Data Analysis
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Curriculum Resource Guide - Mathematics Content: Data Analysis
| The Curriculum Resource Guides describe how to teach the content to students with the most significant cognitive disabilities. |
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| Used in conjunction with the Content Modules that describe the content (what is being taught) in general education they provide teachers with the necessary background knowledge to prepare students for the NCSC alternate assessment. |
| The Curriculum Resource Guides offer examples of how the content is taught in general education, ideas for real life use, examples of universal design for learning, and ways to promote college and career readiness. |
Questions about:
- Data Analysis
- Data Analysis Teaching Activities
- Data Analysis and Common Core Connectors
- Real World Data Analysis Activities
- Promoting College and Career Readiness through Data Analysis
- Making Data Analysis Accessible to ALL Students
1. What is “Data Analysis” and how is it taught in general education settings?
1a.1 The essential knowledge in this content area
(GRAPHICS/TABLES)
Collect data and organize into bar graph
In general education settings, students are taught to pose a question, collect data, organize the data, and interpret the data. Children begin with using concrete objects as their “data.” They begin by classifying and sorting the items. Teachers can shape this into graphing behavior by having them sort the items into lines. Then students can begin to use representations of the objects (e.g., photos or line drawings) and place them onto graphs. This is followed by more advanced graphing which includes labeling the graph, shading in sections, developing a key or scale interval to represent amounts, etc. For example, students take votes on their classmates’ favorite colors. They get the following results: red – 7, blue – 1, green – 5, orange - 3. Then they are asked to graph the data. Below are examples of graphs moving from concrete to symbolic.
(GRAPHICS/TABLES)
Using ordered pairs to graph given points
Ordered pairs are considered bivariate data. Bivariate data are data that consist of two variables such as miles per hour or numbers of hours studied and grades on the test. Line graphs displaying bivariate data help to show trends over time and enable students to make predictions/estimations by looking at points on the line between the plotted data and estimating the value of the variables represented. Creating line graphs requires students to utilize horizontal and vertical axes in order to plot the data points. This prepares students for graphing on coordinate planes.
Below are two line graphs using the following bivariate data set: Several students were surveyed on how many hours they studied for the Algebra test. The average test score for students who studied 1 hour was 72%. The average for 2 hours was 85% and the average for 3 hours was 90%. Graph the data.
(GRAPHICS/TABLES)
As shown above students may graph the data in two different ways based on their interpretation of the data and the axis where they assign the variables (test scores, hours studied). However, if all the students were told to assign hours studied to the x-axis and test scores on the y-axis or given the following ordered pairs (1, 72), (2, 85), (3, 90) the students should all create the same graph (as shown below). These ordered pairs demonstrate points on the graph corresponding with the x-axis (horizontal axis) and y-axis (vertical axis). The first number tells students how far to move away from the point of origin (zero on the graph or coordinate plane) across the horizontal axis. The second number tells students how far to move away from the point of origin up the vertical axis. So in the example below the first point on the graph is (1, 72). To plot this point you would move horizontally away from the origin towards 1, then move up vertically to approximately 72 and draw a point.
(GRAPHICS/TABLES)
Bivariate data can also be graphed as scatter plots. A scatter plot is a graph of plotted points (i.e., ordered pairs) that show the relationship between two sets of data. In the example below, each dot represents one adolescent’s vegetable consumption versus the number of minutes spent helping to prepare meals.
(GRAPHICS/TABLES)
Students learn to analyze scatter plots to describe relationships between the two variables. Based on the plot above students would infer that the more time adolescents spend preparing meals the more likely they are to eat vegetables. Summarizing data using measures of central tendency and variability Data sets can be summarized in relation to measures of central tendency (the middle values of the data set). The three measures of central tendency are mean, median, and mode. See examples below using the following data set which compares the number of vegetable servings eaten weekly versus minutes spent weekly helping prepare meals of 19 adolescents:
(GRAPHICS/TABLES)
Mean, Median, and Mode Mean is the sum of all the values divided by the total number of values. Mean of minutes preparing meals: 0+5+7+15+10+7+16+14+30+25+15+30+45+45+60+65+62+70+180= 701 701÷19= 36.9 minutes Mean number of minutes preparing meals = 36.9 minutes
Median is the middle number in the data set. To find the median, place the numbers in value order and find the middle number. Median of minutes preparing meals: How data are presented:
| 0 | 5 | 7 | 15 | 10 | 7 | 16 | 14 | 30 | 25 | 15 | 30 | 45 | 45 | 60 | 65 | 62 | 70 | 180 |
Data in value order:
| 0 | 5 | 7 | 7 | 10 | 14 | 15 | 15 | 16 | 25 | 25 | 30 | 30 | 45 | 45 | 60 | 62 | 65 | 70 | 180 |
Middle number:
| 0 | 5 | 7 | 7 | 10 | 14 | 15 | 15 | 16 | 25 | 30 | 30 | 45 | 45 | 60 | 62 | 65 | 70 | 180 |
Median number of minutes preparing meals = 25
- Note: if you have an even number of values, find the two middle values add them together and divide by 2 (e.g., middle numbers 24 and 30. 24 + 30 = 54. 54 ÷2 = 27. Median = 27)
Mode is the most often occurring value in the data set. To find the mode, place the numbers in value order and find the most often occurring number(s). Mode of minutes preparing meals: Data in value order:
| 0 | 5 | 7 | 7 | 10 | 14 | 15 | 15 | 16 | 25 | 30 | 30 | 45 | 45 | 60 | 62 | 65 | 70 | 180 |
Mode(s):
| 0 | 5 | 7 | 7 | 10 | 14 | 15 | 15 | 16 | 25 | 30 | 30 | 45 | 45 | 60 | 62 | 65 | 70 | 180 |
The values 7, 15, 30, and 45 all appear twice in this data set. They are the modes. Modes* of minutes preparing meals: 7, 15, 30, 45
- This data set would be considered multimodal (more than 2 modes; bimodal refers to two modes).
Variability (Range and Outliers)
Range The range of a data set is the difference between the highest and lowest values in the set. Range of minutes preparing meals: Highest – lowest = range 180 – 0 = 180 The range of minutes preparing meals is 180 minutes.
Outliers An outlier is a data value that stands out from others in a set. Outliers are most easily determined by looking at a visual graph of the data. Below are two examples of viewing outliers (circled).
(Graphic)
Summarizing data by creating histograms A histogram is a graphical display of data using bars of different heights. It is similar to a bar chart but a histogram groups data values into ranges an uses vertical columns to show the frequencies of the of the data values. The histogram below displays the number of minutes adolescents spend preparing meals per week.
(Graphic)
According to this histogram the overall range of the data values is from 0 to 190. The data values are grouped in ranges of 10. This graph can be analyzed to interpret information about the adolescents in this sample duration of weekly meal preparation. For example, five students spent 10 to 20 minutes per week preparing meals. One student spent 70 to 80 minutes. Most students spent less than 1 hour preparing meals.
Analyzing graphs that include two samples or populations As students learn about measures of central tendency and variability they should be provided opportunities to apply their knowledge to a variety of graphs. Below is a bar graph that includes two samples or populations. This allows students to identify characteristics of each individual group as well as make comparisons between the two groups.
(Graphic)
Examples of questions that could be asked about this data set: (a) Do more boys or girls like vegetables? [girls]; (b) What is the mode for favorite vegetables [most commonly voted for – peas]; (c) What is the difference between the number of boys who voted for broccoli versus girls? [2]; (d) What is the total number of students who voted for potatoes? [6]
1a.2 Common misunderstandings in this content area
- Students may use the wrong type of graph to display data. Below is an example of the correct use of a line graph instead of a bar graph. In this instance students should understand that all points on a line in a line graph should represent a value. What is the value of the midpoint (see purple dot) between red and blue? A student might answer “4”, but “4” of what? This data should have been represented using a bar graph. In order to avoid this misconception, students should be provided practice identifying types of graphs and their purpose. For example, bar graphs tend to display categorical data (data that can only be divided into categories such as colors), whereas line graphs display nominal data (data that can be displayed using numbers).
(Graphic)
- Students may not attend to scale when comparing data in two graphs. See the example below. Both are displaying the same data set but one might appear to a student to have more due to the height of the columns. To avoid this error students should be taught to attend to all the features of the graph (in this case, the y-axis values).
(Graphic)
- Students may have difficulty interpreting pictographs where each picture stands for an amount greater than one.
1a.3 Prior Knowledge/skills needed (can be taught concurrently)
- Number identification
- More/less
- One to one correspondence
- Same/different
2. What are some of the types of activities general educators will use to teach this skill?
2.1 Activities from General Education Resources
- (Lightbulb/hat) Ask students to collect data (e.g., time students spend playing video games or types of video games played) and then have them select the correct graphical representation to display the data
- (Lightbulb/hat) Have students collect graphs from a variety of sources (internet, magazines, etc.) and sort them by type.
- (Lightbulb/hat) Create a scaled pictograph representing classmates’ favorite sport.2
- (Lightbulb/hat) Use line graph which charts height and weight of an individual to answer questions about the pattern of her growth.2
- (Lightbulb/hat) Give students data, such as responses to a survey about favorite dessert, and have them develop a graph with an appropriate scale to represent the data.3
- (Lightbulb/hat) Provide the same data set displayed in two different forms: Bar graph and circle graph. Ask students to compare and contrast the information obtained from each graph.4
- (Lightbulb/hat) Provide students with list of numbers and ask them to calculate the average.4
- (Lightbulb/hat) Have students collect data about students in their school and compile statistics by determining the mean, median, and mode of student characteristics (e.g., height, age, library use, and distance from home to school).4
- (Lightbulb/hat) Ask students to create a circle graph demonstrating how they spend their money.4
- (Lightbulb/hat) Ask students to use the internet to find the number of different species of animals housed in five major zoos, and create a bar graph of the data set.5
- (Lightbulb/hat) Give students a set of data and ask them to create a line graph to represent the data set provided.5
- (Lightbulb/hat) Give students a set of data and ask them to create a stem-and-leaf plot to represent the data provided.5
Links across content areas
- Social Studies:
- (Lightbulb/hat) Have students research the average household income for all the states surrounding their own and then create a pictograph using a dollar bill to represent $1,000.
- (Lightbulb/hat) Create a bar graph displaying distance from where the student lives to major cities in the United States.2
- (Lightbulb/hat) Using election results displaying votes by county have students to calculate the mean, median and mode number of votes for two competing candidates in 10 local counties.5
- Literature:
- (Lightbulb/hat) Read Help is on the way for charts and graphs by Marilyn Berry.
- (Lightbulb/hat) Read The Magic School Bus Inside a Beehive by Joanna Cole and graph an estimate of the number of eggs the queen bee lays in one minute, two minutes, etc. and develop an appropriate scale to match the data.3
- (Lightbulb/hat) Write several sentences up on the board that use the term average but communicate different meanings and discuss this with the class. Then explain and discuss the meaning of average when applied to mathematics.3
- (Lightbulb/hat) Read Peanut Butter and have students graph the relationship between peanuts and amount in ounces of peanut butter.
- (Lightbulb/hat) Ask students to read three different types of genres and count the number of words per minute read over a period of three minutes. Have them graph the data and discuss why some genres may take more time to read than others.5
- Science:
- (Lightbulb/hat) Have students plant a seed and measure its growth over time and graph the data.3
- (Lightbulb/hat) Have students plant a new seed and an old seed and measure their growth over time, graph the data on the same chart, and compare the data between the two seeds.3
- (Lightbulb/hat) Have students collect and graph data showing the number of tornadoes per year in the United States for the last 5 years.5
- Music:
- (Lightbulb/hat) Have students research the length of several popular songs and calculate the average length.3
3. What Connectors to the Common Core Standards Are Addressed in Teaching “Data Analysis”?
| Grade differentiation | Core Content Connectors | Common Core State Standards |
| 3rd grade | 3.DPS.1f1 Develop questions, make a plan for data collection | |
| 3.DPS.1g1 Collect data, organize into picture or bar graph | 3.MD.3 | |
| 3.DPS.1g2 Organize measurement data into a line plot | 3.MD.4 | |
| 3.DPS.1i Select the appropriate statement that describes the data representations based on a given graph (picture, bar, line plots) | 3.MD.3 | |
| 3.DPS.1k1 Apply results of data to a real world situation | ||
| 4th grade | 4.DPS.1f2 Develop questions, make a plan for data collection | |
| 4.DPS.1g3 Collect data, organize in graph (e.g., picture graph, line plot, bar graph) | 3.MD.3 | |
| 4.DPS.1j1 Select an appropriate statement that describes the most frequent or the least frequent data point using a line plot, picture graph, or bar graph | 3.MD.3 | |
| 4.DPS.1k2 Apply results of data to a real world situation | 3.MD.4 | |
| 5th grade | 5.GM.1c1 Locate the x and y axis on a graph | 5.G.1 |
| 5.GM.1c2 Locate points on a graph | 5.G.1 | |
| 5.GM.1c3 Use order pairs to graph given points | 5.G.1 | |
| 5.DPS.1c1 Collect and graph data: bar graph, line plots, picture graph
(e.g., average height among 3 classrooms, # of boys and girls) |
3.MD.3
5.MD.2 | |
| 5.DPS.1d1 Select an appropriate statement about the range of the data for a given graph (bar graph, line plot) (i.e. range of data) up to 10 points | 6.SP.3 | |
| 5.DPS.1e1 Use measures of central tendency to interpret data including overall patterns in the data | 6.SP.3 | |
| 6th gade | 6.GM.1c4 Locate points on a graph | 5.G.1 |
| 6.GM.1c5 Use order pairs to graph given points | 5.G.1 | |
| 6.GM.1c6 Find coordinate values of points in the context of a situation | 5.G.2 | |
| 6.DPS.1a2 Identify statistical questions and make a plan for data collection | 6.SP.1 | |
| 6.DPS.1c2 Collect and graph data: bar graph, line plots, dot plots, histograms | 6.SP.4 | |
| 6.DPS.1d2 Solve for mean of a given data set | 6.SP.3 | |
| 6.DPS.1d3 Select statement that matches mean, mode, and spread of data for 1 measure of central tendency for a given data set | 6.SP.5 | |
| 6.DPS.1d4 Find the range of a given data set | 6.SP.2 | |
| 6.DPS.1d5 Explain or identify what the mean represents in a set of data | 6.SP.3 | |
| 6.DPS.1d6 Explain or identify what the mode represents in a set of data | 6.SP.2 | |
| 6.DPS.1d7 Explain or identify what the median represents in a set of data | 6.SP.5 | |
| 6.DPS.1e2 Use measures of central tendency to interpret data including overall patterns in the data | 6.SP.5 | |
| 7th grade | 7.DPS.1k1 Analyze graphs to determine of select appropriate comparative inferences about two samples or populations | 7.SP.4 |
| 7.DPS.1b1 Determine sample size to answer a given question | 7.SP.1 | |
| 7.DPS.1g1 Graph continuous data using line graphs, histograms, or dot plots | 6.SP.4 | |
| 7.DPS.1i1 Solve for the median of a given data set | 6.SP.5C | |
| 7.DPS.1i2 Identify the range (high/low), median(middle), mean, or mode of a given data set | 7.SP.4 | |
| 7.DPS.1j1 Make or select a statement to compare the distribution of 2 data sets | 7.SP.3 | |
| 7.DPS.1k1 Analyze graphs to determine or select appropriate comparative inferences about two samples or populations | 7.SP.4 | |
| 8th grade | Data: 8.DPS.1h1: Graph bivariate data using scatter plots and identify possible associations between the variables | 8.SP.1 |
| 8.DPS.1k2 Analyze displays of bivariate data to develop or select appropriate claims about those data | 8.SP.4 | |
| Grades 9-12 | H.DPS.1a1 Design study using categorical and continuous data, including creating a question, identifying a sample, and making a plan for data collection | S.ID.4
S.ID.5 |
| H.DPS.1b1 Complete a graph given the data, using dot plots, histograms, or box plots | S.ID.1 | |
| HS.DPS.1c 1 Use descriptive stats; range, median, mode, mean, outliers/gaps to describe the data set | S-ID.4
S-ID.5 | |
| H.DPS.1c2 Compare means, median, and range of 2 sets of data | S.ID.2 | |
| H.DPS.1d1 Represent data on a scatter plot to describe and predict | S.ID.6 | |
| H.DPS.1d2 Select an appropriate statement that describes the relationship between variables | S.ID.6 | |
| H.DPS.1d3 Make or select an appropriate statement(s) about findings | S.IC.6 |
(TABLE WITH GRAPHICS)
4. What are Some Additional Activities That Can Promote Use of this Academic Concept in Real World Contexts?
- (lightbulb/hat)Have students collect nutrition information on their favorite foods from several fast food restaurants and graph the amount of fat and total calories for each of the items. Ask them to identify the healthiest foods displayed.
- (lightbulb/hat)Ask students to collect and graph the average temperatures of weather across the year in the area in which they live; then have them match the type of clothing they need to wear across the year.
- (lightbulb/hat)Have students graph their monthly allowance (or job earnings) and predict how long it would take for them to purchase a desired item. Extend this by having them choose an inexpensive item (such as a t-shirt) and a more expensive item (such as a Nintendo DS) and calculate the difference in time it would take to have the money to purchase these items.
- (lightbulb/hat)Ask students to research the amount of UVB and UVA sunlight that is emitted over time and compare this to what are considered harmful levels of each. Based on this information ask students how often they should reapply sunscreen and/or how long it is safe to stay out in direct sunlight.
- (lightbulb/hat)Have students set a goal time for running or walking two miles. Ask them to time themselves each time they run or walk two miles and predict how soon they will achieve their goal.5
- (lightbulb/hat)Get students to research the cost of living for the city in which they reside. Then have them research the median wages earned for 5 professions they may be interested in pursuing and compare these wages to the cost of living. Ask the students if they will be able to live comfortable on these wages? Will they need to work more than one job?
5. How Can I Further Promote College and Career Readiness when Teaching “Data Analysis”?
Ideas for Promoting Career/ College Ready Outcomes
Communicative competence:
Students will increase their vocabulary to include concepts related to “data analysis.” In addition, they will be learning concepts such as: more, less, most, least, same, different, average, about, and graph
Fluency in reading, writing, and math
Students will have an opportunity to increase their numeracy and sight word fluency while participating in problem solving related to “data analysis” such as addition and division to determine mean and number identification to express mode or median. Writing numerals and developing questions about a data set of visual display of data. Reading and interpreting data displays including legends and labels on graphs.
Age appropriate social skills
Students will engage in peer groups to solve problems related to “data analysis” that will provide practice on increasing reciprocal communication and age appropriate social interactions. For example, students might work together with their peers to survey students in their school and then work together to display the data they collected into an appropriate graph.
Independent work behaviors
By solving real life problems related to “data analysis,” students will improve work behaviors that could lead to employment such as a data entry operator. When providing opportunities for real life problems leave some materials out and prompt/teach the students to determine who they should ask and what they should ask for to be able to solve the problem.
Skills in accessing support systems
At times, students will need to ask for assistance to complete activities related to “data analysis” which will give them practice in accessing supports. Students will gain practice asking for tools such as talking calculators, number lines, graphic organizers, and formulas. They can ask a peer to complete the physical movements of the tasks they are not able to do themselves. Be sure to teach students to ask versus having items or supports automatically given to them.
6. How Do I Make Instruction on “Data Analysis” Accessible to ALL the Students I Teach?
6.1 Teach Prerequisites and Basic Numeracy Skills Concurrently: Remember that students can continue to learn basic numeracy skills in the context of this grade level content. Basic numeracy skills that can be worked on as a part of a lesson relating to equations:
- Number identification
- Counting
- One to one correspondence
- Addition
- Division
- Counting by twos (and other intervals of scale)
6.2 Incorporate UDL: Universal Design of Learning When Teaching Data Analysis Some examples of options for teaching Data Analysis to students who may present instructional challenges due to:
| Options for Representation | |||
| Sensory Differences such as Blindness, Visual Impairment, Deafness, or Deaf/Blindness | Physical Disability or Motor Differences (such as weakness or motor planning difficulty) | Extremely limited evidence of experience/ skill or motivation/attention. | Lack of or extremely limited use of speech. |
Provide auditory options
Provide tactile options:
Provide visual and manipulative options to scaffold representation of concepts:
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Reduce Physical Effort
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Illustrate through multiple media
Illuminations [1] Math Open Reference [2] There are many resources listed here: [3]
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Provide customized display of information
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| Options for Expression | |||
| Sensory Differences such as Blindness, Visual Impairment, Deafness, or Deaf/Blindness | Physical Disability or Motor Differences (such as weakness or motor planning difficulty) | Extremely limited evidence of experience/ skill or motivation/attention. | Lack of or extremely limited use of speech. |
Vary the methods for response by:
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Provide options for responses/expression:
Optimize access to tools/ alternatives for responding
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Provide multimedia options for responses/expression:
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Provide options for modes of communication:
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| Options for Engagement | |||
| Sensory Differences such as Blindness, Visual Impairment, Deafness, or Deaf/Blindness | Physical Disability or Motor Differences (such as weakness or motor planning difficulty) | Extremely limited evidence of experience/ skill or motivation/attention. | Lack of or extremely limited use of speech. |
Recruit interest by providing choices:
Increase personal relevance:
Provide tactile options for engagement:
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Recruit interest by increasing personal relevance:
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Recruit interest by providing choices:
Provide options for sustaining effort and persistence
Increase personal relevance:
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Recruit interest with modes of communication:
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