Statistical Questions and Data Displays: Grade 6 Math Test Answer Key – PDF Download

Question 1: Statistical questions (2 points)

1. Not statistical. It asks about one person on one day, so there is one answer.
2. Statistical. Different students send different numbers of messages.

Scoring: 1 point for each correct classification with a reason.

Question 2: Write a question (2 points)

Sample answer: “How many pets does each student in our sixth-grade class have?” The answers will vary from student to student.

Scoring: 1 point for asking about a group instead of one person; 1 point for a question that would produce different numerical answers.

Question 3: Dot plot (3 points)

1. The dots at 3, 4, and 6 number \(3 + 2 + 1 = 6\). 6 students.
2. Most of the data cluster from 1 to 3 hours, with the tallest stack of 5 dots at 2 hours.
3. The value 6 hours is far from the rest.

Scoring: 1 point for each part.

Question 4: Histogram (3 points)

1. The intervals 0 to 20 and 20 to 40: \(4 + 9 = 13\). 13 students.
2. The tallest bar has 10 students: 40 to 60 minutes.
3. The middle values are the 15th and 16th. The first two intervals hold 13 values, and the first three hold \(13 + 10 = 23\). So the middle lies in 40 to 60 minutes.

Scoring: 1 point for each part.

Question 5: Box plot (3 points)

1. The line in the box is at 24 minutes.
2. The box runs from 18 to 33, so the middle half lies between 18 and 33 minutes.
3. The least value is 12 and the greatest value is 45.

Scoring: 1 point for each part, with units.

Question 6: Draw a box plot (3 points)

1. Ordered: 4, 6, 6, 8, 9, 11, 12, 15, 17. The median is the 5th value, 9. Lower half: 4, 6, 6, 8, so \(Q_1 = \frac{6 + 6}{2} = 6\). Upper half: 11, 12, 15, 17, so \(Q_3 = \frac{12 + 15}{2} = 13.5\). Minimum 4 and maximum 17.
2. The box plot is drawn below.

4, 6, 9, 13.5, 17

Scoring: Part (a): 1 point for the median and extremes, 1 point for both quartiles. Part (b): 1 point for a correctly scaled box plot.

Question 7: Describe the data (2 points)

1. There are 8 observations. The attribute is the time to finish the puzzle, measured in minutes.
2. The value 31 minutes is far from the others, which are all from 12 to 16.

Scoring: 1 point for each part.

Question 8: Compare displays (2 points)

A dot plot shows every individual value as a dot, so the exact data can be read. A histogram groups the values into intervals and shows only how many values are in each interval.

Scoring: 1 point for a correct fact about a dot plot; 1 point for a correct contrasting fact about a histogram. Accept any accurate comparison.

See every chapter on the Grade 6 math page.