Name: reading frequency tables and histograms
Uploaded: 2023-04-30T11:13:00.000Z
Duration: 51 s
Channel: JoVE

K12 Standards

Virginia  Standards of Learning

HIgh School

Physical Science

PS.1

PS.1.c

What is a Frequency Distribution

Рассмотрим группу из 50 человек, участвующих в марафоне. Допустим, организаторы марафона хотят знать, как меняется количество участников с возрастом.
Чтобы выяснить это, данные суммируются с помощью таблицы распределения частот. Это статистический инструмент, который представляет данные, разделенные на несколько категорий или классов, в зависимости от количества значений для каждого класса, называемого частотой.
Таблицы частот помогают понять вхождение и распределение данных в наборе данных.
Например, таблица частот помогает визуализировать распределение учащихся по росту.
Аналогичным образом, изменение частоты пульса в группе пациентов можно легко визуализировать с помощью таблицы распределения частот.

Что такое частотное распределение

Частота — это количество раз, когда встречается значение данных. Сумма всех значений частоты представляет собой общее количество студентов, включенных в выборку. Обычно используется для группировки данных количественного типа. Частотное распределение можно отобразить в виде таблицы, гистограммы, линейного графика, точечной или круговой диаграммы, и это лишь некоторые из них. Гистограмма представляет собой графическое представление табулированных частот, показанных в виде соседних прямоугольников, расположенных на дискретных интервалах (диапазонах), с площадью, равной частоте наблюдений в интервале.

В таблице распределения частот значения данных группируются в классы одинаковой ширины. Границы классов — это отдельные значения, выбранные для разделения классов (часто являющиеся средними точками между верхними и нижними пределами соседних классов), в то время как наименьшие и самые большие наблюдения в каждом классе называются пределами класса. Распределения частот обычно могут иметь от 5 до 20 классов, все с одинаковой шириной, взаимоисключающие, непрерывные и исчерпывающие.

Частота — это количество повторений значения данных. Сумма всех значений частоты представляет собой общее количество студентов, включенных в ...

Education

JoVE Core

Statistics

Статистика

Unit 1

Блок 1

Summarizing and Visualizing Data

Обобщение и визуализация данных

KEY TERMS AND CONCEPTS

ОСНОВНЫЕ ТЕРМИНЫ И ПОНЯТИЯ

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, or bins. The area of each bar matches the frequency of the observations in that interval.

A frequency distribution table groups data values into classes of equal width. Class limits are the smallest and largest observations in each class. Class boundaries are the values used to separate neighboring classes, often at the midpoint between upper and lower class limits. In many cases, frequency distributions use 5 to 20 classes. The classes should have equal widths and should be mutually exclusive, continuous, and exhaustive.

Reading Frequency Tables and Histograms

review and preview

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

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 frequency distributions organize quantitative data in tables, histograms, dot plots, and more. See class limits, class boundaries, and binning clearly.

Reading Frequency Tables and Histograms | 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

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.

Next Generation Science Standards

Life Science

ecosystems-interactions-energy-and-dynamics

Ecosystems: Interactions, Energy, and Dynamics

HS-LS2-1

PHYS.2

PHYS.2.B

Chemistry and Physics

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 ...

What is a Hypothesis?

A hypothesis can be a simple sentence or statement about a property or any phenomenon observed or predicted for a population. It is usually a claim about ...

Null and Alternative Hypotheses

The actual hypothesis testing begins by considering two hypotheses. They are termed&#160; the null hypothesis and the alternative hypothesis. These ...

Types of Hypothesis Testing

There are three types of hypothesis tests: right-tailed, left-tailed, and two-tailed.
When the null and alternative hypotheses are stated, it is observed ...

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 ...

Hypothesis Test for Test of Independence

The test of independence is a chi-square-based test used to determine whether two variables or factors are independent or dependent. This hypothesis test ...

Decision Making: P-value Method

The process of hypothesis testing based on the P-value method includes calculating the P- value using the sample data and interpreting it.
First, a ...

Decision Making: Traditional Method

The process of hypothesis testing based on the traditional method includes calculating the critical value, testing the value of the test statistic using ...

empirical-method-to-interpret-standard-deviation

Empirical Method to Interpret Standard Deviation

The empirical rule, also known as the three-sigma rule, allows a statistician to interpret the standard deviation in a normally distributed dataset. 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 ...

Solving Problems in Physics

Problem-solving is the ability to apply general physical principles to specific situations, usually expressed by equations. It is an essential skill in ...

The student will demonstrate an understanding of scientific and engineering practices by asking questions and defining problems
• ask questions that require empirical evidence to answer
• develop hypotheses indicating relationships between independent and dependent variables
• offer simple solutions to design problems

PS.1.a

What is an Experiment?

An experiment is a planned activity carried out under controlled conditions. The purpose of an experiment is to investigate the relationship between two ...

Study Design in Statistics

A study design is a set of techniques that allow a researcher to collect and analyze data from different variables defined for a specific research ...

Observational Studies

Observational studies are a type of analytical study where researchers observe events without any interventions. In other words, the researcher does not ...

Experimental Designs

An experimental design is a systematic process that allows researchers to evaluate the relationship between dependent and independent variables. There are ...

Randomized Experiments

The randomization process involves assigning study participants randomly to experimental or control groups based on their probability of being equally ...

Crossover Experiments

Crossover experiments, also called the repeated-measurements design, is a study design in which all experimental units are exposed to all treatments in ...

Controls in Experiments

When conducting an experiment, it is crucial to have control to reduce bias and accurately measure the dependent variables. It also marks the results more ...

Bias

Bias refers to any tendency that prevents a question from being considered unprejudiced. In research, bias occurs when one outcome or answer is selected ...

Blinding

Blinding is a commonly used method of not telling participants which treatment a subject is receiving. Blinding is a critical part of a randomized control ...

Clinical Trials

Clinical trials are prospective experimental studies conducted on humans to determine the safety and efficacy of treatments, drugs, diet methods, and ...

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 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 ...

Units and Standards of Measurement

A physical quantity is defined either by specifying its measurement method or by stating how it is calculated from other measurements. For example, ...

Estimation of the Physical Quantities

On many occasions, physicists, other scientists, and engineers need to make estimates of a particular quantity. These are sometimes referred to as ...

/files/media/science-education/science-education-thumbs/14734.jpg

Base Quantities and Derived Quantities

In any system of units, the units for some physical quantities must be specified through a measurement process. These measurements are the base quantities ...

Conversion of Units

Sometimes, there is a need to convert from one unit to another one. For instance, reading a cookbook in which quantities are expressed in units of liters ...

The student will demonstrate an understanding of scientific and engineering practices by planning and carrying out investigations
• independently and collaboratively plan and conduct observational and experimental investigations; identify variables, constants, and controls where appropriate and include the safe use of chemicals and equipment
• evaluate the accuracy of various methods for collecting data
• take metric measurements using appropriate tools and technologies
• apply scientific ideas or principles to design, construct, and/or test a design of an object, tool, process or system

PS.1.b

Review and Preview

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

A frequency is the number of times a value of the data occurs. The sum of all the frequency values represents the total number of students included in the ...

Ogive Graph

An ogive graph is sometimes called a cumulative frequency polygon. It is one type of frequency polygon that shows cumulative frequency. In other words, ...

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 ...

Relative Frequency Histogram

The relative frequency depicts the proportion of data points that have each value. The frequency tells the number of data points that have each value. ...

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 ...

Time-Series Graph

A time-series graph is a line graph with repeated measurements taken at successive intervals of time. It is also called a time series chart. To construct ...

Bar Graph

A bar graph is also called a bar chart and consists of bars that are separated from each other. It either uses horizontal or vertical bars to show ...

Multiple Bar Graph

As the name suggests, a multiple bar graph is the same as a bar graph but has multiple bars to depict relationships between different data values. One can ...

Pareto Chart

A Pareto chart is a bar graph or a combination of both line and bar graphs. The bar lengths represent the individual values or the frequency, while the ...

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 ...

What is Central Tendency?

Descriptive statistics describe or summarize relevant characteristics of a sample and aid in the analysis of data of interest. When analyzing large ...

What is Variation?

Apart from the measures of central tendency, distribution, outliers, and the changing characteristics of data with time, an important characteristic of ...

Range

The range is one of the measures of variation. It can be defined as the difference between a dataset&#39;s highest and lowest values. For example, in the ...

Standard Deviation

The most commonly used measure of variation is the standard deviation. It is a numerical value measuring how far data values are from their mean. The ...

Calculating Standard Deviation

The standard deviation is the most common measure of variation. It is a value that tells us how far a data value is from the mean value in a dataset. ...

Variance

&#160;The deviations show how spread out the data are about the mean. A positive deviation occurs when the data value exceeds the mean, whereas a negative ...

Coefficient of Variation

The coefficient of variation measures the dispersion of the data points or distribution around the mean. Using the coefficient of variation, we can ...

Contingency Table

A contingency table provides a way of portraying data that can facilitate calculating probabilities. It is a method of displaying a frequency distribution ...

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 ...

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 to evaluate and refine design solutions to best meet criteria

Models, Theories, and Laws

Scientists frequently use models to help them comprehend a specific collection of phenomena. In physics, a model is a condensed version of a physical ...

/files/media/science-education/science-education-thumbs/14686.jpg

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 ...

Deductive Reasoning

Deductive reasoning, or deduction, is the type of logic used in hypothesis-based science. In deductive reasoning, the pattern of thinking moves in the ...

The student will demonstrate an understanding of scientific and engineering practices by constructing and critiquing conclusions and explanations
• construct scientific explanations based on valid and reliable evidence obtained from sources (including the students' own investigations)
• construct arguments supported by empirical evidence and scientific reasoning
• generate and compare multiple solutions to problems based on how well they meet the criteria and constraints
• differentiate between a scientific hypothesis, theory, and law

PS.1.d

Reading Frequency Tables and Histograms

Description

Transcript

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