Probability and statistics (frequency distributions)
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- Frequency distributions organize and summarize data by grouping it into classes and counting the frequency of observations in each class. They can be presented in tables or graphically. - Common graphical representations include histograms, relative frequency histograms, frequency polygons, and ogives. - Categorical frequency distributions are used for nominal or ordinal data by tallying the frequency of observations in each category.
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Frequency DistributionTeacherMariza This document discusses frequency distributions and methods for graphically presenting frequency distribution data. It defines a frequency distribution as a tabulation or grouping of data into categories showing the number of observations in each group. The document outlines the parts of a frequency table as class limits, class size, class boundaries, and class marks. It then provides steps for constructing a frequency distribution table from a set of data. Finally, it discusses histograms and frequency polygons as methods for graphically presenting frequency distribution data, and provides examples of how to construct these graphs in Excel.
Frequency distribution
Frequency distributionMOHAMMED NASIH IMPORTANT CONSIDERATION IN THE CONSTRUCTION OF A FREQUENCY DISTRIBUTION and
GRAPHICAL REPRESENTATION OF A FREQUENCY DISTRIBUTION
Biostatistics (L2)...................pdf
Biostatistics (L2)...................pdfNhipumazP What is Biostatistics?
• Biostatistics is the application of statistics in medical research,
e.g.:– Clinical trials– Epidemiology– Pharmacology– Medical decision making– Comparative Effectiveness Research – etc.
6
Statistical Analysis
Key steps for a complete and accurate statistical
analysis:
• State a valid research question
• Collect information (DATA) for answering this question
• Validate/clean/organize the collected information
• Exploratory Data Analysis (EDA)
• Analyze this information
• Translate numerical results into answers
• Interpret results and derive conclusions
• Present the results and communicate with people
7
Terms in Biostatistics
• Data : – all the information we collect to answer the research question
• Variables :– Outcome, treatment, study population characteristics
• Subjects :– units on which characteristics are measured
• Observations :– data elements
• Population :– all the subjects of interest
• Sample :– a subset of the population for which data are collected
8
Reference: Introductory Statistics, page 45-46
Sample from Population
Population
Descriptive
Measure
Size
Mean
Variance
Parameter
N
Sample
statistic
Summary of a characteristic
n
μ
𝜎2
x
ത
𝑠2
Total # of subjects
Average
Variance
Impossible/impractical to analyze the entire population →
→ thus we only analyze a sample
9
Statistical Inference
Collect and analyze data from samples →
→Calculate summary statistics →
→Make Inference about unknown population
parameters (e.g., population average from sample
mean)
10
The Framingham Heart Study
https://www.framinghamheartstudy.org/fhs-about/history/epidemiological
background/
• … “a long term prospective study of the etiology of
cardiovascular disease among a population of free living
subjects in the community of Framingham, Massachusetts.”…
• Identifying risk factors for cardiovascular disease (CVD)
• N=4,434participants (subset of the original sample)
• Follow-up period: 1956– 1968
• Longitudinal data: measurements approximately every 6 years
• 1to3observations for each participant (total 11,627 obs) • Analyze this information
• Translate numerical results into answers
• Interpret results and derive conclusions
• Present the results and communicate with people
7
Terms in Biostatistics
• Data : – all the information we collect to answer the research question
• Variables :– Outcome, treatment, study population characteristics
• Subjects :– units on which characteristics are measured
• Observations :– data elements
• Population :– all the subjects of interest
• Sample :– a subset of the population for which data are collected
8
Reference: Introductory Statistics, page 45-46
Sample from Population
Population
Descriptive
Measure
Size
Mean
Variance
Parameter
N
Sample
statistic
Summary of a characteristic
n
μ
𝜎2
x
ത
𝑠2
Total # of subjects
Average
Variance
Impossible/impractical to analyze the entire population →
→ thus we only
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2. Common data collection methods are surveys, observation, interviews, and existing sources; data must then be processed, organized, and cleaned before analysis.
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Chap002
Chap002hareshdc This document discusses methods for organizing and presenting qualitative and quantitative data, including:
1. Organizing qualitative data into frequency tables and presenting them as bar charts or pie charts.
2. Organizing quantitative data into frequency distributions by grouping data into classes and showing the number of observations in each class. Frequency distributions can be presented as histograms, frequency polygons, or cumulative frequency distributions.
3. An example is provided of constructing a frequency distribution table by determining the number of classes, class interval, class limits, and tallying data into classes using vehicle selling prices. Relative frequency distributions are also discussed.
Chapter 2
Chapter 2guest3720ca This document discusses different types of graphs and distributions that can be used to organize and represent data. It covers frequency distributions, histograms, frequency polygons, ogives, relative frequency graphs, Pareto charts, time series graphs, pie charts, and stem-and-leaf plots. Rules for constructing frequency distributions are provided, such as having between 5-20 classes and equal class widths. Examples are given to illustrate each type of graph or distribution.
Chapter 2
Chapter 2Rose Jenkins This document discusses different types of graphs and distributions that can be used to organize and represent data. It explains frequency distributions, histograms, frequency polygons, ogives, relative frequency graphs, Pareto charts, time series graphs, pie charts, and stem-and-leaf plots. Rules for constructing frequency distributions and examples of each type of graph are provided.
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Tabular and Graphical Representation of Data 
Tabular and Graphical Representation of Data Sir Parashurambhau College, Pune This slideshow describes about type of data, its tabular and graphical representation by various ways. It is slideshow is useful for bio statisticians and students.
Chapter 02 mis
Chapter 02 misRong Mohol This document discusses methods for organizing and presenting data through frequency tables, distributions, and graphs. It covers creating frequency tables to organize qualitative and quantitative data. Frequency distributions group quantitative data into classes with class limits, frequencies, and midpoints. These distributions can be presented as histograms, frequency polygons, or cumulative frequency distributions. The document provides an example using data on vehicle selling prices to demonstrate constructing a frequency table and distribution, calculating relative frequencies, and graphing the results as a histogram.
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Data Presenetation
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Probability and statistics (frequency distributions)
- 2. Charts and Frequency Distributions
- 3. When the variable of interest is qualitative, the statistical table is a list of the categories being considered along with measure of how often each value occurred. The measure can be presented in the following way:The frequency or number of measurements in each categoryThe relative frequency, or proportion of measurements in each categoryThe percentage of measurement in each category
- 4. Example1. 4000 freshmen were admitted in Don Bosco Technical College in Mandaluyong for the school year 2010-2011. The Students were enrolled in the following program:
- 5. Bar GraphUses the height of the bar to display the amount in a particular category.Pie ChartDisplays how the total quantity is distributed among the categories.
- 6. When a quantitative variable is recorded over time at equally spaced intervals, the data set forms a time series. Time series data are most effectively presented on a line chart.
- 7. Example. Table that shows the daily production of Gardenia BreadLine Graph
- 8. Stem and Leaf PlotA stem and leaf plot presents a graphical display of the data using the actual numerical values of each data point.
- 9. Steps in constructing:Divide each measurement into two parts: stem and leafList the stem in column, with a vertical line to the right.For each measurement, record the leaf portion in the same row as its corresponding stem.Order the leaves from lowest to highest in each stem.
- 10. Example Daily sales of desktop computers of JRC Computer Company for 40 days.
- 12. Frequency DistributionSteps in Constructing a Frequency Distribution TableDetermine the number of classes by using Sturges’ Formula: K = 1 + 3.322 log n = approximate number of classes n = number of observations2. Determine the approximate class size. Whenever possible, all classes should be of the same size. The following steps can be used to determine the class size:* Solve for the range, R = max- min*Compute for C’ = R / K *Round-off C’ to a convenient number(nearest whole number)
- 13. Frequency DistributionSteps in Constructing a Frequency Distribution Table3. Determine the lowest class limit. The first class must include the smallest value in the data set.Determine all class limits by adding the class size , C, to the limit of the previous class.Tally the frequencies for each class. Sum the frequencies and check against the total number of observations.
- 14. ExampleConstruct a frequency distribution from the final grades of Stat 101 Students given below:SolutionConstruct a stem and leaf plot.
- 15. The Complete Frequency Distribution Table
- 16. Graphical Representation of a Frequency DistributionFrequency Histogram – a bar graph that displays the classes on the horizontal axis and frequencies of the classes on the vertical axis; the vertical lines of the bars are erected at the class boundaries and the height of the bars correspond to the class frequency.Relative Frequency Histogram – a graph that displays the classes on the horizontal axis and the relative frequencies on the vertical axis.
- 17. Graphical Representation of a Frequency Distribution3. Frequency Polygon – a line chart that is constructed by plotting the frequencies at the class marks and connecting the plotted points by means of straight lines; the polygon is closed by considering an additional class at each end and the ends of the lines are brought down to the horizontal axis at the midpoints of the additional classes.Ogives – graphs of the cumulative frequency distribution.< ogive – the <CF is plotted against the UCB> ogive – the >CF is plotted against the LCB
- 18. Categorical Frequency DistributionThe Categorical frequency distribution is used for data that can be placed in specific categories, such as nominal or ordinal-level data.ExampleTwenty five students were given the following grades. The data set is: C A B A D F B A C A C D F B B A B D F C B C C B D
- 19. SolutionMake a table with A, B, C, D, and F as classes.Tally the data and count the tallies.Find the percentage of values in each class by using the formulaFind the total frequency and percent .
- 20. Table of frequency and percent