th Grade math worksheet solutions: Mean, Median, Spread and Box Plots – Maths PDF

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This center spread answers for 6th Grade covers mean, median, spread and box plots (Common Core 6.SP.A.3, 6.SP.B.5c, 6.SP.B.5d), with a free PDF to print.

Check each statistic here. The solutions show the ordered data, the sums and distances used, and each final answer in bold. Box plots and dot plots support several solutions.

Grade 6 · Common Core State Standards: 6.SP.A.3, 6.SP.B.5c, 6.SP.B.5d

Center spread answers: exercises 1 to 10

Exercise 1 – Mean

Add: \(4 + 8 + 6 + 10 + 12 = 40\).

Divide by 5: \(40 \div 5 = 8\).

Exercise 2 – Median (odd)

Order: 1, 3, 5, 7, 9. The middle value is the 3rd.

Exercise 3 – Median (even)

The middle two values are 4 and 6.

\(\frac{4 + 6}{2} = 5\)

Exercise 4 – Mode and range

The value 5 appears 3 times, more than any other.

Range: \(9 – 3 = 6\).

mode 5; range 6

Exercise 5 – Mean as a fair share

Total \(3 + 5 + 7 = 15\); \(15 \div 3 = 5\).

5 books each; the mean is 5

Each has 5 books.

Exercise 6 – Missing value

Total of five: \(5 \cdot 12 = 60\).

Four numbers: \(10 + 14 + 9 + 13 = 46\).

\(60 – 46 = 14\)

Exercise 7 – Mean absolute deviation

Mean: \(20 \div 4 = 5\).

Distances from 5: 3, 1, 1, 3. Their mean: \(\frac{3 + 1 + 1 + 3}{4} = 2\).

Exercise 8 – MAD of five values

Mean: \(70 \div 5 = 14\).

Distances: 4, 2, 0, 2, 4. Sum 12.

MAD: \(12 \div 5 = 2.4\).

mean 14; MAD 2.4

The values are 4, 2, 0, 2, 4 away from the mean 14.

Exercise 9 – Quartiles and IQR

Median (5th value): 10.

Lower half 3, 5, 7, 8: Q1 = 6. Upper half 12, 14, 15, 18: Q3 = 14.5.

IQR: \(14.5 – 6 = 8.5\).

median 10; Q1 6; Q3 14.5; IQR 8.5

Exercise 10 – Make a box plot

Min 2, max 14. Median: \(\frac{7 + 8}{2} = 7.5\). Q1 = 4.5 and Q3 = 10.5.

2, 4.5, 7.5, 10.5, 14

The box runs from 4.5 to 10.5.

Exercises 11 and up

Exercise 11 – Read a box plot

Median 18. Range \(30 – 10 = 20\). IQR \(25 – 14 = 11\).

median 18; range 20; IQR 11

The box length is the IQR.

Exercise 12 – Effect of an outlier

With 40: mean \(75 \div 6 = 12.5\), median 7.5.

Without 40: mean \(35 \div 5 = 7\), median 7.

The mean changes much more (from 12.5 to 7) than the median (7.5 to 7).

Exercise 13 – Choose the measure

Mean: \(421 \div 6 \approx 70.2\). Median: \(\frac{35 + 36}{2} = 35.5\).

The value 250 pulls the mean up.

The median (35.5) is better because the data are skewed by an outlier.

Exercise 14 – Compare two box plots

A: median 75, IQR \(85 – 70 = 15\). B: median 80, IQR \(90 – 65 = 25\).

Class B has the greater median and the greater spread.

Exercise 15 – Mean from a table

Students: \(1 + 3 + 4 + 2 = 10\).

Total: \(6 + 21 + 32 + 18 = 77\).

Mean: \(77 \div 10 = 7.7\).

10 students; mean 7.7

Exercise 16 – Basketball points

Mean: \(116 \div 8 = 14.5\).

Ordered: 9, 12, 12, 15, 15, 15, 18, 20; median \(\frac{15 + 15}{2} = 15\).

Mode: 15.

mean 14.5; median 15; mode 15

Exercise 17 – Weekly temperatures

Mean: \(306 \div 7 = 43.714286\).

Ordered: 38, 39, 41, 44, 45, 47, 52; median 44.

Range: \(52 – 38 = 14\).

mean 43.714286; median 44; range 14

Exercise 18 – Mean and median together

Sum: \(1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 = 55\).

Mean: \(55 \div 10 = 5.5\). Median: \(\frac{5 + 6}{2} = 5.5\).

Both are 5.5

Exercise 19 – Interpret the IQR

IQR: \(20 – 8 = 12\).

The middle half of the students have travel times that span 12 minutes, from 8 to 20 minutes.

Exercise 20 – Adding a score

First mean: \(350 \div 4 = 87.5\).

New total: \(350 + 70 = 420\); new mean: \(420 \div 5 = 84\).

87.5, then 84; the mean went down

Key facts behind this center spread answers

Key facts

Mean = sum divided by the number of values; median = middle value.
Range = greatest minus least; IQR = Q3 minus Q1.
MAD is the average distance of the values from the mean.
A box plot shows the minimum, Q1, median, Q3, and maximum.
Outliers pull the mean but not the median.

How to use this center spread answers

Cover each solution, solve the exercise again, then uncover it and compare every line. If your answer differs, find the first step that changed and redo the exercise from there.

Download the center spread answers as a PDF with the button below and keep it with your notes.

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