data analysis practice worksheet

Science and Engineering Practices

Below is the progression of the Science and Engineering Practice of Analyzing and Interpreting Data , followed by Performance Expectations that make use of this Science and Engineering Practice.

Scientific investigations produce data that must be analyzed in order to derive meaning. Because data patterns and trends are not always obvious, scientists use a range of tools—including tabulation, graphical interpretation, visualization, and statistical analysis—to identify the significant features and patterns in the data. Scientists identify sources of error in the investigations and calculate the degree of certainty in the results. Modern technology makes the collection of large data sets much easier, providing secondary sources for analysis.

Primary School (K-2)

Elementary School (3-5)

Middle School (6-8)

High School (9-12)

This is a table of the Science and Engineering Practice of Analyzing and Interpreting Data . If coming from a Standard the specific bullet point used is highlighted and additional performance Expectations that make use of the Science and Engineering Practice can be found below the table. To see all Science and Engineering Practices, click on the title "Science and Engineering Practices."

Once collected, data must be presented in a form that can reveal any patterns and relationships and that allows results to be communicated to others. Because raw data as such have little meaning, a major practice of scientists is to organize and interpret data through tabulating, graphing, or statistical analysis. Such analysis can bring out the meaning of data—and their relevance—so that they may be used as evidence.

Engineers, too, make decisions based on evidence that a given design will work; they rarely rely on trial and error. Engineers often analyze a design by creating a model or prototype and collecting extensive data on how it performs, including under extreme conditions. Analysis of this kind of data not only informs design decisions and enables the prediction or assessment of performance but also helps define or clarify problems, determine economic feasibility, evaluate alternatives, and investigate failures. (NRC Framework, 2012, p. 61-62)

As students mature, they are expected to expand their capabilities to use a range of tools for tabulation, graphical representation, visualization, and statistical analysis. Students are also expected to improve their abilities to interpret data by identifying significant features and patterns, use mathematics to represent relationships between variables, and take into account sources of error. When possible and feasible, students should use digital tools to analyze and interpret data. Whether analyzing data for the purpose of science or engineering, it is important students present data as evidence to support their conclusions.

Other Standards That Use This Practice:

Kindergarten.

First Grade

Space Systems: Patterns and Cycles

Second Grade

Structure and Properties of Matter

Third Grade

Fourth Grade

Earth's Systems: Processes That Shape the Earth

Fifth Grade

Space Systems: Stars and the Solar System

Middle School

High School

Lesson Worksheet: Statistical Analysis Mathematics

In this worksheet, we will practice choosing the suitable measure of central tendency to represent data, finding the margin of sampling error, and using the measure of variation to compare between sets of data.

What is the denominator in the calculation of population standard deviation for a data set with 𝑛 items?

Which of the following sets of data has a mode of 48 and a median of 20?

Faisal wants to find out the average age of people who go swimming on a Saturday morning. He records the following data on a particular Saturday morning: 5, 12, 24, 19, 64, 38, 71, 13, 14, 41, 3.

Calculate the mean of the data giving your answer accurate to one decimal place.

Calculate the median of the data.

Calculate the mode of the data.

E There is no mode.

Calculate the range of the data.

What does high sample variability mean?

Using the data given in the table, calculate the standard deviation of the ages. Give your answer to three decimal places.

Calculate, to the nearest hundredth, the sample standard deviation for each data set.

What do these values reveal about the two data sets?

In general, what does a larger value of σ mean?

Using the data given in the table, calculate the standard deviation of the number of children. If necessary, give your answer to three decimal places.

The data set shown contains a potentially outlying value of 32. What effect would removing this value have on the standard deviation?

Calculate, to the nearest hundredth, the sample standard deviation for each of the shown data sets.

Which of these statements helps explain the large difference between the sample standard deviations for the two data sets?

Practice Means Progress

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Statistics and Data Analysis Worksheets

The key to growth is to bring order to chaos. Learn to organize data with the statistics worksheets here featuring exercises to present data in visually appealing pictographs, line graphs, bar graphs and more. Determine the mean, median, mode and also find worksheets on permutation, combination, probability and factorials to mention a few.

List of Statistics and Data Analysis Worksheets

Explore the Statistics and Data Analysis Worksheets in Detail

Tally Mark Worksheets

Let's go back in history and learn a fun way to count with this batch of Tally worksheets, featuring colorful and engaging activities to count and read tally marks, spinner board activities, classifying and counting tally marks, word problems and a lot more.

Pictograph Worksheets

The assemblage here provides interesting printable pictograph worksheets with themed activities to present or interpret information in the form of pictures. Find tasks like drawing and comprehending a pictograph, counting and grouping pictures with varied levels of difficulty.

Line plot Worksheets

This collection of line plot worksheets provides plenty of engaging activities that emphasize on making, comprehending and interpreting line plots and also provide ideas for surveys. Templates are included for children to take up surveys of their interest.

Bar graph Worksheets

The meticulously designed bar graph worksheets here, grab the attention of the learners with colorful pictures and interesting themes. Learn to draw and read bar graphs, double bar graphs, write titles, label axis, make a scale and represent data as bar graphs to mention a few.

Line graph Worksheets

Build your skills with this set of line graph worksheets to analyze and interpret line graphs. Enrich your knowledge with activities like drawing line graphs, interpreting line graphs, double line graphs with appropriate scales, titles and labelled axis.

Pie graph Worksheets

Focusing on pie graphs or circle graphs, these printable worksheets involve exercises to observe, visualize and comprehend pie graphs, convert percentages, whole numbers, fractions to pie graphs and vice-versa, drawing pie graphs with 30° increment, using a protractor to draw a pie graph and a lot more.

Average or Mean Worksheets

Check out this extensive range of mean worksheets encompassing exercises to find the arithmetic mean of whole numbers and decimals with varied levels of difficulty, calculate the mean with practical units, find the average and more.

Mean, Median, Mode and Range Worksheets

This array of mean, median, mode worksheets covers the most important aspect of statistics, comprising exercises to determine the mean, median, mode, average, quartiles and range to mention a few. Interesting word problems to apply the concept have also been enclosed.

Mean Absolute Deviation Worksheets

This collection of mean absolute deviation (MAD) worksheets comprises exercises in tabular format and as word problems involving 2-digit, 3-digit and decimal data values. Find the mean, absolute deviation and average absolute deviation using the mean absolute deviation formula. Learn comparing two data sets as well.

Stem and Leaf Plot Worksheets

The stem and leaf plot worksheets here offer an innovative way to organize and plot data. Consisting of umpteen exercises like making and interpreting Stem and Leaf plots, back to back plots, truncate and round off to make a plot, the worksheets help in visualizing the distribution of data.

Box and Whisker Plot Worksheets

Utilize this assemblage of box and whisker plot worksheets to make and interpret box and whisker plots and to summarize a set of data. A wide range of exercises to find the five number summary, quartiles, range, inter-quartile range, outliers and word problems have been included here.

Venn Diagram Worksheets

Learn to interpret and create Venn diagrams with a variety of exercises in two or three sets, shade the union or intersection, name the shaded portions, write the set notations, complete the Venn diagram and more.

Factorial Worksheets

This collection of factorial worksheets introduces factorials and encompasses ample exercises to write the factorial in a product form or vice-versa, simplify and evaluate factorial expressions to hone your skills.

Permutation Worksheets

Figure out the possible ways of arranging a list of objects or events with this exclusive set of Permutation worksheets; packed with intriguing exercises such as listing the number of permutations, finding the number of unique permutations, evaluating expressions and solving equations involving permutations.

Combination Worksheets

This cluster of combination worksheets deals solely with exercises involving combination, like listing out the combinations, finding the number of combinations, evaluating and solving combinations. Real-world scenarios and a multitude of exercises help students master combinations with ease.

Probability Worksheets

Access a vast collection of probability worksheets involving exercises on probability, covering varied levels of difficulty. Find exercises to identify the sample space, likely and unlikely outcomes of an event, spinner problems, probability with single and double coins, pair of dice, deck of cards to mention a few.

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$data analysis practice worksheet$

Analyzing Data Worksheet for Middle and High School

April 26, 2017

Do you struggle to find good examples of data to help your students learn and practice data analysis skills ? The struggle is real! A data analysis lesson can encompass a lot of things, and depending on the data set, can be overwhelming for students. But in the real world, this is an important math skill , as we’re bombarded with information and data all the time. So I hope today’s data analysis worksheet (part of my Math+Technology series) provides an interesting data set and a great opportunity to review important math skills (such as working with percents).

Want an interesting and engaging data set to help your students practice important math skills? This data analysis worksheet and project is sure to stir up great conversations and help your students explore a variety of math skills! FREE for middle and high school classes.

* Please Note : This post contains affiliate links which help support the work of this site. Read our full disclosure policy here .*

Using Technology to Aid in Data Analysis

Just because students need to know how to analyze and draw conclusions from sets of data, doesn’t mean they need to do every calculation by hand.

Depending on the data, they can use graphing calculators to plot the information on a graph. This allow them to better visualize what’s happening.

Using a calculator can also be helpful in making calculations and comparisons with the data. This shifts the emphasis to what the data says , rather than on the calculations themselves .

It can also be helpful to use a calculator to find measures of center (mean, median and mode) or compare data from one set to another.

This will give students a clearer picture of what the data is telling them, allowing them to form reasonable conclusions. They can then make better decisions based on the data and their conclusions.

Data Analysis Worksheet and Project

Today’s lesson includes some fascinating data about shoplifting trends and thoughts for kids to consider. They will use the data to answer questions based on the information given.

Students then solve related problems, reviewing skills involving percents and money.

There are a variety of skills necessary to complete this assignment, making it a great opportunity to apply what they know to a real world situation. Plus, they’ll review concepts (especially involving percents) that they may have forgotten.

Finally, this data analysis exploration includes a simple data analysis project, which students could complete for homework. In it, they gather their own sample data and compare it to the data they were given.

I hope this provides a fun and interesting data analysis exploration for your students!

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**Psst! This lesson is a sample from my ebook, Graphing Calculator Activities: Data Analysis . If you like this lesson, check out the complete resource .

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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

$Mean, Median, Mode and Range -- Sorted Sets (Sets of 5 from 10 to 99)$

Mean, Median, Mode and Range Worksheets

Worksheets for students to practice finding the mean, median, mode and range or number sets.

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.

Determining Mean, Median, Mode and Range from Sorted lists of numbers

$data analysis practice worksheet$

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 worksheets include the lists of numbers already sorted.

Determining Mean, Median, Mode and Range from Unsorted lists of numbers

$data analysis practice worksheet$

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.

Collecting and Organizing Data

Collecting and organizing data worksheets including line plots and stem-and-leaf diagrams.

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 smaller data sets

$data analysis practice worksheet$

Constructing line plots from larger data sets

$data analysis practice worksheet$

Interpreting and Analyzing Data Worksheets

Interpreting and analyzing data worksheets including worksheets with stem-and-leaf plots, line plots and various graph types.

Answering questions about graphs and other data helps students build critical thinking skills. The versions with no questions are intended for those who want to write their own questions and answers.

Questions about Stem-and-leaf plots

$data analysis practice worksheet$

Standard questions include determining the minimum, maximum, range, count, median, mode, and mean.

Questions about Line plots

$data analysis practice worksheet$

Questions about Broken-Line Graphs

$data analysis practice worksheet$

Questions about Circle Graphs

$data analysis practice worksheet$

Questions about Pictographs

$data analysis practice worksheet$

Probability Worksheets

Probability worksheets including probabilities of dice and spinners with various numbers of sections.

Probability with Dice

$data analysis practice worksheet$

Probability with Number Spinners

$data analysis practice worksheet$

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.

Probability with Non-Numerical Spinners

$data analysis practice worksheet$

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.

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Data Analysis Microsoft Excel

12 minute read

12 Most Useful Excel Functions for Data Analysis

Alan Murray

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There are over 475 functions in Excel . This can make it overwhelming when you are getting started with data analysis.

With such a large variety of functions, it can be difficult to know which one to use for specific Excel tasks.

The most useful Excel functions are those that make the task seem easy. And the good news is that most Excel users have a toolkit of just a few functions that complete most of their needs.

This resource covers the 12 most useful Excel functions for data analysis . These functions provide you with the tools to handle the majority of your Excel data analysis tasks.

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Don't forget to download the exercise file to help you follow along with this article and learn the best functions for data analysis.

Learn the most useful Excel functions

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The IF function is extremely useful. This function means we can automate decision making in our spreadsheets.

With IF, we could get Excel to perform a different calculation or display a different value dependent on the outcome of a logical test (a decision).

The IF function asks you for the logical test to perform, what action to take if the test is true, and the alternative action if the result of the test is false.

=IF(logical test, value if true, value if false)

In this example, we have displayed the word “Yes” if the delivery date in column C is more than 7 days later than the order date in column B. Otherwise, the word “No” is displayed.

=IF(D2>7,"Yes","no")

SUMIFS is one of the most useful Excel functions. It sums values that meet specified criteria .

Excel also has a function named SUMIF which does the same task except it can only test one condition, while SUMIFS can test many.

So you can essentially ignore SUMIF as SUMIFS is a superior function.

The function asks you for the range of values to sum, and then each range to test and what criteria to test it for.

=SUMIFS(sum range, criteria range 1, criteria 1, …)

In this example, we are summing the values in column C for the region entered into cell E3.

=SUMIFS(C2:C9,B2:B9,E3)

It is definitely worth exploring the SUMIFS function in more detail. It is an extremely useful Excel function.

3. COUNTIFS

The COUNTIFS function is another mega function for Excel data analysis.

The COUNTIFS function will count the number of values that meet specified criteria . It, therefore, does not require a sum range like SUMIFS.

=COUNTIFS(criteria range 1, criteria 1, …)

In this example, we count the number of sales from the region entered into cell E3 that have a value of 200 or more.

=COUNTIFS(B2:B9,E3,C2:C9,">=200”)

When using the SUMIFS and COUNTIFS functions, the criteria must be entered as text or as a cell reference. This example uses both techniques in the same formula.

This brilliant function will remove all spaces from a cell except the single spaces between words.

The most common use of this function is to remove trailing spaces. This commonly occurs when content is pasted from somewhere else or when users accidentally type spaces at the end of text.

In this example, the COUNTIFS function from before is not working because a space has been accidentally used at the end of cell B6.

Users cannot see this space, which means it is not identified until something stops working.

The TRIM function will prompt you for the text to remove spaces from.

=TRIM(text)

In this example, the TRIM function is used in a separate column to clean the data in the region column ready for analysis .

The COUNTIFS function then has clean data and works correctly.

5. CONCATENATE

The CONCATENATE function combines the values from multiple cells into one.

This is useful for piecing together the different parts of text such as someone's name, an address, a reference number or a file path or URL.

It prompts you for the different values to use.

=CONCATENATE(text1, text2, text3, …)

In this example, CONCATENATE is used to combine the firstname and lastname into a fullname. A space is entered for the text2 argument.

=CONCATENATE(A2," ",B2)

6. LEFT/RIGHT

The LEFT and RIGHT functions will do the opposing action of CONCATENATE. They will extract a specified number of characters from the start and end of text.

This can be used to extract parts of an address, URL, or reference for further analysis.

The LEFT and RIGHT functions request the same information. They want to know where the text is and how many characters you want to extract.

=LEFT(text, num chars)

=RIGHT(text, num chars)

In this example, column A contains a reference that is made up of the client ID (first two characters), a transaction ID, and then the region code (final character).

The following LEFT function is used to extract the client ID.

=LEFT(A2,2)

The RIGHT function can be used to extract the last character from the cells in column A. This example indicates whether the client is in the South or the North.

=RIGHT(A2,1)

The VLOOKUP function is one of the most commonly used and recognizable functions in Excel .

It will look for a value in a table and return information from another column relating to that value.

It is great for combining data from different lists into one or comparing two lists for matching or missing items. It is an important tool in Excel data analysis.

It prompts for four pieces of information:

=VLOOKUP(lookup value, table array, column index number, range lookup)

In this example, we have a table containing sales from our employees. There is another table with further information about these employees (tables are kept small for the example).

We would like to bring the data showing which region the employee is based into the sales table for analysis.

The following formula is used in column D:

=VLOOKUP(B2,$G$2:$H$12,2,FALSE)

This can be one of the more difficult functions to learn for beginners to Excel formulas. You can learn VLOOKUP more in-depth in this article , or from our comprehensive Excel course .

Sometimes errors happen that may be innocent and sometimes these errors may be things you can predict. The VLOOKUP function from before is a typical example of this.

We have an error because there is a typo in the name in the sales table. This means that VLOOKUP cannot find that name and produces an error.

Using IFERROR we could display a more meaningful error than the one Excel provides, or even perform a different calculation.

The IFERROR function requires two things. The value to check for the error and what action to perform instead.

In this example, we wrap the IFERROR function around VLOOKUP to display a more meaningful message.

=IFERROR(VLOOKUP(B2,$G$2:$H$12,2,FALSE),"Name not found. Check both lists")

Often the set of data you need to analyze has been imported from another system or copied and pasted from somewhere.

This can often lead to data being in the wrong format, such as a number being stored as text. You cannot perform data analysis tasks such as SUM if Excel does not recognize them as a number.

Fortunately, the VALUE function is here to help. Its job is to convert numbers stored as text to numbers .

The function prompts for the text to convert.

=VALUE(text)

In this example, the following formula converts the sales values stored as text in column B to a number.

The UNIQUE function is a new function available to those using the Microsoft 365 version only.

The function wants to know three things:

=UNIQUE(array, by col, exactly once)

In this example, we have a list of product sales and we want to extract a unique list of the product names. For this, we only need to provide the range.

=UNIQUE(B2:B15)

This is a dynamic array function and therefore spills the results. The blue border indicates the spilled range.

We can then use the SUMIFS function, mentioned earlier in this article, to sum the sales for each of those products.

This should look familiar to earlier. However, a # was used to reference the spilled range this time.

This is another function only available to Microsoft 365 subscribers . As the name suggests, it will sort a list.

The SORT function prompts for four arguments:

=SORT(array, sort index,sort order, by col)

This is fantastic. And it can be used with the previous UNIQUE example to sort the product names in order.

For this, we only need to provide it with the range to sort.

=SORT(UNIQUE(B2:B15))

Following the SORT function , there is also a function to filter a list. Another function only available to Microsoft 365 users .

This function will filter a range . This is an extremely powerful function and is a dream for analyzing data and producing reports.

The FILTER function takes three arguments:

=FILTER(array, include, if empty)

In this example, only the results for the subject entered in cell F2 are returned.

=FILTER(B2:C12,A2:A12=F2,"No scores")

Learning the most useful Excel functions for data analysis mentioned in this article will go a long way to making Excel data analysis easier.

But there are still many more functions and also Excel features to learn to be a true data analysis whizz.

Two other essential Excel tools to master are Power Query and Power Pivot .

Power Query makes importing and transforming data for analysis a breeze. And Power Pivot is the perfect tool if you analyze large volumes of data. It can store huge volumes of data outside Excel and has its own formula language called DAX.

Take the Power Query and Power Pivot courses on GoSkills to fast-track your data analysis skills in Excel today.

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Alan is a Microsoft Excel MVP, Excel trainer and consultant. Most days he can be found in a classroom spreading his love and knowledge of Excel. When not in a classroom he is writing and teaching online through blogs, YouTube and podcasts. Alan lives in the UK, is a father of two and a keen runner.

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