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

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ES.1.c

Review and Preview

נזכיר כי הנתונים מסווגים באופן רחב לנתונים כמותיים ונתונים איכותיים.
נתונים כמותיים מייצגים את המדידות או הספירות של ערכים מספריים, כגון גבהים משתנים של תלמידים בכיתה.
לעומת זאת, נתונים איכותיים, הידועים גם בשם נתונים קטגוריאליים, מייצגים משתנים לא מספריים כגון צבעי השיער השונים.
לצורך ניתוח סטטיסטי יעיל, ערכות נתונים גדולות ולא מאורגנות אלה מסוכמות ומיוצגות מספרית בצורה טבלאית או חזותית בצורה גרפית.
לדוגמה, ניתן לסכם את שינויי הטמפרטורה הנמדדים במהלך היום בצורה של טבלה.
נתונים אלה יכולים להיות מיוצגים גם באופן גרפי. כאן, הזמן ניתן לאורך הציר האופקי, והטמפרטורה מוצגת לאורך הציר האנכי.
הנקודות בגרף מחוברות ליצירת התבנית ומספקות הבנה חזותית של האופן שבו טמפרטורת היום משתנה עם הזמן.
הגרף מזהה גם את החריגים משאר ערכי הנתונים המצביעים על טמפרטורות קיצוניות שנצפו ביום.

סקירה ותצוגה מקדימה

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נתונים הם פריטי מידע בודדים המתקבלים מאוכלוסייה או מדגם. נתונים עשויים להיות מסווגים כאיכותיים (קטגוריים), רציפים כמותיים או בדידים כמותיים. מכיוון שזה לא מעשי למדוד את כל האוכלוסייה במחקר, החוקרים משתמשים במדגמים כדי לייצג את האוכלוסייה. מדגם אקראי הוא קבוצה מייצגת מהאוכלוסייה שנבחרה בשיטה המעניקה לכל פרט באוכלוסייה סיכוי שווה להיכלל במדגם. שיטות דגימה אקראית כוללות דגימה אקראית פשוטה, דגימה שכבתית, דגימת אשכולות ודגימה שיטתית. דגימת נוחות היא שיטה לא אקראית לבחירת מדגם שלעתים קרובות מייצרת נתונים מוטים.

לאחר איסוף הנתונים, ניתן לתאר אותם ולהציג אותם בפורמטים רבים ושונים. לדוגמה, נניח שאדם מעוניין לקנות בית באזור מסוים. ללא מידע רב על מחירי הבתים, הקונה עשוי לבקש מסוכן הנדל"ן לתת אוסף נתונים לדוגמה של מחירים. לקרוא את כל המחירים במדגם יכול להיות קצת מכריע. דרך טובה יותר עשויה להיות לבחון את המחיר החציוני ואת השונות במחירים. החציון והשונות הם רק שתי דרכים שבהן אפשר להשתמש כדי לתאר נתונים. הסוכן עשוי גם לספק גרף של הנתונים, שיכול להיות דרך נוחה יותר להבין את מחירי הדירות.

תחום הסטטיסטיקה המפרט את הדרכים המספריים והגרפיים לתיאור והצגה של נתוני המדגם נקרא "סטטיסטיקה תיאורית". גרף סטטיסטי הוא כלי שעוזר ללמוד על הצורה או ההתפלגות של מדגם או אוכלוסייה. גרף יכול להיות דרך יעילה יותר להצגת נתונים מאשר ערימה של מספרים מכיוון שקל לצפות באשכולות נתונים ולזהות מיקומים שבהם יש רק כמה ערכי נתונים. עיתונים ואינטרנט משתמשים בגרפים כדי להציג מגמות וכדי לאפשר לקוראים להשוות עובדות ונתונים במהירות. סוגים מסוימים של גרפים המשמשים לסיכום וארגון נתונים הם גרף הנקודות, גרף העמודות, ההיסטוגרמה, גרף הגבעול והעלה, מצולע השכיחות (סוג של גרף קו שבור), תרשים העוגה ותרשים קופסה.
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נתונים הם פריטי מידע בודדים המתקבלים מאוכלוסייה או מדגם. הנתונים עשויים להיות מסווגים כאיכותיים (קטגוריים), כמותיים ...

Education

JoVE Core

Statistics

סטטיסטיקה

Unit 1

יחידה 1

Summarizing and Visualizing Data

סיכום והדמיה של נתונים

KEY TERMS AND CONCEPTS

מונחים ומושגים מרכזיים

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

review and preview

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

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Physical Science

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Physics

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Texas Essential Knowledge and Skills

High School

Specialised Topic in Science

112.51.c.1.

112.51.c.1.F.

Biology

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PHYS.1

PHYS.1.F

PHYS.2

PHYS.2.B

Chemistry and Physics

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IPC.2

IPC.2.B

Scientific Method

The scientific method is used to solve problems and explain phenomena. The development of the scientific method coincided with changes in philosophy ...

Scientific Laws and Theories

Scientific Laws

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When the null and alternative hypotheses are stated, it is observed ...

Hypothesis: Accept or Fail to Reject?

The outcome of any hypothesis testing leads to rejecting or not rejecting the null hypothesis. This decision is taken based on the analysis of the data, ...

The student will demonstrate an understanding of scientific and engineering practices by asking questions and defining problems
• ask questions that arise from careful observation of phenomena, examination of a model or theory, or unexpected results, and/or to seek additional information
• determine which questions can be investigated within the scope of the school laboratory or field experience
• generate hypotheses based on research and scientific principles
• make hypotheses that specify what happens to a dependent variable when an independent variable is manipulated
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Inductive Reasoning

Inductive reasoning is a form of logical thinking that uses related observations to arrive at a general conclusion. It is uncertain and operates in ...

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Demonstrating the Scientific Method with Tree Branches
ExpandObtain branches containing a few dozen typical leaves from five different local tree species. ...

Observation and Background Research
ExpandNOTE: The first two steps in the scientific process involve studying and observing natural phenomena of ...

The student will demonstrate an understanding of scientific and engineering practices by planning and carrying out investigations
• individually and collaboratively plan and conduct observational and experimental investigations
• plan and conduct investigations to test design solutions in a safe and ethical manner including considerations of environmental, social and personal effects
• select and use appropriate tools and technology to collect, record, analyze, and evaluate data

ES.1.b

Introduction to Test of Independence

In statistics, the term independence means that one can directly obtain the probability of any event involving both variables by multiplying their ...

Statistical Analysis: Overview

An analysis is usually conducted by replicated sampling or repeated measurements on the same sample. This leads to scattered results rather than a single ...

Statistical Significance

Once data is collected from both the experimental and the control groups, a statistical analysis is conducted to find out if there are meaningful ...

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

Data: Types and Distribution

In biostatistics, data refers to the collected observations that are subject to analysis. Data can be parametric or nonparametric.
Nonparametric data ...

Histogram

The histogram is a graphical representation in the x-y form of data distribution in a data set. The horizontal x-axis is labeled with what the data ...

Scatter Plot

The most common and easiest way to display the relationship between two variables, x and y, is a scatter plot. A scatter plot shows the direction of a ...

Bar Graph

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Pie Chart

A pie chart (or a pie graph) is a circular graphical chart or a pictorial representation of categorical data. It is divided into slices of pie each ...

Numerical Calculations

In engineering applications, the representation of the numerical value is critical. Presenting or reporting the answer is one of the essential parts of ...

Accuracy and Precision

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Significant Figures in Calculations

Uncertainty in measurements can be avoided by reporting the results of a calculation with the correct number of significant figures. This can be ...

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Source: Laboratories of Gary Lewandowski, Dave Strohmetz, and Natalie Ciarocco&#8212;Monmouth University

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The student will demonstrate an understanding of scientific and engineering practices by pnterpreting, analyzing, and evaluating data
• construct and interpret data tables showing independent and dependent variables, repeated trials, and means
• construct, analyze, and interpret graphical displays of data and consider limitations of data analysis
• apply mathematical concepts and processes to scientific questions
• use data in building and revising models, supporting explanations of phenomena, or testing solutions to problems
• analyze data using tools, technologies, and/or models in order to make valid and reliable scientific claims or determine an optimal design solution

Data Collection by Observations

Data collection refers to a systematic way of obtaining, observing, measuring, and analyzing accurate information. Observational studies are one of the ...

Data Collection by Experiments

Data collection is a systematic method of obtaining, observing, measuring, and analyzing accurate information. An experimental study is a standard method ...

Data Collection by Survey

The systematic method of obtaining and analyzing accurate information of a population is called data collection. A survey is a standard method of data ...

Reliability and Validity

Reliability and validity are two important considerations that must be made with any type of data collection. Reliability refers to the ability to ...

Reasoning

Reasoning involves transforming information into conclusions, which is essential for problem-solving, decision-making, and critical thinking.
Reasoning ...

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
• apply scientific ideas, principles, and/or evidence to provide an explanation of phenomena or design solutions
• construct arguments or counterarguments based on data and evidence
• differentiate between a scientific hypothesis, theory, and law

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using-topographic-maps-to-generate-topographic-profiles

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Source: Laboratory of Alan Lester - University of Colorado Boulder
Topographic maps are &#34;plan-view&#34; representations of Earth&#39;s ...

The student will demonstrate an understanding of scientific and engineering practices by developing and using models
• evaluate the merits and limitations of models
• develop, revise, and/or use models based on evidence to illustrate or predict relationships
• construct and interpret scales, diagrams, classification charts, graphs, tables, imagery, models, including geologic cross sections and topographic profiles
• read and interpret topographic and basic geologic maps and globes, including location by latitude and longitude

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Levels of Communication II: Organizational, Public, and Group Dynamics

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The student will demonstrate an understanding of scientific and engineering practices by obtaining, evaluating, and communicating information
• compare, integrate, and evaluate sources of information presented in different media or formats to address a scientific question or solve a problem
• gather, read, and evaluate scientific and/or technical information from multiple sources, assessing the evidence and credibility of each source
• communicate scientific and/or technical information about phenomena and/or a design process in multiple formats

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Descriptive Statistics and Graphs

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