Name: descriptive statistics and graphs
Uploaded: 2023-04-30T11:12:52.000Z
Duration: 1 min 13 s
Channel: JoVE

K12 Standards

Virginia  Standards of Learning

HIgh School

Earth Science

ES.1

ES.1.c

Review and Preview

Recall that data are broadly classified into quantitative data and qualitative data.
Quantitative data represent the measurements or counts of numerical values, such as varying heights of students in a class.
Conversely, qualitative data, also known as categorical data, represent non-numerical variables such as the different colors of hair.
For efficient statistical analysis, these unorganized, large data sets are summarized and represented numerically in tabular form or visually in graphical form.
For example, the temperature changes measured during a day can be summarized in the form of a table.
These data can also be represented graphically. Here, the time is given along the horizontal axis, and the temperature is displayed along the vertical axis.
The points in the graph are joined to form the pattern providing a visual understanding of how the daytime temperature changes with time.
The graph also identifies the outliers from the other data values that indicate extreme temperatures observed in the day.

review and preview

Data are individual items of information obtained from a population or sample. Data may be classified as qualitative (categorical), quantitative continuous, or quantitative discrete. Because it is not practical to measure the entire population in a study, researchers use samples to represent the population. A random sample is a representative group from the population chosen by using a method that gives each individual in the population an equal chance of being included in the sample. Random sampling methods include simple random sampling, stratified sampling, cluster sampling, and systematic sampling. Convenience sampling is a nonrandom method of choosing a sample that often produces biased data.
Once the data is collected, it can be described and presented in many different formats. For example, suppose a person is interested in buying a house in a particular area. Not having much information about the house prices, the buyer might ask the real estate agent to give a sample data set of prices. Reading through all the prices in the sample can be a little overwhelming. A better way might be to look at the median price and the variation in the prices. The median and variation are just two ways that one can use to describe data. The agent might also provide a graph of the data, which could be a more convenient way to understand the house prices.
The area of statistics that details the numerical and graphical ways to describe and display the sample data is called &#34;Descriptive Statistics.&#34; A statistical graph is a tool that helps one learn about the shape or distribution of a sample or a population. A graph can be a more effective way of presenting data than a stack of numbers because it is easy to observe data clusters and identify positions where there are only a few data values. Newspapers and the Internet use graphs to show trends and to enable readers to compare facts and figures quickly. Some types of graphs that are used to summarize and organize data are the dot plot, the bar graph, the histogram, the stem-and-leaf plot, the frequency polygon (a type of broken line graph), the pie chart, and the box plot.

Data are individual items of information obtained from a population or sample. Data may be classified as qualitative (categorical), quantitative ...

Education

JoVE Core

Statistics

Unit 1

Summarizing and Visualizing Data

KEY TERMS AND CONCEPTS

descriptive statistics and graphs

Descriptive statistics help summarize data with numbers and graphs. Data are individual pieces of information collected from a population or a sample. They can be qualitative, which means categorical, or quantitative, which includes continuous and discrete data.

In many studies, researchers do not measure every member of a population. Instead, they use a sample to represent the population. A random sample is a representative group chosen so that each individual has an equal chance of being selected. Random sampling methods include simple random sampling, stratified sampling, cluster sampling, and systematic sampling. Convenience sampling is nonrandom and often leads to biased data.

After data are collected, they can be described in different ways. For example, when someone wants to buy a house in a certain area, a real estate agent might share a sample set of house prices. Looking at every price can be overwhelming, so the buyer may focus on the median price and the variation in the prices. The median and variation are two ways to describe the data.

Graphs also help organize and present sample data. A statistical graph shows the shape or distribution of data and can make patterns easier to see than a long list of numbers. Clusters and gaps in the data are often easier to notice on a graph. Newspapers and the Internet use graphs to show trends and help readers compare facts and figures quickly. Common graphs include the dot plot, bar graph, histogram, stem-and-leaf plot, frequency polygon, pie chart, and box plot.

Descriptive Statistics and Graphs

Descriptive statistics help summarize data with numbers and graphs. Data are individual pieces of information collected from a population or a sample. They can be qualitative, which means categorical, or quantitative, which includes continuous and discrete data. In many studies, researchers do not measure every member of a population. Instead, they use a sample to represent the population. A random sample is a representative group chosen so that each individual has an equal chance of being...

what is a frequency distribution

Reading Frequency Tables and Histograms

Frequency distributions organize quantitative data by showing how often each value appears. A frequency is the number of times a data value occurs. When the frequency values are added together, the total equals the number of students in the sample. These distributions are useful for grouping numerical data into clear patterns. They can be shown in a table, histogram, line graph, dot plot, or pie chart. A histogram displays tabulated frequencies as adjacent rectangles over discrete intervals,...

construction of frequency distribution

Building a Frequency Table from Data

A frequency distribution table organizes data by showing how often each value appears. It starts with two columns: one for the data labels and one for frequency. A third column for tally marks can be added if needed. The next step is to look at the data set and decide whether an ungrouped frequency distribution table or a grouped frequency distribution table is more suitable. If the data includes a large set of different values, a grouped frequency distribution table is the better choice. This...

relative frequency distribution

Relative Frequency in Data Tables

Relative frequency distribution shows how often each value or class appears in a data set as a fraction of the whole. To find a relative frequency, divide each class frequency by the total number of data points in the sample. The result can be written as a fraction, decimal, or percent. This type of distribution is very similar to a regular frequency distribution. The same data are grouped in classes, and the same rules are used to build those classes. The main difference is in the way the...

percentage frequency distribution

Survey Data as Percentage Frequencies

Survey data can be shown as percentage frequencies to display how observations are spread across each data point or group. This format shows the share of the total for each response or category. It is a common way to present relative frequency in survey results and other data. Percentage frequency distributions are often displayed as bar graphs, pie charts, or tables. These displays make it easier to compare groups and see how much each category contributes to the whole. They are useful...

cumulative frequency distribution

Building a Cumulative Frequency Table

A cumulative frequency distribution shows how data build up across class intervals. Instead of counting only the values in one class, it counts the values in that class and in every class to its left. It is a useful way to track how data accumulate as the table progresses. A cumulative frequency is found by adding the frequency of each class lower than the class interval or category being studied. In other words, each new total includes the current class and the frequencies from the lower...

ogive graph

Cumulative Frequency Graph for Medians

An ogive graph is a cumulative frequency graph used in statistics. It is also called a cumulative frequency polygon. Instead of showing each class on its own, it adds the cumulative percentages from left to right. An ogive graph plots cumulative frequency on the vertical y-axis and class boundaries on the horizontal x-axis. It looks similar to a histogram, but it uses single points instead of rectangles. Each point appears where the top right corner of a histogram bar would be. This graph is...

histogram

Reading Data Patterns with Histograms

A histogram shows how data is distributed in a data set. It uses an x-y graph to display the pattern of the data. The x-axis is labeled with what the data represents, such as distance from home to school. The y-axis shows frequency, relative frequency, percent frequency, or probability. A histogram is made of adjoining bars. The height of each bar matches the frequency value for that class. Even with different labels, the graph keeps the same overall shape. Like a stemplot, a histogram can...

relative frequency histogram

Reading Relative Frequency in Histograms

A relative frequency histogram shows how data are spread across classes using percentages instead of counts. The relative frequency tells the proportion of data points in each value or class. The frequency tells the number of data points in each value or class. This graph has the same overall shape as a histogram. It uses a horizontal scale on the x-axis, and it marks the y-axis with relative frequencies, which are percentages of the whole. Each bar shows how many data values fall into a...

scatter plot

Reading Relationships in a Scatter Plot

A scatter plot shows the relationship between two variables, x and y. It is one of the easiest ways to display how the variables are connected. The graph can show the direction of the relationship. It can also show whether the points suggest a clear pattern or little pattern at all. A clear direction appears when high values of one variable go with high values of the other variable. It can also appear when low values of one variable go with low values of the other variable. Another pattern...

time-series graph

Reading Trends with Time-Series Graphs

A time-series graph shows repeated measurements taken at successive intervals of time. It is also called a time series chart. This type of line graph helps organize data that changes over time. To build a time-series graph, use both parts of a paired data set. Plot the time increments on the horizontal axis. Plot the measured values on the vertical axis. Each point then shows one time and one quantity, and the points are usually connected with straight lines in the order they occur. <br...

bar graph

Comparing Categories with Bar Charts

A bar graph, also called a bar chart, compares categories with separate bars. The bars may be horizontal or vertical. Each bar stands apart so the viewer can compare groups clearly.

multiple bar graph

Comparing Data with Multiple Bar Graphs

A multiple bar graph compares two or more sets of data with grouped bars. It works like a bar graph, but it uses several bars to show related values side by side. Each bar or column stands for one data value. This graph is useful when the data share the same unit of measurement. You can include many parameters, as long as they use that same unit. The categories are placed on the horizontal x-axis, and the frequency is shown on the vertical y-axis. Multiple bar graphs are used mainly to relate...

pareto chart

Pareto Chart for Ranking Data

A Pareto chart is a bar graph used to rank data by size or frequency. It can also combine bars with a line graph. In the chart, the bar lengths show the individual values or how often each category appears, and the line shows the cumulative total. The bars are arranged from longest on the left to shortest on the right. This order makes the data easier to read and interpret. A Pareto chart is also called a Pareto diagram or Pareto analysis. The chart is named after the Italian economist...

pie chart

Pie Chart Data and Percentages

A pie chart shows categorical data in a circular graph. It is divided into slices, and each slice shows a numerical proportion. This makes it easy to compare the relative size of parts in one chart. In a pie chart, the central angle, the arc length of each slice, and the area are directly proportional to the quantity or percentage it represents. That means larger values take up larger slices. Smaller values take up smaller slices. Pie charts are useful for real-world data such as marks...

key terms and concepts

Learn how descriptive statistics summarize data with numbers and graphs, including samples, random sampling, median, variation, and common graph types.

Descriptive Statistics and Graphs | JoVE K12

statistics

JoVE Core Statistics introduces the concepts and application of the collection, analysis, presentation, and interpretation of data to students. These animated lessons provide an understanding of statistics beneficial to students from a wide range of disciplines. Additionally, the scientist-in-action videos demonstrate the application of related concepts in classical and original research experiments performed in today's laboratories worldwide

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Life Science

LS.1

LS.1.c

LS.1.e

Physical Science

PS.1

PS.1.c

Physics

PH.1

PH.1.c

PH.1.e

Texas Essential Knowledge and Skills

High School

Specialised Topic in Science

112.51.c.1.

112.51.c.1.F.

Biology

BIO.1

BIO.1.E

PHYS.1

PHYS.1.F

PHYS.2

PHYS.2.B

Chemistry and Physics

IPC.1

IPC.1.F

IPC.2

IPC.2.B

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ES.1.a

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ES.1.b

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Reliability and Validity

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Reasoning

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The student will demonstrate an understanding of scientific and engineering practices by constructing and critiquing conclusions and explanations
• make quantitative and/or qualitative claims based on data
• construct and revise explanations based on valid and reliable evidence obtained from a variety of sources, including students' own investigations, models, theories, simulations, and peer review
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• construct arguments or counterarguments based on data and evidence
• differentiate between a scientific hypothesis, theory, and law

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Descriptive Statistics and Graphs

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