The document discusses frequency distribution tables, including how to construct them from raw data by grouping data into classes of equal intervals and determining the frequency of observations within each class. Key aspects covered include determining class limits, boundaries, frequencies, widths, and cumulative frequencies. Examples are provided to demonstrate how to build a frequency distribution table and corresponding graphical representations like histograms, frequency polygons, and ogives from sets of data.
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.
Descriptive statistics can summarize and graphically present data. Tabular presentations display data in a grid, with tables showing frequencies of categories. Graphical presentations include bar graphs to show frequencies, pie charts to show proportions, and line graphs to show trends over time. Frequency distributions organize raw data into meaningful patterns for analysis by specifying class intervals and calculating frequencies and cumulative frequencies.
- A frequency distribution organizes data into classes and displays the frequency of observations in each class.
- Grouped data uses classes with cut-offs to group interval or ratio level data, while ungrouped data lists each observation individually for smaller data sets.
- To make a frequency distribution, the data's range is found and classes are determined. Each observation is tallied and frequencies per class are calculated. This displays the distribution of the data.
lesson 3 presentation of data and frequency distributionNerz Baldres
This document provides an overview of key concepts for presenting data and constructing frequency distributions. It defines different methods for presenting data including textual, tabular, and graphical forms. Tabular methods include components like table headings and stubs. Graphical methods are shown like bar graphs, line graphs, and pie charts. Frequency distributions arrange data by class intervals and calculate frequencies. Terms are defined for range, class interval, and cumulative and relative frequency. Examples demonstrate how to construct frequency distributions and calculate cumulative and relative frequencies.
This document discusses methods for summarizing data, including frequency distributions, measures of central tendency, and measures of dispersion. It provides examples and formulas for constructing frequency distributions and calculating the mean, median, mode, range, variance, and standard deviation. Key points covered include using frequency distributions to group data, calculating central tendency measures for grouped data, and methods for measuring dispersion both for raw data and grouped data.
Frequency Distribution (Class-interval- Tally).pptxAlwinCAsuncion
The document defines various measures of central tendency including mean, median, and mode for both ungrouped and grouped data. It also defines key terms related to frequency distributions such as lower class limit, upper class limit, class boundaries, class marks, class width, and cumulative frequency. An example is provided to illustrate the construction of a grouped frequency distribution table involving 7 classes with a class width of 7 using data on exam scores of 40 students.
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.
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.
Descriptive statistics can summarize and graphically present data. Tabular presentations display data in a grid, with tables showing frequencies of categories. Graphical presentations include bar graphs to show frequencies, pie charts to show proportions, and line graphs to show trends over time. Frequency distributions organize raw data into meaningful patterns for analysis by specifying class intervals and calculating frequencies and cumulative frequencies.
- A frequency distribution organizes data into classes and displays the frequency of observations in each class.
- Grouped data uses classes with cut-offs to group interval or ratio level data, while ungrouped data lists each observation individually for smaller data sets.
- To make a frequency distribution, the data's range is found and classes are determined. Each observation is tallied and frequencies per class are calculated. This displays the distribution of the data.
lesson 3 presentation of data and frequency distributionNerz Baldres
This document provides an overview of key concepts for presenting data and constructing frequency distributions. It defines different methods for presenting data including textual, tabular, and graphical forms. Tabular methods include components like table headings and stubs. Graphical methods are shown like bar graphs, line graphs, and pie charts. Frequency distributions arrange data by class intervals and calculate frequencies. Terms are defined for range, class interval, and cumulative and relative frequency. Examples demonstrate how to construct frequency distributions and calculate cumulative and relative frequencies.
This document discusses methods for summarizing data, including frequency distributions, measures of central tendency, and measures of dispersion. It provides examples and formulas for constructing frequency distributions and calculating the mean, median, mode, range, variance, and standard deviation. Key points covered include using frequency distributions to group data, calculating central tendency measures for grouped data, and methods for measuring dispersion both for raw data and grouped data.
Frequency Distribution (Class-interval- Tally).pptxAlwinCAsuncion
The document defines various measures of central tendency including mean, median, and mode for both ungrouped and grouped data. It also defines key terms related to frequency distributions such as lower class limit, upper class limit, class boundaries, class marks, class width, and cumulative frequency. An example is provided to illustrate the construction of a grouped frequency distribution table involving 7 classes with a class width of 7 using data on exam scores of 40 students.
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.
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.
Taking of a measurement and the process of counting yield numbers that contain information. The objective of a person applying the tools of statistics to these numbers is to determine the nature of this information.
This task is made much easier if the numbers are organized and summarized.
Even quite small data sets are difficult to understand without some summarization. Statistical quantities such as the mean and variance can be extremely helpful in summarizing data but first we discuss tabular and graphical summaries.
There are several ways to present a statistical data like;
Frequency table
Simple bar diagrams
Multiple Bar Diagrams
Histogram
Frequency Polygon etc.
Steam and Leaf plots
Pie Charts
A frequency distribution is a tabular arrangement of data in which various items are arranged into classes or groups and the number of items falling in each class is stated.
The number of observations falling in a particular class is referred to as class frequency and is denoted by "f".
In frequency distribution all the values falling in a class are assumed to be equal to the midpoint of that class.
Data presented in the form of a frequency distribution is also called grouped data. A frequency distribution table contains a condensed summary of the original data.
There are two types of frequency distribution i) Simple Frequency distribution ) ii) Grouped Frequency distribution.
1. The document discusses different topics related to data collection and presentation including sources of data, data collection methods, processing data, and presenting data through graphs, tables, frequency distributions, and other visual formats.
2. Common data collection methods are surveys, observation, interviews, and existing sources; data must then be processed, organized, and cleaned before analysis.
3. Data can be presented visually through tables, graphs, frequency distributions and other charts to reveal patterns and insights in the data in a clear, understandable format.
This document discusses methods for presenting tabular and graphical data summaries. It covers constructing frequency distributions for grouped and ungrouped data, and different types of graphs that can be used to summarize quantitative and qualitative data, including histograms, frequency polygons, ogives, stem and leaf plots, pie charts, and bar charts. Examples are provided for constructing frequency distributions and different graph types.
The document discusses organizing and presenting data through descriptive statistics. It covers types of data, constructing frequency distribution tables, calculating relative frequencies and percentages, and using graphical methods like bar graphs, pie charts, histograms and polygons to summarize categorical and quantitative data. Examples are provided to demonstrate how to organize data into frequency distributions and calculate relative frequencies to graph the results.
This document discusses frequency distributions and graphs. It defines frequency distributions as organizing raw data into a table using classes and frequencies. There are three main types: categorical, grouped, and ungrouped. Guidelines are provided for constructing frequency distributions, such as having 5-20 classes of equal width. Common graphs discussed are histograms, frequency polygons, ogives, Pareto charts, time series graphs, and pie charts. These graphs represent frequency distributions in visual formats.
This document discusses frequency distributions and graphs. It defines frequency distributions as organizing raw data into a table using classes and frequencies. There are three main types: categorical, grouped, and ungrouped. Guidelines are provided for constructing frequency distributions, such as having 5-20 classes of equal width. Common graphs discussed are histograms, frequency polygons, ogives, Pareto charts, time series graphs, and pie charts. These graphs represent frequency distributions in visual formats.
The document provides instructions for organizing raw data into a frequency distribution table and describes different ways to represent the distribution graphically, including histograms, frequency polygons, and cumulative frequency curves. It explains how to calculate class intervals and frequencies from raw data and construct tables showing the distribution. It also discusses representing the same data through vertical bar graphs, line graphs connecting class points, and curves showing cumulative frequencies below given values.
The document provides information and instructions for analyzing student exam score data. It includes:
1) A table of 80 exam scores ranging from 53 to 97.
2) Instructions to calculate descriptive statistics like minimum, maximum, range, and percentiles of the scores.
3) Directions to construct a frequency distribution table and histogram of the scores binned into intervals of 5.
4) A calculation of measures of central tendency (mean, median, mode) and dispersion (variance, standard deviation) of the scores.
5) An analysis of the distribution's asymmetry and kurtosis.
This section expands on frequency distributions by discussing additional features: midpoints, which are the averages of class limits; relative frequency, which shows what portion of the data falls in each class; and cumulative frequency, which is the running total of all previous classes' frequencies. It provides an example calculating these values for a given
Group 3 measures of central tendency and variation - (mean, median, mode, ra...reymartyvette_0611
This document discusses various measures of central tendency and variation. It defines central tendency as indicating where the center of a distribution tends to be, and mentions that measures of central tendency answer whether scores are generally high or low. It then discusses specific measures of central tendency - the mean, median, and mode - and how to calculate each one for both ungrouped and grouped data. It also discusses other measures of variation like range and standard deviation, and how to compute standard deviation for ungrouped and grouped data.
This document discusses analyzing and interpreting test data using measures of central tendency, variability, position, and co-variability. It defines these statistical measures and how to calculate and apply them. Key points covered include calculating the mean, median, and mode of a data set; measures of variability like standard deviation; and how these measures can be used to analyze test scores and interpret results to improve teaching. Formulas and examples are provided to demonstrate calculating and applying these statistical concepts to educational test data.
This document provides instructions for constructing a frequency distribution table. It explains that a frequency distribution table arranges data into categories with corresponding frequencies and class marks. It outlines four steps to construct the table: 1) Find the range of the data, 2) Divide the range into intervals, 3) Organize the table with class intervals, and 4) Determine the frequency of each class interval by tallying the data points that fall into each interval. An example is provided to illustrate these steps.
Data Presentation using Descriptive Graphs.pptxJeanettebagtoc
The document discusses different methods for presenting data graphically and numerically, including frequency distributions, histograms, and frequency polygons. It provides details on how to construct each type of graph or table. A frequency distribution displays the number of observations within intervals and can be shown graphically or in a table. A histogram uses rectangular bars to show the frequency distribution where the area of each bar is proportional to the frequency. A frequency polygon connects the midpoints of the bars on a histogram to form a polygonal shape.
The document outlines key concepts in statistics including frequency distributions, measures of central tendency, dispersion, position, and distribution. It discusses grouped and ungrouped data, mean, median, mode, range, variance, standard deviation, quartiles, percentiles, skewness, kurtosis, and z-scores. Graphs like histograms, pie charts, and ogives are presented as ways to visually represent data. Formulas and examples are provided for calculating various statistical measures.
This document discusses frequency distribution and methods for presenting grouped data. It defines key terms like class interval, class frequency, and class midpoint. It also provides steps for constructing a frequency distribution, including determining the number of classes and class interval. Examples are given to illustrate a frequency distribution table, relative frequency distribution, and different types of graphs - histograms, frequency polygons, cumulative frequency curves, line graphs, bar charts and pie charts - that can be used to present grouped quantitative data.
Analysis and interpretation of Assessment.pptxAeonneFlux
The document provides information on statistics, frequency distributions, measures of central tendency (mean, median, mode), and how to calculate and interpret them. It defines statistics, descriptive and inferential statistics, and frequency distributions. It outlines the steps to construct a frequency distribution and calculate the mean, median, and mode for both ungrouped and grouped data. Examples are provided to demonstrate calculating each measure of central tendency.
How to Get CNIC Information System with Paksim Ga.pptxdanishmna97
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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.
Taking of a measurement and the process of counting yield numbers that contain information. The objective of a person applying the tools of statistics to these numbers is to determine the nature of this information.
This task is made much easier if the numbers are organized and summarized.
Even quite small data sets are difficult to understand without some summarization. Statistical quantities such as the mean and variance can be extremely helpful in summarizing data but first we discuss tabular and graphical summaries.
There are several ways to present a statistical data like;
Frequency table
Simple bar diagrams
Multiple Bar Diagrams
Histogram
Frequency Polygon etc.
Steam and Leaf plots
Pie Charts
A frequency distribution is a tabular arrangement of data in which various items are arranged into classes or groups and the number of items falling in each class is stated.
The number of observations falling in a particular class is referred to as class frequency and is denoted by "f".
In frequency distribution all the values falling in a class are assumed to be equal to the midpoint of that class.
Data presented in the form of a frequency distribution is also called grouped data. A frequency distribution table contains a condensed summary of the original data.
There are two types of frequency distribution i) Simple Frequency distribution ) ii) Grouped Frequency distribution.
1. The document discusses different topics related to data collection and presentation including sources of data, data collection methods, processing data, and presenting data through graphs, tables, frequency distributions, and other visual formats.
2. Common data collection methods are surveys, observation, interviews, and existing sources; data must then be processed, organized, and cleaned before analysis.
3. Data can be presented visually through tables, graphs, frequency distributions and other charts to reveal patterns and insights in the data in a clear, understandable format.
This document discusses methods for presenting tabular and graphical data summaries. It covers constructing frequency distributions for grouped and ungrouped data, and different types of graphs that can be used to summarize quantitative and qualitative data, including histograms, frequency polygons, ogives, stem and leaf plots, pie charts, and bar charts. Examples are provided for constructing frequency distributions and different graph types.
The document discusses organizing and presenting data through descriptive statistics. It covers types of data, constructing frequency distribution tables, calculating relative frequencies and percentages, and using graphical methods like bar graphs, pie charts, histograms and polygons to summarize categorical and quantitative data. Examples are provided to demonstrate how to organize data into frequency distributions and calculate relative frequencies to graph the results.
This document discusses frequency distributions and graphs. It defines frequency distributions as organizing raw data into a table using classes and frequencies. There are three main types: categorical, grouped, and ungrouped. Guidelines are provided for constructing frequency distributions, such as having 5-20 classes of equal width. Common graphs discussed are histograms, frequency polygons, ogives, Pareto charts, time series graphs, and pie charts. These graphs represent frequency distributions in visual formats.
This document discusses frequency distributions and graphs. It defines frequency distributions as organizing raw data into a table using classes and frequencies. There are three main types: categorical, grouped, and ungrouped. Guidelines are provided for constructing frequency distributions, such as having 5-20 classes of equal width. Common graphs discussed are histograms, frequency polygons, ogives, Pareto charts, time series graphs, and pie charts. These graphs represent frequency distributions in visual formats.
The document provides instructions for organizing raw data into a frequency distribution table and describes different ways to represent the distribution graphically, including histograms, frequency polygons, and cumulative frequency curves. It explains how to calculate class intervals and frequencies from raw data and construct tables showing the distribution. It also discusses representing the same data through vertical bar graphs, line graphs connecting class points, and curves showing cumulative frequencies below given values.
The document provides information and instructions for analyzing student exam score data. It includes:
1) A table of 80 exam scores ranging from 53 to 97.
2) Instructions to calculate descriptive statistics like minimum, maximum, range, and percentiles of the scores.
3) Directions to construct a frequency distribution table and histogram of the scores binned into intervals of 5.
4) A calculation of measures of central tendency (mean, median, mode) and dispersion (variance, standard deviation) of the scores.
5) An analysis of the distribution's asymmetry and kurtosis.
This section expands on frequency distributions by discussing additional features: midpoints, which are the averages of class limits; relative frequency, which shows what portion of the data falls in each class; and cumulative frequency, which is the running total of all previous classes' frequencies. It provides an example calculating these values for a given
Group 3 measures of central tendency and variation - (mean, median, mode, ra...reymartyvette_0611
This document discusses various measures of central tendency and variation. It defines central tendency as indicating where the center of a distribution tends to be, and mentions that measures of central tendency answer whether scores are generally high or low. It then discusses specific measures of central tendency - the mean, median, and mode - and how to calculate each one for both ungrouped and grouped data. It also discusses other measures of variation like range and standard deviation, and how to compute standard deviation for ungrouped and grouped data.
This document discusses analyzing and interpreting test data using measures of central tendency, variability, position, and co-variability. It defines these statistical measures and how to calculate and apply them. Key points covered include calculating the mean, median, and mode of a data set; measures of variability like standard deviation; and how these measures can be used to analyze test scores and interpret results to improve teaching. Formulas and examples are provided to demonstrate calculating and applying these statistical concepts to educational test data.
This document provides instructions for constructing a frequency distribution table. It explains that a frequency distribution table arranges data into categories with corresponding frequencies and class marks. It outlines four steps to construct the table: 1) Find the range of the data, 2) Divide the range into intervals, 3) Organize the table with class intervals, and 4) Determine the frequency of each class interval by tallying the data points that fall into each interval. An example is provided to illustrate these steps.
Data Presentation using Descriptive Graphs.pptxJeanettebagtoc
The document discusses different methods for presenting data graphically and numerically, including frequency distributions, histograms, and frequency polygons. It provides details on how to construct each type of graph or table. A frequency distribution displays the number of observations within intervals and can be shown graphically or in a table. A histogram uses rectangular bars to show the frequency distribution where the area of each bar is proportional to the frequency. A frequency polygon connects the midpoints of the bars on a histogram to form a polygonal shape.
The document outlines key concepts in statistics including frequency distributions, measures of central tendency, dispersion, position, and distribution. It discusses grouped and ungrouped data, mean, median, mode, range, variance, standard deviation, quartiles, percentiles, skewness, kurtosis, and z-scores. Graphs like histograms, pie charts, and ogives are presented as ways to visually represent data. Formulas and examples are provided for calculating various statistical measures.
This document discusses frequency distribution and methods for presenting grouped data. It defines key terms like class interval, class frequency, and class midpoint. It also provides steps for constructing a frequency distribution, including determining the number of classes and class interval. Examples are given to illustrate a frequency distribution table, relative frequency distribution, and different types of graphs - histograms, frequency polygons, cumulative frequency curves, line graphs, bar charts and pie charts - that can be used to present grouped quantitative data.
Analysis and interpretation of Assessment.pptxAeonneFlux
The document provides information on statistics, frequency distributions, measures of central tendency (mean, median, mode), and how to calculate and interpret them. It defines statistics, descriptive and inferential statistics, and frequency distributions. It outlines the steps to construct a frequency distribution and calculate the mean, median, and mode for both ungrouped and grouped data. Examples are provided to demonstrate calculating each measure of central tendency.
How to Get CNIC Information System with Paksim Ga.pptxdanishmna97
Pakdata Cf is a groundbreaking system designed to streamline and facilitate access to CNIC information. This innovative platform leverages advanced technology to provide users with efficient and secure access to their CNIC details.
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1. STAT 1 – Elementary Statistics
Frequency Distribution
2. Recall: Types of Data Presentation
• Textual Form
- Data presentation using sentences and paragraphs in
describing data
• Tabular Form
- Data presentation that uses tables arranged in rows
and columns for various parameters
• Graphical Form
- Pictorial representation of data
3. Grouped and Ungrouped Data
• Ungrouped Data
- Data points are treated individually.
• Grouped Data
- Data points are treated and grouped according to
categories.
4. Frequency Distribution Table
Frequency Distribution Table
Numerous data can be analyzed by grouping the data
into different classes with equal class intervals and
determining the number of observations that fall within
each class. This procedure is done to lessen work done
in treating each data individually by treating the data by
group.
5. Frequency Distribution Table
Class limits
- The smallest and the largest values that fall within
the class interval (class)
- Taken with equal number of significant figures as the
given data.
Class boundaries (true class limits)
- More precise expression of the class interval
- It is usually one significant digit more than the class
limit.
- Acquired as the midpoint of the upper limit of the
lower class and the lower limit of the upper class
6. Frequency Distribution Table
Frequency
- The number of observations falling within a particular
class.
- Counting and tallying
Class width (class size)
- Numerical difference between the upper and lower class
boundaries of a class interval.
Class mark (class midpoint)
- Middle element of the class
- It represents the entire class and it is usually
symbolized by x.
7. Frequency Distribution Table
Cumulative Frequency Distribution
- can be derived from the frequency distribution and can
be also obtained by simply adding the class frequencies
- Partial sums
Types of Cumulative Frequency Distribution
- Less than cumulative frequency (<cf) refers to the
distribution whose frequencies are less than or below
the upper class boundary they correspond to.
- Greater than cumulative frequency (>cf) refers to the
distribution whose frequencies are greater than or
above the lower class boundary the correspond to.
8. Frequency Distribution Table
Relative Frequency
- Percentage frequency of the class with respect to the
total population
- For presenting pie charts
Relative Frequency (%rf) Distribution
- The proportion in percent the frequency of each class
to the total frequency
- Obtained by dividing the class frequency by the total
frequency, and multiplying the answer by 100
11. Frequency Distribution Table
Steps in Constructing a Frequency Distribution Table (FDT)
1. Get the lowest and the highest value in the
distribution. We shall mark the highest and lowest
value in the distribution.
2. Get the value of the range. The range denoted by R,
refers to the difference between the highest and the
lowest value in the distribution. Thus,
R = H ─ L.
12. Frequency Distribution Table
3. Determine the number of classes. In the
determination of the number of classes, it should be
noted that there is no standard method to follow.
Generally, the number of classes must not be less than
5 and should not be more than 15. In some instances,
however, the number of classes can be approximated
by using the relation
𝑘 = 1 + 3.322 log 𝑛 (Sturges’ Formula),
where k = number of classes and n = sample size. is
the ceiling operator (meaning take the closest integer
above the calculated value).
Square root principle: 𝑘 = 𝑛
13. Frequency Distribution Table
4. Determine the size of the class interval. The value of C
can be obtained by dividing the range by the desired
number of classes. Hence, 𝐶 = 𝑅 𝑘.
5. Construct the classes. In constructing the classes, we
first determine the lower limit of the distribution. The
value of this lower limit can be chosen arbitrarily as
long as the lowest value shall be on the first interval
and the highest value to the last interval.
14. Frequency Distribution Table
6. Determine the frequency of each class. The
determination of the number of frequencies is done
by counting the number of items that shall fall in each
interval.
15. Frequency Distribution Table
Ex: 1. Using the steps discussed, construct the frequency
distribution of the following results of a test in statistics of
50 students given below.
88 62 63 88 65
85 83 76 72 63
60 46 85 71 67
75 78 87 70 43
63 90 63 60 73
55 62 62 83 79
78 43 51 56 80
90 47 48 54 77
86 55 76 52 76
43 52 72 43 60
16. Frequency Distribution Table
1. Using the steps discussed, construct the frequency
distribution of the following results of a test in statistics of
50 students given below.
Answer: 88 62 63 88 65
85 83 76 72 63
60 46 85 71 67
75 78 87 70 43
63 90 63 60 73
55 62 62 83 79
78 43 51 56 80
90 47 48 54 77
86 55 76 52 76
43 52 72 43 60
Class Interval Frequency
43-49 7
50-56 7
57-63 10
64-70 3
71-77 9
78-84 6
85-91 8
17. Frequency Distribution Table
2. The following are the scores of 40 students in a Math
quiz. Prepare a frequency distribution for these scores
using a class size of 10.
22 31 55 76 48 49 50 85 17 38
92 62 94 88 72 65 63 25 88 88
86 75 37 41 76 64 66 58 66 76
52 40 42 76 29 72 59 42 54 62
18. Frequency Distribution Table
2. The following are the scores of 40 students in a Math
quiz. Prepare a frequency distribution for these scores
using a class size of 10.
Answer: 22 31 55 76 48 49 50 85 17 38
92 62 94 88 72 65 63 25 88 88
86 75 37 41 76 64 66 58 66 76
52 40 42 76 29 72 59 42 54 62
Class Interval Frequency
17-26 3
27-36 2
37-46 6
47-56 6
57-66 9
67-76 7
77-86 2
87-96 5
19. Frequency Distribution Table
3. The thickness of a particular metal of an optical
instrument was measured on 121 successive items as they
came off a production line under what was believed to be
normal conditions. The results are shown in Table 4.5.
21. Data Presentation
Graphical Form of Frequency Distribution
Frequency Polygon
- Line graph
- The points are plotted at the midpoint of the classes.
Histogram (Frequency Histogram or Relative Frequency
Histogram)
- Bar graph
- Plotted at the exact lower limits of the classes
22. Data Presentation
Graphical Form of Frequency Distribution
Ogive
- Line graph
- Graphical representation of the cumulative frequency
distribution
- The < ogive represents the <cf while the > ogive
represents the >cf.
23. Data Presentation
5. Construct a frequency polygon, histogram, and ogives
of the given distribution.
Class Interval Frequency
25-29 1
30-34 1
35-39 5
40-44 8
45-49 15
50-54 4
55-59 4
60-64 3
65-69 4
70-74 3
75-79 2
24. Data Presentation
In the preparation of a polygon, the frequency values are
always plotted on the y-axis (vertical) while the classes are
plotted on the x-axis (horizontal). Here we use the class
midpoints.
17 22 27 32 37 42 47 52 57 62 67 72 77 82 87
87
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Class Midpoint (x)
Frequency
(f)
Frequency Polygon
25. Data Presentation
The preparation of the histogram is similar to the construction
of the frequency polygon. While the frequency polygon is
plotted using the frequencies against the class midpoints, the
histogram is plotted using the frequencies against the exact limit
of the classes.
19.5 24.5 29.5 34.5 39.5 44.5 49.5 54.5 59.5 64.5 69.5 74.5 79.5
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Exact Class Limit
Frequency
(f)
Frequency Histogram
26. Data Presentation
Frequency Histogram
22 27 32 37 42 47 52 57 62 67 72 77 82
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Class Midpoint (x)
Frequency
(f)
Frequency Histogram
28. Data Presentation
Ex: Construct a frequency polygon, histogram, and ogives
of the frequency distribution from problem #1.
Class Interval Frequency
43-49 7
50-56 7
57-63 10
64-70 3
71-77 9
78-84 6
85-91 8