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

تذكر أن البيانات مصنفة على نطاق واسع إلى بيانات كمية وبيانات نوعية.
تمثل البيانات الكمية قياسات أو أعداد القيم العددية ، مثل الارتفاعات المتفاوتة للطلاب في الفصل.
على العكس من ذلك ، تمثل البيانات النوعية ، والمعروفة أيضا باسم البيانات الفئوية ، متغيرات غير رقمية مثل ألوان الشعر المختلفة.
من أجل التحليل الإحصائي الفعال ، يتم تلخيص مجموعات البيانات الكبيرة غير المنظمة هذه وتمثيلها عدديا في شكل جدولي أو بصريا في شكل رسومي.
على سبيل المثال ، يمكن تلخيص التغيرات في درجات الحرارة المقاسة خلال اليوم في شكل جدول.
يمكن أيضا تمثيل هذه البيانات بيانيا. هنا ، يتم إعطاء الوقت على طول المحور الأفقي ، ويتم عرض درجة الحرارة على طول المحور الرأسي.
يتم ربط النقاط الموجودة في الرسم البياني لتشكيل النمط الذي يوفر فهما مرئيا لكيفية تغير درجة حرارة النهار بمرور الوقت.
يحدد الرسم البياني أيضا القيم المتطرفة من قيم البيانات الأخرى التي تشير إلى درجات الحرارة القصوى التي لوحظت في اليوم.

المراجعة والمعاينة

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البيانات هي عناصر فردية من المعلومات التي تم الحصول عليها من مجتمع إحصائي أو عينة. يمكن تصنيف البيانات على أنها نوعية (فئوية)، أو كمية مستمرة، أو كمية منفصلة. نظرًا لأنه ليس من العملي قياس إجمالي عدد المجتمع الإحصائي في الدراسة، يستخدم الباحثون عينات لتمثيل المجتمع الإحصائي. العينة العشوائية هي مجموعة تمثيلية من المجتمع الإحصائي يتم اختيارها باستخدام طريقة تمنح كل فرد في المجتمع فرصة متساوية لإدراجه في العينة. تشمل طرق أخذ العينات العشوائية أخذ العينات العشوائية البسيطة، وأخذ العينات الطبقية، وأخذ العينات العنقودية، وأخذ العينات المنهجية. أخذ العينات الملائمة هو طريقة غير عشوائية لاختيار عينة تنتج في كثير من الأحيان بيانات متحيزة.

بمجرد جمع البيانات، يمكن وصفها وعرضها في العديد من التنسيقات المختلفة. على سبيل المثال، لنفترض أن شخصًا ما مهتم بشراء منزل في منطقة معينة. نظرًا لعدم وجود الكثير من المعلومات حول أسعار المنازل، قد يطلب المشتري من الوكيل العقاري تقديم مجموعة بيانات عينة عن الأسعار. قد تكون قراءة جميع الأسعار الموجودة في العينة أمرًا مربكًا بعض الشيء. قد تكون الطريقة الأفضل هي النظر إلى السعر المتوسط ​​والتباين في الأسعار. الوسيط والتباين هما طريقتان فقط يمكن للمرء استخدامهما لوصف البيانات. قد يقدم الوكيل أيضًا رسمًا بيانيًا للبيانات، والذي قد يكون وسيلة أكثر ملاءمة لفهم أسعار المنازل.

يُطلق على مجال الإحصائيات الذي يعرض تفاصيل الطرق الرقمية والرسومية لوصف بيانات العينة وعرضها اسم "الإحصائيات الوصفية". الرسم البياني الإحصائي هو أداة تساعد الشخص على التعرف على شكل أو توزيع العينة أو المجتمع الإحصائي. يمكن أن يكون الرسم البياني وسيلة أكثر فعالية لعرض البيانات من مجموعة الأرقام لأنه من السهل مراقبة مجموعات البيانات وتحديد المواضع التي لا يوجد فيها سوى عدد قليل من قيم البيانات. تستخدم الصحف والإنترنت الرسوم البيانية لإظهار الاتجاهات ولتمكين القراء من مقارنة الحقائق والأرقام بسرعة. بعض أنواع الرسوم البيانية المستخدمة لتلخيص البيانات وتنظيمها هي الرسم النقطي، والرسم البياني الشريطي، والرسم البياني، ومخطط الجذع والأوراق، والمضلع التكراري (نوع من الرسم البياني الخطي المتقطع)، والمخطط الدائري، ومخطط الصندوق.
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البيانات هي عناصر فردية من المعلومات التي تم الحصول عليها من السكان أو العينة. يمكن تصنيف البيانات على أنها نوعية (فئوية) وكمية ...

Education

JoVE Core

Statistics

الإحصائيات

Unit 1

الوحدة الأولى

Summarizing and Visualizing Data

تلخيص البيانات وتصورها

KEY TERMS AND CONCEPTS

المصطلحات والمفاهيم الأساسية

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

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

Scientific Method

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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
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ES.1.a

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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
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ES.1.b

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

Data: Types and Distribution

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Histogram

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Accuracy and Precision

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Data Collection by Experiments

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Data Collection by Survey

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

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• 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

ES.1.f

Descriptive Statistics and Graphs

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