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Here you will learn about representing data, including how to create and interpret the different tables, charts, diagrams and graphs you can use to represent data.
Students first learn how to represent and interpret data in the first grade and expand their knowledge as they progress through elementary school, middle school and high school. Being data literate is essential for success in the real world.
Representing data allows you to display and interpret collected data. Data literacy is essential to understanding the world around us.
There are different types of data that can be represented in different formats.
For example,
Let’s take a look in detail at some of the different ways to represent data.
Use this quiz to check your grade 6th to 7th students’ understanding of representing data. 10+ questions with answers covering a range of grades 6 and 7 representing data topics to identify areas of strength and support!
DOWNLOAD FREEUse this quiz to check your grade 6th to 7th students’ understanding of representing data. 10+ questions with answers covering a range of grades 6 and 7 representing data topics to identify areas of strength and support!
DOWNLOAD FREEA histogram is a graphical representation used to display quantitative continuous data (numeric data). The graphical display uses bars that are different heights and each bar groups numbers into ranges. The horizontal axis represents the numerical range, and the vertical axis represents the frequency, which is the number of times the data falls in the particular numerical range.
For example, the frequency table shows the salaries of katex is not defined employees at a small company. Create a histogram from the data.
Step by step guide: Histograms
A stem and leaf plot is a method of organizing numerical data based on the place value of the numbers.
Each number is split into two parts.
The first digit(s) form the stem,
The last digit forms the leaf.
For example, the data below represents the age of all the employees at Millstown Elementary School. Create a stem and leaf plot from the data
Step by step guide: Stem and Leaf Plot
A frequency distribution is a way of representing data from a frequency distribution table. Frequency distributions can be represented by frequency graphs such as pie graphs, bar graphs, line plots, vertical line graphs, and/or frequency polygons where the frequency is displayed on the vertical axis katex is not definedaxiskatex is not defined
There are two types of data that can be represented using a frequency graph.
Categorical data – data that are words rather than numbers, for example, colors, makes of cars, types of music.
Numerical data – data that is in the form of numbers. There are two types of numerical data.
Here are some examples of frequency graphs:
Step by step guide: Frequency distribution
Step by step guide: Line graph
A cumulative frequency graph, also called an ogive, shows the frequencies of each category accumulated together. This allows you to analyze the distribution of the data in more detail than if you used a frequency polygon and calculate statistics.
Here is an example of a cumulative frequency graph along with the data set.
Similar to a frequency graph, the horizontal axis katex is not definedaxiskatex is not defined represents the numerical interval and the vertical axis katex is not definedaxiskatex is not defined represents the cumulative frequency.
A pie chart also known as a circle chart or pie graph is a visual representation of data that is made by a circle divided into sectors (pie slices). Each sector represents a part of the whole (whole pie). Pie charts are used to represent categorical data.
Here is an example of a pie chart that displays students’ favorite subjects in percentages at a particular school. Notice how each sector represents a percent of the whole circle.
The sectors of the circle graphs can be represented as the number data points in the category or as percents.
Step by step guide: Pie chart
A box plot also known as a box and whisker plot is a graph that represents the five number summary of a set of data.
The five number summary includes the following:
Here is an example of a box plot for the given data set:
katex is not defined
Like with a stem and leaf plot, it is helpful to put the data points in order from least to greatest.
katex is not defined
Quartiles are values that divide the data set into three quarters. From the box plot, you can see that the first quartile is the value where the katex is not defined of the data set falls under.
The median or the second quartile is the value where katex is not defined of the data falls under and the third quartile katex is not defined is the value where katex is not defined of the data set falls under.
From the box plot, you can also determine the interquartile range katex is not defined which is found by finding the difference between katex is not defined and katex is not defined
katex is not defined
Step by step guide: Box plot
Step by step guide: Quartile
Step by step guide: Interquartile range
How does this relate to katex is not definedth and katex is not definedth grade math?
For a more detailed step-by-step approach on how to represent data, go to the links highlighted in the “What is representing data” section above or follow the examples below.
The data below represents the heights of trees at a tree farm in feet.
katex is not defined
katex is not defined
2Split the numbers into two parts; the last part must be one digit only.
The numbers in the data will be split into tens and ones, so katex is not defined will be katex is not defined and katex is not defined katex is not defined represents katex is not defined or katex is not defined ten and katex is not defined is katex is not defined oneskatex is not defined
3Put the values into the diagram and create a key.
Create histogram for the given test scores.
katex is not defined
Decide what bin size to use and how many bins are needed.
Bin size is the same as interval size.
The lowest test score is katex is not defined, and the highest test score is katex is not defined Let’s use bins (intervals) of katex is not defined There are katex is not defined bins all together.
Group the data by the bin sizes to find the frequency.
Create bars based on the bin sizes and frequencies within the bins.
Label the katex is not defined and katex is not defined axes with units.
katex is not defined pupils were asked which subject was their favorite. Here is a pie chart to show the results. How many students said science was their favorite subject?
Identify the categories.
There are katex is not defined categories, science katex is not defined English katex is not defined history katex is not defined art katex is not defined and other katex is not defined
Calculate and analyze the data.
There are katex is not defined students that were surveyed, and katex is not defined said that science was their favorite subject.
katex is not defined
katex is not defined
katex is not defined students say that science is their favorite subject.
Create a box plot for the data below.
katex is not defined
Determine the median and quartiles.
Placing the data in order from least to greatest.
katex is not defined
Draw a scale, and mark the five key values: minimum value, lower quartile (LQ), median, upper quartile (UQ), and maximum value.
Join the lower quartile and upper quartile to form the box, and draw horizontal lines to the minimum and maximum values.
At the local zoo, the zoologist was taking a count of the animals.
Create a dot plot representing this data.
Create a dot plot representing this data.
Read the question and determine what type of graph you need to create.
This question asks you to create a dot plot to represent the data.
Use the data to create the specific frequency graph.
A vet weighs all the dogs she sees in a week. Here are the results.
Draw a frequency polygon to show the results.
Read the question and determine what type of graph you need to create.
This question asks you to create a frequency polygon to represent the data.
Use the data to create the specific frequency graph.
Use the midpoints of the groups representing mass, katex is not defined and so on, to label the horizontal axis. The frequency is on the vertical axis.
Plot points with a sharp pencil and crosses to be accurate, and then connect the points to create the frequency polygon.
1. Use the stem and leaf plot to determine the mode.
The value katex is not defined occurs twice. Therefore, the mode is katex is not defined
2. Use the box plot to determine the median.
On a box plot, the line in the box represents the median.
3. Which histogram represents the data?
The table shows the number of deer Karen sees in her yard over the course of a month.
Look to make sure the axes are numbered correctly. The horizontal axis should be labeled katex is not defined to katex is not defined counting by katex is not defineds. The vertical axis should be numbered katex is not defined to katex is not defined
Each bar height should be equal to the frequency in each interval.
4. Which pie chart represents the data in this frequency table?
The total of the frequencies is katex is not defined The frequency of katex is not defined is katex is not defined which is a quarter of katex is not defined So, section katex is not defined needs to be a quarter of the pie chart.
Similarly section katex is not defined needs to be a quarter too. The frequency of katex is not defined is katex is not defined which is half of katex is not defined Section katex is not defined needs to be half of the pie chart.
5. The table below shows the number of flowers in a garden.
Which dot plot represents the data in the table?
There are katex is not defined types of flowers: tulip, lily, rose, and marigold. Label the horizontal axes with the flower types. For each flower, place the number of dots vertically that matches the frequency.
6. Which of these is the correct frequency polygon for the frequency table below?
The points should be plotted using the midpoints of the groups: katex is not defined and katex is not defined They should be plotted using the correct frequencies: katex is not defined and katex is not defined The points need joining up, but NOT the last and the first points.
Continuous data can be any value within a range of values or in an interval. Discrete data is a specific value within a range.
When you study algebra katex is not defined you will learn how to create scatter plots. A straight line going through the points on a scatter plot is known as a line of best fit.
Step-by-step guide: Scatterplots
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