## Science and Engineering Practices

Analyzing and interpreting data.

## Primary School (K-2)

- Record information (observations, thoughts, and ideas).
- Use and share pictures, drawings, and/or writings of observations.
- Use observations (firsthand or from media) to describe patterns and/or relationships in the natural and designed world(s) in order to answer scientific questions and solve problems.
- Compare predictions (based on prior experiences) to what occurred (observable events).
- Analyze data from tests of an object or tool to determine if it works as intended.

## Elementary School (3-5)

- Represent data in tables and/or various graphical displays (bar graphs, pictographs, and/or pie charts) to reveal patterns that indicate relationships.
- Analyze and interpret data to make sense of phenomena, using logical reasoning, mathematics, and/or computation.
- Compare and contrast data collected by different groups in order to discuss similarities and differences in their findings.
- Analyze data to refine a problem statement or the design of a proposed object, tool, or process.
- Use data to evaluate and refine design solutions.

## Middle School (6-8)

- Construct, analyze, and/or interpret graphical displays of data and/or large data sets to identify linear and nonlinear relationships.
- Use graphical displays (e.g., maps, charts, graphs, and/or tables) of large data sets to identify temporal and spatial relationships.
- Distinguish between causal and correlational relationships in data.
- Analyze and interpret data to provide evidence for phenomena.
- Apply concepts of statistics and probability (including mean, median, mode, and variability) to analyze and characterize data, using digital tools when feasible.
- Consider limitations of data analysis (e.g., measurement error), and/or seek to improve precision and accuracy of data with better technological tools and methods (e.g., multiple trials).
- Analyze and interpret data to determine similarities and differences in findings.
- Analyze data to define an optimal operational range for a proposed object, tool, process or system that best meets criteria for success.

## High School (9-12)

- Analyze data using tools, technologies, and/or models (e.g., computational, mathematical) in order to make valid and reliable scientific claims or determine an optimal design solution.
- Apply concepts of statistics and probability (including determining function fits to data, slope, intercept, and correlation coefficient for linear fits) to scientific and engineering questions and problems, using digital tools when feasible.
- Consider limitations of data analysis (e.g., measurement error, sample selection) when analyzing and interpreting data.
- Compare and contrast various types of data sets (e.g., self-generated, archival) to examine consistency of measurements and observations.
- Evaluate the impact of new data on a working explanation and/or model of a proposed process or system.
- Analyze data to identify design features or characteristics of the components of a proposed process or system to optimize it relative to criteria for success.

## Other Standards That Use This Practice:

- Forces and Interactions: Pushes and Pulls
- Interdependent Relationships in Ecosystems: Animals, Plants, and Their Environment
- Weather and Climate

## First Grade

## Second Grade

## Third Grade

## Fourth Grade

## Fifth Grade

## Middle School

- Chemical Reactions
- Matter and Energy in Organisms and Ecosystems
- Natural Selection and Adaptations
- Space Systems
- History of Earth
- Human Impacts
- Engineering Design

## High School

## Lesson Worksheet: Statistical Analysis Mathematics

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

- A 20, 48, 48, 11, 11, 19
- B 10, 16, 19, 21, 47, 47
- C 48, 21, 11, 48, 20, 17
- D 47, 47, 11, 48, 20, 17
- E 21, 48, 19, 48, 17, 11

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.

Calculate the range of the data.

What does high sample variability mean?

- A The means of the samples have large values.
- B A large variety of methods have been used to generate the samples.
- C Given multiple samples from the same population, we should expect the sample statistics, for example, the calculated means, to have largely different values.
- D There is a large number of samples.

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

- A data set 1: 14.86, data set 2:3.43
- B data set 1: 3.85, data set 2: 1.85
- C data set 1: 3.61, data set 2: 1.73
- D data set 1: 1.85, data set 2: 3.85
- E data set 1: 13.00, data set 2:3.00

What do these values reveal about the two data sets?

- A The spread of the two data sets is very similar.
- B Data set 2 is more widely spread than data set 1.
- C Data set 2 is more variable than data set 1.
- D Data set 1 is more widely spread than data set 2.
- E The distributions of the two data sets are very similar.

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

- A The data is less spread out.
- B The mean of the data is smaller.
- C The data is more spread out.
- D The mean of the data is larger.
- E The median is larger than the mean.

- A The standard deviation would decrease.
- B The standard deviation would increase.
- C The standard deviation would not change.

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

- A data set 1: 𝑠 = 8 . 3 6 , data set 2: 𝑠 = 2 . 8 5
- B data set 1: 𝑠 = 8 . 9 4 , data set 2: 𝑠 = 3 . 0 4
- C data set 1: 𝑠 = 8 . 9 4 , data set 2: 𝑠 = 2 . 8 5
- D data set 1: 𝑠 = 6 9 . 8 6 , data set 2: 𝑠 = 8 . 1 1
- E data set 1: 𝑠 = 7 9 . 8 4 , data set 2: 𝑠 = 9 . 2 7

- A The lowest value is in data set 2, so this makes the standard deviation smaller.
- B The single large value of 51 in data set 1 causes the standard deviation to increase significantly.
- C The median of data set 1 is greater, which explains why the standard deviation is greater.
- D The mode of data set 1 value of 28 causes the standard deviation to increase significantly.
- E The mean of data set 1 is greater, which explains why the standard deviation is greater.

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## Statistics and Data Analysis Worksheets

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- Average or Mean
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## Explore the Statistics and Data Analysis Worksheets in Detail

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## Mean, Median, Mode and Range Worksheets

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

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

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## Collecting and Organizing Data

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## 12 Most Useful Excel Functions for Data Analysis

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

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

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

=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.

## 3. COUNTIFS

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

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

=COUNTIFS(B2:B9,E3,C2:C9,">=200”)

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

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.

The COUNTIFS function then has clean data and works correctly.

## 5. CONCATENATE

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

It prompts you for the different values to use.

=CONCATENATE(text1, text2, text3, …)

## 6. LEFT/RIGHT

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

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

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

It prompts for four pieces of information:

- The value you want to look for
- Which table to look in
- Which column has the information you want to return
- What type of lookup you would like to perform.

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

The following formula is used in column D:

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

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")

The function prompts for the text to convert.

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

The function wants to know three things:

- The range to return the unique list from
- Whether you would like to check for unique values by column or by row
- Whether you want a unique list, or a distinct list (items that occur only once).

=UNIQUE(array, by col, exactly once)

The SORT function prompts for four arguments:

- The range to sort
- Which column to sort the range by
- What order to sort the range (ascending or descending)
- Whether to sort the rows or the columns.

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

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

The FILTER function takes three arguments:

- The range to filter
- The criteria that specifies which results to return
- What action to take if no results are returned.

=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")

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

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## Unit: Data analysis

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## Bias in machine learning

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