year 2 statistics problem solving

Statistics in Year 2 (age 6–7)

In Year 2, your child will learn to draw simple charts and graphs. They will be able to sort categories by their quantities and will be able to compare sets of data.

The key words for this section are  block graph , pictogram , and tally chart .

What your child will learn

Take a look at the National Curriculum expectations for statistics in Year 2 (age 6–7):

Draw pictograms, tally charts, block diagrams, and tables

A pictogram is a graph that uses pictures to represent quantity:

A tally chart uses marks to represent numbers:

Your child will use block graphs (or block diagrams) where types of items are shown on the x -axis , the number of items is shown on the y -axis , and one block represents one item. A block graph is made up of separate blocks, and children can count the blocks to find out how many are in the group:

Count objects in multiple category and sort the categories by quantity

Your child will ask and answer simple questions about  pictograms , tally charts , block graphs , and simple tables. For example:

How many children like grapes? How many children like apples and bananas? How many more children prefer apples to grapes?

Total and compare categorical data

Your child will ask and answer questions about data they collect. For example:

How many children took part in the survey? What was their most popular option?

How to help at home

There are lots of everyday ways you can help your child to understand statistics. Here are just a few ideas.

1. Present data

In school, your child will be learning to present data with simple tables, pictograms , tally charts , and block graphs . You can encourage your child at home by having them investigate topics that particularly interest them and then present their data in tables, charts, and graphs.

For instance, your child could collect information about the planets in our solar system, favourite book characters, or football. See if they can create their own tables, charts, and graphs to represent the data in new and interesting ways. For example, they could by compare football players by goals scored so far this season.

Your child can record their findings using tables and present them with pictograms or block graphs.

Your child might need extra help when it comes to creating block graphs. Block graphs show types of items on the x -axis ,  the number of items on the y -axis , and have one block representing each item:

Once your child has practised lots of different ways of showing data, your child should be able to pick when it is best to use a block graph and when it is best to use a different method. They should be able to explain why.

2. Conduct a survey

If your child would prefer to gather their own data, why not do a survey? They could ask family and friends about their favourite food, film, sport, or anything else that takes their fancy.

Encourage your child to analyse their data and discuss any interesting findings. For example, did lots of people have the same favourite food? How many more people chose the most popular choice compared to the least popular choice?

Ask questions about the data they have found and encourage your child to begin asking their own questions, such as, ‘If I asked this question at school, would I get different results?’

3. Interpret data

You can help your child learn to interpret data in the form of tables,  pictograms , tally charts , and block graphs by encouraging them to explore interesting topics. For example, if your child is interested in football, encourage them to interpret football team statistics in tables, charts, and graphs. You can find lots of examples online and in football magazines.

Look at non-fiction texts together. Can your child find any data presented in interesting ways? Encourage them to chat about the data they find and point out anything they would not have expected.

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Statistics and Probability Worksheets

Welcome to the statistics and probability page at Math-Drills.com where there is a 100% chance of learning something! This page includes Statistics worksheets including collecting and organizing data, measures of central tendency (mean, median, mode and range) and probability.

Students spend their lives collecting, organizing, and analyzing data, so why not teach them a few skills to help them on their way. Data management is probably best done on authentic tasks that will engage students in their own learning. They can collect their own data on topics that interest them. For example, have you ever wondered if everyone shares the same taste in music as you? Perhaps a survey, a couple of graphs and a few analysis sentences will give you an idea.

Statistics has applications in many different fields of study. Budding scientists, stock market brokers, marketing geniuses, and many other pursuits will involve managing data on a daily basis. Teaching students critical thinking skills related to analyzing data they are presented will enable them to make crucial and informed decisions throughout their lives.

Probability is a topic in math that crosses over to several other skills such as decimals, percents, multiplication, division, fractions, etc. Probability worksheets will help students to practice all of these skills with a chance of success!

Most Popular Statistics and Probability Worksheets this Week

Mean, Median, Mode and Range Worksheets

Calculating the mean, median, mode and range are staples of the upper elementary math curriculum. Here you will find worksheets for practicing the calculation of mean, median, mode and range. In case you're not familiar with these concepts, here is how to calculate each one. To calculate the mean, add all of the numbers in the set together and divide that sum by the number of numbers in the set. To calculate the median, first arrange the numbers in order, then locate the middle number. In sets where there are an even number of numbers, calculate the mean of the two middle numbers. To calculate the mode, look for numbers that repeat. If there is only one of each number, the set has no mode. If there are doubles of two different numbers and there are more numbers in the set, the set has two modes. If there are triples of three different numbers and there are more numbers in the set, the set has three modes, and so on. The range is calculated by subtracting the least number from the greatest number.

Note that all of the measures of central tendency are included on each page, but you don't need to assign them all if you aren't working on them all. If you're only working on mean, only assign students to calculate the mean.

In order to determine the median, it is necessary to have your numbers sorted. It is also helpful in determining the mode and range. To expedite the process, these first worksheets include the lists of numbers already sorted.

• Calculating Mean, Median, Mode and Range from Sorted Lists Sets of 5 Numbers from 1 to 10 Sets of 5 Numbers from 10 to 99 Sets of 5 Numbers from 100 to 999 Sets of 10 Numbers from 1 to 10 Sets of 10 Numbers from 10 to 99 Sets of 10 Numbers from 100 to 999 Sets of 20 Numbers from 10 to 99 Sets of 15 Numbers from 100 to 999

Normally, data does not come in a sorted list, so these worksheets are a little more realistic. To find some of the statistics, it will be easier for students to put the numbers in order first.

• Calculating Mean, Median, Mode and Range from Unsorted Lists Sets of 5 Numbers from 1 to 10 Sets of 5 Numbers from 10 to 99 Sets of 5 Numbers from 100 to 999 Sets of 10 Numbers from 1 to 10 Sets of 10 Numbers from 10 to 99 Sets of 10 Numbers from 100 to 999 Sets of 20 Numbers from 10 to 99 Sets of 15 Numbers from 100 to 999

Collecting and Organizing Data

Teaching students how to collect and organize data enables them to develop skills that will enable them to study topics in statistics with more confidence and deeper understanding.

• Constructing Line Plots from Small Data Sets Construct Line Plots with Smaller Numbers and Lines with Ticks Provided (Small Data Set) Construct Line Plots with Smaller Numbers and Lines Only Provided (Small Data Set) Construct Line Plots with Smaller Numbers (Small Data Set) Construct Line Plots with Larger Numbers and Lines with Ticks Provided (Small Data Set) Construct Line Plots with Larger Numbers and Lines Only Provided (Small Data Set) Construct Line Plots with Larger Numbers (Small Data Set)
• Constructing Line Plots from Larger Data Sets Construct Line Plots with Smaller Numbers and Lines with Ticks Provided Construct Line Plots with Smaller Numbers and Lines Only Provided Construct Line Plots with Smaller Numbers Construct Line Plots with Larger Numbers and Lines with Ticks Provided Construct Line Plots with Larger Numbers and Lines Only Provided Construct Line Plots with Larger Numbers

Interpreting and Analyzing Data

Answering questions about graphs and other data helps students build critical thinking skills. Standard questions include determining the minimum, maximum, range, count, median, mode, and mean.

• Answering Questions About Stem-and-Leaf Plots Stem-and-Leaf Plots with about 25 data points Stem-and-Leaf Plots with about 50 data points Stem-and-Leaf Plots with about 100 data points
• Answering Questions About Line Plots Line Plots with Smaller Data Sets and Smaller Numbers Line Plots with Smaller Data Sets and Larger Numbers Line Plots with Larger Data Sets and Smaller Numbers Line Plots with Larger Data Sets and Larger Numbers
• Answering Questions About Broken-Line Graphs Answer Questions About Broken-Line Graphs
• Answering Questions About Circle Graphs Circle Graph Questions (Color Version) Circle Graph Questions (Black and White Version) Circle Graphs No Questions (Color Version) Circle Graphs No Questions (Black and White Version)
• Answering Questions About Pictographs Answer Questions About Pictographs

Probability Worksheets

• Calculating Probabilities with Dice Sum of Two Dice Probabilities Sum of Two Dice Probabilities (with table)

Spinners can be used for probability experiments or for theoretical probability. Students should intuitively know that a number that is more common on a spinner will come up more often. Spinning 100 or more times and tallying the results should get them close to the theoretical probability. The more sections there are, the more spins will be needed.

• Calculating Probabilities with Number Spinners Number Spinner Probability (4 Sections) Number Spinner Probability (5 Sections) Number Spinner Probability (6 Sections) Number Spinner Probability (7 Sections) Number Spinner Probability (8 Sections) Number Spinner Probability (9 Sections) Number Spinner Probability (10 Sections) Number Spinner Probability (11 Sections) Number Spinner Probability (12 Sections)

Non-numerical spinners can be used for experimental or theoretical probability. There are basic questions on every version with a couple extra questions on the A and B versions. Teachers and students can make up other questions to ask and conduct experiments or calculate the theoretical probability. Print copies for everyone or display on an interactive white board.

• Probability with Single-Event Spinners Animal Spinner Probability ( 4 Sections) Animal Spinner Probability ( 5 Sections) Animal Spinner Probability ( 10 Sections) Letter Spinner Probability ( 4 Sections) Letter Spinner Probability ( 5 Sections) Letter Spinner Probability ( 10 Sections) Color Spinner Probability ( 4 Sections) Color Spinner Probability ( 5 Sections) Color Spinner Probability ( 10 Sections)
• Probability with Multi-Event Spinners Animal/Letter Combined Spinner Probability ( 4 Sections) Animal/Letter Combined Spinner Probability ( 5 Sections) Animal/Letter Combined Spinner Probability ( 10 Sections) Animal/Letter/Color Combined Spinner Probability ( 4 Sections) Animal/Letter/Color Combined Spinner Probability ( 5 Sections) Animal/Letter/Color Combined Spinner Probability ( 10 Sections)

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Year 2 Maths Worksheets (age 6-7)

Hundreds of maths worksheets for children ages 6 and 7, covering counting, number, shape, time and much more. We also have a great selection of challenges and problem solving activities.

Each category has many resources within so why not jump in and explore the site?

Popular Resources

Have a look at some of our popular resources in this category.

Use the number line to add three small numbers.

An assessment paper for children at the end of Year 2 (6-7 years old).Please note these are not intended to be used as a set of written questions where the child answers on paper in silence. The questions could be presented over a period of several days and can be read out loud. Encouraging discussion of the questions will give a much greater insight into the child's understanding.

Missing numbers to fill in to make number sentences correct.

I've got three coins. They are all different. What possible totals could I have?

Doubling and halving numbers up to 20.

What possible scores could I get with four darts?

Try working out these addition sentences using teen numbers and single digits.

Bar modelling: subtract a single digit from 2-digits (easier)

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Teach yourself statistics

Statistics Problems

One of the best ways to learn statistics is to solve practice problems. These problems test your understanding of statistics terminology and your ability to solve common statistics problems. Each problem includes a step-by-step explanation of the solution.

• Use the dropdown boxes to describe the type of problem you want to work on.
• click the Submit button to see problems and solutions.

Main topic:

Problem description:

In one state, 52% of the voters are Republicans, and 48% are Democrats. In a second state, 47% of the voters are Republicans, and 53% are Democrats. Suppose a simple random sample of 100 voters are surveyed from each state.

What is the probability that the survey will show a greater percentage of Republican voters in the second state than in the first state?

The correct answer is C. For this analysis, let P 1 = the proportion of Republican voters in the first state, P 2 = the proportion of Republican voters in the second state, p 1 = the proportion of Republican voters in the sample from the first state, and p 2 = the proportion of Republican voters in the sample from the second state. The number of voters sampled from the first state (n 1 ) = 100, and the number of voters sampled from the second state (n 2 ) = 100.

The solution involves four steps.

• Make sure the sample size is big enough to model differences with a normal population. Because n 1 P 1 = 100 * 0.52 = 52, n 1 (1 - P 1 ) = 100 * 0.48 = 48, n 2 P 2 = 100 * 0.47 = 47, and n 2 (1 - P 2 ) = 100 * 0.53 = 53 are each greater than 10, the sample size is large enough.
• Find the mean of the difference in sample proportions: E(p 1 - p 2 ) = P 1 - P 2 = 0.52 - 0.47 = 0.05.

σ d = sqrt{ [ P1( 1 - P 1 ) / n 1 ] + [ P 2 (1 - P 2 ) / n 2 ] }

σ d = sqrt{ [ (0.52)(0.48) / 100 ] + [ (0.47)(0.53) / 100 ] }

σ d = sqrt (0.002496 + 0.002491) = sqrt(0.004987) = 0.0706

z p 1 - p 2 = (x - μ p 1 - p 2 ) / σ d = (0 - 0.05)/0.0706 = -0.7082

Using Stat Trek's Normal Distribution Calculator , we find that the probability of a z-score being -0.7082 or less is 0.24.

Therefore, the probability that the survey will show a greater percentage of Republican voters in the second state than in the first state is 0.24.

See also: Difference Between Proportions

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Problem-solving maths investigations for year 2.

Hamilton provide an extensive suite of problem-solving maths investigations for Year 2 to facilitate mathematical confidence, investigative inquiry and the development of maths meta skills in 'low floor – high ceiling' activities for all.

Explore all our in-depth problem solving investigations for Year 2 .

Use problem-solving investigations within every unit to encourage children to develop and exercise their ability to reason mathematically and think creatively.

Investigations provide challenges that offer opportunities for the development of the key mathematical skills while deepening conceptual understanding. They are designed to be accessible in different ways to all children. An added bonus is the substantial amount of extra calculation practice they often incorporate! The problems are designed to help children identify patterns, to explore lines of thinking and to reason and communicate about properties of numbers, shapes and measures.

Hamilton provide a mix of our own specially commissioned investigations, that include guidance for teachers together with a child-friendly sheet to guide your pupils through the investigation, as well as links to investigations on other highly regarded websites.

I am very grateful for Hamilton Trust resources, particularly the maths investigations. Julia, teacher in Wiltshire

You can find Hamilton's investigations for Year 2:

• Individually, they are incorporated into every unit in our Year 2 flexible maths blocks .
• Collectively, they appear on our resources page where you can explore all our in-depth problem solving investigations for Year 2 .

Do read our extensive range of advice for more information about the investigations and for tips on how to use them effectively.

Hamilton’s problem-solving investigations are 'low floor, high ceiling' activities that give all children opportunities to develop mastery and mathematical meta-skills. Explore a set for a whole year group.

Hamilton’s Problem-solving Investigations provide school-wide solutions to the challenges of building investigative skills from Early Years to Year 6.

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Solved Statistics Problems – Practice Problems to prepare for your exams

In this section we present a collection of solved statistics problem, with fairly complete solutions. Ideally you can use these problems to practice any statistics subject that you are in need of, for any practicing purpose, such as stats homework or tests.

The collection contains solved statistic problems of various different areas in statistics, such as Descriptive Statistics, Confidence Intervals, Calculation of Normal Probabilities, Hypothesis Testing, Correlation and Regression, and Analysis of Variance (For a list of 30,00+ step-by-step solved math problems, click here )

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Handling Data KS2

This collection is one of our Primary Curriculum collections - tasks that are grouped by topic.

How Big Are Classes 5, 6 and 7?

Use the two sets of data to find out how many children there are in Classes 5, 6 and 7.

Take Your Dog for a Walk

Use the interactivity to move Pat. Can you reproduce the graphs and tell their story?

Real Statistics

Have a look at this table of how children travel to school. How does it compare with children in your class?

Venn Diagrams

How will you complete these interactive Venn diagrams?

The Car That Passes

What statements can you make about the car that passes the school gates at 11am on Monday? How will you come up with statements and test your ideas?

Class 5's Names

Class 5 were looking at the first letter of each of their names. They created different charts to show this information. Can you work out which member of the class was away on that day?

The Domesday Project

Take a look at these data collected by children in 1986 as part of the Domesday Project. What do they tell you? What do you think about the way they are presented?

If the World Were a Village

This activity is based on data in the book 'If the World Were a Village'. How will you represent your chosen data for maximum effect?

This problem explores the range of events in a sports day and which ones are the most popular and attract the most entries.

Going for Gold

Looking at the 2012 Olympic Medal table, can you see how the data is organised? Could the results be presented differently to give another nation the top place?

Now and Then

Look at the changes in results on some of the athletics track events at the Olympic Games in 1908 and 1948. Compare the results for 2012.

I See Problem-Solving - Y2

The eBook I See Problem-Solving - Y2 gives coherent sequences of mathematical problem-solving tasks to build understanding and deepen learning. The initial tasks in each 'task family', with visual representations, allow children to build confidence and practice key skills. Then the challenges are opened up and extended! The ultimate resource for building children as problem-solvers.

Download I See Problem-Solving - Y2, Task Build-Up (PowerPoint)

Download I See Problem-Solving - Y2, Task Build-Up (PDF)

The purchase price is £30  (which includes VAT) for the PDF digital download. I See Problem-Solving - Y2 Sample provides 3 free sample task families for you to try out.

For each 'task family', the Task Build-Up examples introduce children to the format of the activities and help to build the key skills step-by-step. Children are able to practice these skills using the introductory tasks in each task family. Visual representations are used and misconceptions are addressed. Then, the tasks become progressively more open and extended. This will ensure that all children are both supported and challenged. It will give all children the excitement of engaging in rich problem-solving!

The 28 Task Families of I See Problem-Solving - Y2 , written by Gareth Metcalfe, cover all areas of the English mathematics curriculum. This corresponds to US Grade 1. To purchase, click on the link below. If you need any assistance with ordering, please email [email protected].

Online Training: Inspiring Mathematical Thinking Using I See Problem-Solving - Y2

You can access the recording of this 60-minute online training session by emailing [email protected] stating the name of your school and the number of people who will view the recording. The cost is £15+VAT per person. This video gives an overview of the session: