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6th Grade · 6.SP.A.1

Statistical questions in 6th grade

Statistical questions are questions that expect different answers, such as "How tall are the students in our class?" In 6th grade, your child learns to tell a statistical question from a question with a single answer. Your child also learns that a good answer describes the whole set of answers, not just one value.

What the standard says

The official Common Core wording, quoted exactly. The plain version follows.

6.SP.A.1 Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers.

What it means, in plain words

What is a statistical question? It is a question you answer by collecting data, where you expect the answers to vary. Data is the set of answers or measurements you collect. "How tall is the classroom door?" has one answer, so it is not a statistical question. "How tall are the students in our class?" is a statistical question, because the students have different heights.

Variability means that the answers are not all the same. A statistical question expects variability and plans for it. The question can be about many people. It can also be about one person or one place at many times. "How much rain fell in our town each day in April?" is statistical, because the amount changes from day to day.

The answer to a statistical question describes the group, not one value. "Most students are between 52 and 60 inches tall" answers the height question better than "55 inches" does. In 6th grade, statistical questions lead into the rest of the year's data work: dot plots, histograms and ways to describe the center and the spread of the data.

Your child should be able to:

  • Tell whether a question is a statistical question
  • Explain why the answers to a statistical question will vary
  • Rewrite a question that has one answer as a statistical question
  • Answer a statistical question by describing the range of answers, not one value

Example

Which of these are statistical questions? How many days are in April? How many hours of screen time did each person in our family have yesterday? How many letters are in the first names of the students in our class?

  1. April always has 30 days. There is one answer, so this is not a statistical question.
  2. Each person in the family can have a different amount of screen time, so the answers vary. This is a statistical question.
  3. First names have different lengths, so the answers vary here too. This is also a statistical question.

Example

How can you turn "How long is my pencil?" into a statistical question?

  1. "How long is my pencil?" has one answer, so it is not statistical.
  2. Ask about many pencils instead: "How long are the pencils in our classroom?"
  3. New pencils and worn-down pencils have different lengths, so the answers vary.
  4. The new question is a statistical question. Its answer describes the group, such as the shortest pencil, the longest pencil and the most common length.

Where children usually get stuck

  • Your child says "How many minutes are in an hour?" is a statistical question because the answer is a number.

    The child links statistics with numbers. What makes a question statistical is that the answers vary, and every hour has 60 minutes.

    What helps. Ask, "If we asked 20 people, would they give different answers?" If everyone would say the same thing, it is not a statistical question.

  • Your child says "How much did I spend on lunch each day this month?" is not statistical, because it asks about only one person.

    The child learned that statistical questions ask many people. What matters is whether the answers vary, and the cost of lunch can change from day to day.

    What helps. Ask whether the answer is one number or a list of numbers. A list of numbers that change from day to day means the question is statistical.

  • Asked "How many hours did students in our class spend on sports last week?", your child answers with one number, such as 4 hours.

    Most math questions so far had one right answer, so the child gives one. The answer to a statistical question has to show that the answers were different.

    What helps. Ask, "Did everyone say 4?" Then help your child describe the group: the smallest answer, the largest answer and where most answers fall.

Try four practice questions

Real 6th grade questions from our question bank, easiest first. Answer them right here, check each one, and see a worked solution for any question.

  1. 1Warm-up
    The table below shows how many minutes 5 students said it takes them to get to school.
    Minutes
    8
    9
    10
    11
    13
    Select the answer that describes the times from shortest to longest.
    A
    8 to 13 minutes
    B
    8 minutes
    C
    13 minutes
    D
    10 minutes
    Show the answer and how to solve it

    The correct choice is "8 to 13 minutes" because the smallest time is 8 minutes, the largest time is 13 minutes, and using both endpoints shows that students gave different answers.

    1. 1Scan every value in the table: 8, 9, 10, 11, and 13 minutes.
    2. 2Find the smallest value and the largest value. The least time is 8 minutes, and the greatest time is 13 minutes.
    3. 3A good answer must show that the students said DIFFERENT times, not just one number. The choice that shows both ends of the data is "8 to 13 minutes," so that is the correct choice.

    Common mistake. A common mistake is picking just one number from the table, such as 8, 13, or the middle value 10. One number cannot show that students gave different answers, so a range from the smallest to the largest value is a stronger summary.

    The idea underneath. To show differences in the data, use the two endpoints of the data set together: the least value and the greatest value. One single value can never show that students gave different answers.

  2. 2On level
    Someone asked, "How many pages did Chloe read on Monday?" Rewrite it so it asks about Chloe's reading one time per day across last week, so the number of pages can vary from day to day.
    Complete the revised question by choosing an option from each dropdown.
    How many pages did
    read
    ?
    Show the answer and how to solve it

    The completed question is 'How many pages did Chloe read each day last week?' Keep 'Chloe' because the prompt anchors the subject; choose the time that gives one value per day so the data can vary across the week.

    1. 1The original question asks about one person, Chloe, on one specific day, Monday. That gives exactly one number, so it is not a statistical question.
    2. 2The prompt says to keep the question about Chloe and change the time so it captures one reading count per day across last week. The subject is anchored; only the time dropdown should change.
    3. 3For the subject dropdown, choose 'Chloe' (id: chloe). The prompt asks about Chloe's reading, so choosing 'Chloe's teacher' (id: teacher) or 'Chloe's classmates' (id: classmates) would change who the question is about, which is not what the prompt directs.
    4. 4For the time dropdown, choose 'each day last week' (id: each-day). That gives one reading count per day, so the answers can vary across days. 'On Monday' (id: monday) leaves it as a single-day question. 'Last week' (id: last-week) asks for one weekly total, which is still only one number.
    5. 5The completed question is 'How many pages did Chloe read each day last week?' It is statistical because Chloe's page count can be different on different days, so the data form a set of values that can vary.

    Common mistake. A common mistake is choosing 'last week' for the time dropdown. 'Last week' asks for one weekly total -- still just one number -- so the question is not yet statistical. 'Each day last week' is what makes the data vary.

    The idea underneath. A question becomes statistical when it is written to collect a set of values that can vary. In a template like this one, you need to pick options that make the question ask for several values (one per day, one per person, etc.) rather than one.

  3. 3On level
    A class answered the statistical question, "How many minutes did you practice your instrument last night?" Look at the line plot below.
    510152025
    Minutes practiced
    Sofia's answer: "The answer is 15 minutes because that is the most common value."
    Which statement best explains whether Sofia's answer shows how the values differ?
    A
    It is wrong because the answer should use only the greatest value, 25 minutes.
    B
    It is wrong because a good answer must list every practice time exactly.
    C
    It is wrong because 15 minutes is only one common value, and the plot shows several different practice times from 5 to 25.
    D
    It is not wrong, because using the most common value is enough to account for the data.
    Show the answer and how to solve it

    15 minutes is only one common value, but the plot includes several different practice times from 5 to 25, so Sofia's answer hides the variation across the data. The best description is the statement that says a single common value does not show all the differences in the data.

    1. 1Look at the line plot. The practice times are 5, 10, 10, 15, 15, 15, 20, and 25 minutes.
    2. 2These values are not all the same. The data vary from 5 minutes all the way up to 25 minutes.
    3. 3Sofia gave only one value, 15 minutes. Even though 15 is the most common value, that leaves out students who practiced 5, 10, 20, and 25 minutes.
    4. 4The best description is the statement that says one common value does not show all the different practice times in the data.

    Common mistake. A common mistake is thinking the tallest stack on the line plot gives a complete answer. The most common value, 15 minutes, can help, but it still does not show how the rest of the data are spread from 5 to 25 minutes.

    The idea underneath. A statistical answer should show that data vary; naming one value, even a common one, does not describe the whole distribution.

  4. 4Stretch
    A teacher asks: "How many minutes does it take students in this class to travel to school each morning?" The choices below are proposed answers.
    Which proposed answer describes the group without giving one exact answer for everyone?
    A
    Many students said 15 minutes, so the answer is 15 minutes.
    B
    Students gave different answers, but most said 10 to 20 minutes.
    C
    Jordan said it takes him 10 minutes to travel to school.
    D
    25 students answered the question.
    Show the answer and how to solve it

    Select "Students gave different answers, but most said 10 to 20 minutes." This proposed answer describes the group and allows variation.

    1. 1The question asks about travel times for a group of students. Their answers could differ.
    2. 2"Many students said 15 minutes, so the answer is 15 minutes." This gives one value as the whole answer, even though a common value need not be the only value. "Jordan said it takes him 10 minutes to travel to school." This reports one person's answer. It does not describe the group's travel times. "25 students answered the question." This counts the students who answered, not their travel times.
    3. 3The proposed answer "Students gave different answers, but most said 10 to 20 minutes." describes the group and explicitly says the answers are not all the same. That is the kind of answer this task asks for.
    4. 4A common answer need not be the only answer. A group summary can name a common answer and still allow other answers.

    Common mistake. An answer about a group can be true without showing variation. For this task, check whether the proposed answer allows more than one result.

    The idea underneath. Variation means that answers are not all the same. Look for a proposed answer that describes the group and allows variation.