Fdt
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The document describes the steps to construct a frequency distribution table (FDT) which groups numerical data into intervals or classes and counts the number of observations in each class. It provides an example of an FDT for average monthly kilowatt-hours used by 32 households, with classes ranging from 20 to over 150. The 7 steps include finding the range and number of classes, estimating the class width, listing the class intervals, tallying observations in each interval, and calculating additional metrics like class marks and boundaries.
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Mean for Grouped Data
This document discusses measures of central tendency, specifically how to calculate the mean of grouped data. It provides the formula for calculating the mean of grouped data and walks through an example of finding the mean test scores of students. The document demonstrates how to find the midpoint of each score group, multiply by the frequency, sum the results, and divide by the total frequency to determine the mean.
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THIS TOPIC GIVES A STEP BY STEP METHOD TO CALCULATE QUARTILES, DECILES AND PERCENTILES FOR A GROUPED AND DISCRETE FREQUENCY DISTRIBUTION.
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Measures of position. gouped data
Here are the steps to solve the problem:
1. Calculate the cumulative frequency:
<cf for 60-64 = 1
<cf for 55-59 = 1 + 2 = 3
<cf for 50-54 = 3 + 8 = 11
<cf for 45-49 = 11 + 4 = 15
<cf for 40-44 = 15 + 3 = 18
<cf for 35-39 = 18 + 2 = 20
2. Find Q1, Q3 and 20th percentile:
a. Q1 = 50 + (4)(20)/4 - 11/8 = 47.5
b. Q3 = 50 + (12)(20)/4 - 11/12 = 52.
Median of grouped data
This document provides steps for calculating the median of grouped data:
1. Create a frequency distribution table with class intervals, frequencies, and cumulative frequencies.
2. Find the median class by calculating N/2, where N is the total number of data points.
3. The median is calculated using the formula: x = L + (n2 - F2)/f2 * i, where L is the lower limit of the median class, n2 is the median class, F2 is the cumulative frequency before the median class, f2 is the frequency of the median class, and i is the class interval.
frequency distribution table
The document discusses the steps to construct a frequency distribution table (FDT):
1. Find the range and number of classes or intervals.
2. Estimate the class width and list the lower and upper class limits.
3. Tally the observations in each interval and record the frequencies.
It also describes how to calculate relative frequencies and cumulative frequencies to vary the FDT.
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This document discusses measures of variability and quartile deviation. It defines quantiles as values that divide a data set into equal parts, including the median, quartiles, deciles, and percentiles. Quartiles (Q1, Q2, Q3) divide the data into four equal parts. The interquartile range is the difference between Q3 and Q1. The quartile deviation is half the interquartile range, or (Q3 - Q1)/2. The document provides steps for calculating quartiles and quartile deviation from both ungrouped and grouped data sets. An example calculation is shown for grouped test score data.
MEASURES OF CENTRAL TENDENCY AND VARIABILITY
The document introduces focus questions about norms, standards, and how data is analyzed using descriptive statistics. It then provides an overview of different measures used to analyze ungrouped and grouped data, including measures of central tendency (mean, median, mode) and measures of variability (range, standard deviation). Finally, it includes sample pre-assessment questions about these concepts.
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Mean for Grouped Data
This document discusses measures of central tendency, specifically how to calculate the mean of grouped data. It provides the formula for calculating the mean of grouped data and walks through an example of finding the mean test scores of students. The document demonstrates how to find the midpoint of each score group, multiply by the frequency, sum the results, and divide by the total frequency to determine the mean.
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Here are the steps to solve the problem:
1. Calculate the cumulative frequency:
<cf for 60-64 = 1
<cf for 55-59 = 1 + 2 = 3
<cf for 50-54 = 3 + 8 = 11
<cf for 45-49 = 11 + 4 = 15
<cf for 40-44 = 15 + 3 = 18
<cf for 35-39 = 18 + 2 = 20
2. Find Q1, Q3 and 20th percentile:
a. Q1 = 50 + (4)(20)/4 - 11/8 = 47.5
b. Q3 = 50 + (12)(20)/4 - 11/12 = 52.
Median of grouped data
This document provides steps for calculating the median of grouped data:
1. Create a frequency distribution table with class intervals, frequencies, and cumulative frequencies.
2. Find the median class by calculating N/2, where N is the total number of data points.
3. The median is calculated using the formula: x = L + (n2 - F2)/f2 * i, where L is the lower limit of the median class, n2 is the median class, F2 is the cumulative frequency before the median class, f2 is the frequency of the median class, and i is the class interval.
frequency distribution table
The document discusses the steps to construct a frequency distribution table (FDT):
1. Find the range and number of classes or intervals.
2. Estimate the class width and list the lower and upper class limits.
3. Tally the observations in each interval and record the frequencies.
It also describes how to calculate relative frequencies and cumulative frequencies to vary the FDT.
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The steps to construct a frequency distribution table are:
1. Determine the range of data and number of class intervals using Sturge's formula.
2. Calculate the class interval size by dividing the range by the number of intervals.
3. Establish the class boundaries and tally frequencies within each class.
4. Calculate the class mark or midpoint of each class.
The key steps are to determine the number of class intervals, calculate the class interval size, tally frequencies within classes, and compute class marks. This process organizes a data set into a table to visualize frequency distributions.
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Here are the steps to solve this problem:
1. Prepare the frequency distribution table with the class intervals, frequencies, and calculate fX.
2. Find the mean (x) using the formula x = fX/f.
3. Calculate the deviations (X - x).
4. Square the deviations to get (X - x)2.
5. Multiply the frequencies and squared deviations to get f(X - x)2.
6. Calculate the variance using the formula σ2 = f(X - x)2 / (f - 1).
7. Take the square root of the variance to get the standard deviation.
8. The range is the difference between the upper
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Here are the steps to solve this problem:
1. Find the 3rd quartile, 72nd percentile, and 8th decile from the data:
- 3rd quartile (Q3) = 38
- 72nd percentile = 36
- 8th decile (D8) = 35
2. Find the percentile ranks of Jaja and Krisha:
- Jaja scored 32. From the table, 27 students scored lower than 32. So Jaja's percentile rank is 27/50 x 100 = 54%
- Krisha scored 23. From the table, 20 students scored lower than 23. So Krisha's percentile rank is 20/50 x 100 = 40%
3.
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- Class limits, which define the groupings by lower and upper limits.
- Class size, which is the width of each interval. It is calculated as the range divided by the number of classes.
- Class boundaries and marks, which separate and indicate the midpoints of categories.
The document provides steps for constructing a frequency distribution, including computing the range, determining class size, setting limits, tallying scores, and counting frequencies. An example uses exam scores to demonstrate these steps.
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Here are the scores of the three students in their Mathematics quizzes:
Student A: 75, 80, 85, 90
Student B: 70, 72, 78, 82
Student C: 65, 68, 73, 77
Range of Student A: 90 - 75 = 15
Range of Student B: 82 - 70 = 12
Range of Student C: 77 - 65 = 12
Mean Deviation of Student A: |75 - 82.5| + |80 - 82.5| + |85 - 82.5| + |90 - 82.5| = 17.5
Mean Deviation of Student B: |70 - 76| + |72 - 76| + |
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1. Determine the range of data and number of class intervals using Sturge's formula.
2. Calculate the class interval size by dividing the range by the number of intervals.
3. Establish the class boundaries and tally frequencies within each class.
4. Calculate the class mark or midpoint of each class.
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The document provides instructions for teaching students about measures of central tendency (mean, median, mode) using ungrouped data. It outlines objectives, subject matter, materials, and procedures for the lesson. The teacher's activity is to define and provide examples to calculate the mean, median, and mode. The students' activity is to practice calculating these measures and describing data sets in terms of them. The lesson concludes with an assignment for students to find the mean, median, and mode of additional data sets.
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The document is a grade 10 daily lesson plan on measures of position, specifically quartiles of ungrouped data. It contains the following key points:
1. The objectives are to illustrate and calculate quartiles and appreciate their use in real life.
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3. Quartiles (Q1, Q2, Q3) divide a data set into four equal parts, with formulas given to find their positions.
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Here are the steps to solve this problem:
1. Prepare the frequency distribution table with the class intervals, frequencies, and calculate fX.
2. Find the mean (x) using the formula x = fX/f.
3. Calculate the deviations (X - x).
4. Square the deviations to get (X - x)2.
5. Multiply the frequencies and squared deviations to get f(X - x)2.
6. Calculate the variance using the formula σ2 = f(X - x)2 / (f - 1).
7. Take the square root of the variance to get the standard deviation.
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This document defines and provides examples of the three measures of central tendency: mean, median, and mode. It explains that the mean is the average value found by summing all values and dividing by the total number. The median is the middle value when data is arranged in order. The mode is the most frequently occurring value. The document provides examples of calculating and interpreting these measures. It then gives practice problems asking to find and analyze these values for different data sets.
Percentile For Grouped Data
Here are the steps to solve this problem:
1. Find the 3rd quartile, 72nd percentile, and 8th decile from the data:
- 3rd quartile (Q3) = 38
- 72nd percentile = 36
- 8th decile (D8) = 35
2. Find the percentile ranks of Jaja and Krisha:
- Jaja scored 32. From the table, 27 students scored lower than 32. So Jaja's percentile rank is 27/50 x 100 = 54%
- Krisha scored 23. From the table, 20 students scored lower than 23. So Krisha's percentile rank is 20/50 x 100 = 40%
3.
Assessment of Learning 2 (Overview)
The document discusses frequency distributions and their components. A frequency distribution arranges data into categories and shows the number of observations in each category. Key parts include:
- Class limits, which define the groupings by lower and upper limits.
- Class size, which is the width of each interval. It is calculated as the range divided by the number of classes.
- Class boundaries and marks, which separate and indicate the midpoints of categories.
The document provides steps for constructing a frequency distribution, including computing the range, determining class size, setting limits, tallying scores, and counting frequencies. An example uses exam scores to demonstrate these steps.
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This document discusses six measures of variation used to determine how values are distributed in a data set: range, quartile deviation, mean deviation, variance, standard deviation, and coefficient of variation. It provides definitions and examples of calculating each measure. The range is defined as the difference between the highest and lowest values. Quartile deviation uses the interquartile range (Q3-Q1). Mean deviation is the average of the absolute deviations from the mean. Variance and standard deviation measure how spread out values are from the mean, with variance using sums of squares and standard deviation taking the square root of variance.
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This document defines and provides the formula for calculating mean deviation, which is a measure of variation that uses all the scores in a distribution. It is more reliable than range. Mean deviation is calculated by finding the absolute difference between each score and the mean, summing the absolute differences, and dividing by the number of observations. Two examples of calculating mean deviation for sets of data are provided, along with exercises asking students to find the mean deviation of additional data sets and define standard deviation.
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The document discusses various methods of presenting data, including textual, tabular, and graphical displays. It provides examples and definitions of key terms used in data presentation, such as frequency distribution tables, class intervals, class boundaries, class marks, and cumulative frequencies. The document also outlines steps for constructing a frequency distribution table, including determining the number of classes, range, class size, and class limits.
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The document discusses the table of specifications (TOS), which is a blueprint that shows the topics and objectives that will be covered on a test. It ensures all elements of a course are properly emphasized and guides test writing. The steps to prepare a TOS are: 1) List topics to include, 2) Determine content standards and time spent on each topic, 3) Assign a percentage allocation of test items to each topic, 4) Determine the number of items for each topic based on the percentage allocation, and 5) Distribute item numbers to the objectives.
Measures of Variability of Grouped and Ungrouped Data
Here are the scores of the three students in their Mathematics quizzes:
Student A: 75, 80, 85, 90
Student B: 70, 72, 78, 82
Student C: 65, 68, 73, 77
Range of Student A: 90 - 75 = 15
Range of Student B: 82 - 70 = 12
Range of Student C: 77 - 65 = 12
Mean Deviation of Student A: |75 - 82.5| + |80 - 82.5| + |85 - 82.5| + |90 - 82.5| = 17.5
Mean Deviation of Student B: |70 - 76| + |72 - 76| + |
Frequency distribution table
The document discusses frequency distribution tables and how to create them. It defines statistics, frequency distribution tables, and key terms like data, class, range, and class interval. It provides steps to create a frequency distribution table: 1) arrange data in ascending order, 2) find the range, 3) determine the number of classes, 4) form classes based on class interval, and 5) create a table with classes and frequencies. The document uses an example dataset to demonstrate how to apply these steps to create a frequency distribution table.
quartiles,deciles,percentiles.ppt
This document defines and discusses quartiles, deciles, and percentiles. Quartiles divide a data set into four equal parts, with the first quartile (Q1) representing the lowest 25% of values. Deciles divide data into ten equal parts. Percentiles indicate the value below which a certain percentage of observations fall. Examples are provided for calculating Q1, Q3, D1 using formulas for grouped and ungrouped data sets. Quartiles, deciles, and percentiles are commonly used to summarize and report on statistical data.
Mean, Median, Mode: Measures of Central Tendency
There are three common measures of central tendency: mean, median, and mode. The mean is the average value found by dividing the sum of all values by the total number of values. The median is the middle value when values are arranged from lowest to highest. The mode is the value that occurs most frequently. Each measure provides a single number to represent the central or typical value in a data set.
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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.
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Lecture 03.
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.
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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.
Educational statistics
This document discusses measures of central tendency including mean, median, and mode. It provides definitions and formulas for calculating these measures from individual data series, discrete series, and continuous series. For mean, it describes both direct and shortcut methods for different data types. For median, it explains how to calculate it from individual and discrete series when the number of observations is odd or even. For mode, it gives methods to determine the modal value from individual and discrete series through inspection or tallying frequencies. Examples of calculations are also included.
Basic statics
The document defines basic statistics and discusses frequency distribution and types of frequency distributions. It provides steps to construct discrete and continuous frequency distributions, including determining class limits and boundaries. Examples are given to demonstrate creating frequency tables from raw data for discrete and continuous variables. Key concepts discussed include tally marks, frequencies, class intervals, midpoints, and cumulative frequencies.
Algebra unit 9.2
This document provides instructions and examples for creating stem-and-leaf plots, frequency tables, histograms, and cumulative frequency tables from data sets. It includes step-by-step explanations and examples of how to organize and summarize data using these graphical representations. Key terms like stem, leaf, frequency, interval, and cumulative frequency are also defined. Quiz problems at the end ask the reader to apply the methods by creating a stem-and-leaf plot, frequency table, and histogram from sample data sets.
Graphical presentation of data
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.
Analysis and interpretation of Assessment.pptx
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.
Measures of central tendency
The document provides information about various measures of central tendency including arithmetic mean, median, mode, geometric mean, and harmonic mean. It defines each measure and provides examples of calculating them using data from frequency distributions. The arithmetic mean is the most common average and is calculated by summing all values and dividing by the total number of values. The median is the middle value when values are arranged in order. The mode is the most frequent value. The geometric mean is calculated by taking the nth root of the product of n values. The harmonic mean gives the greatest weight to the smallest values and is used to average rates.
The Frequency distribution table.pptx
- 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.
Freq & Histo
The document provides examples and explanations for creating different types of data displays, including stem-and-leaf plots, frequency tables, histograms, and cumulative frequency tables. It includes sample data sets and step-by-step instructions for making each type of display. Key terms defined include stem, leaf, frequency, interval, and cumulative frequency.
DATA ANALYSIS FOR BUSINESS ch02-Discriptive Statistics_Tabular and Graphical ...
DATA ANALYSIS FOR BUSINESS CH2
Quartile Deviation
This document discusses the calculation of quartile deviation from both ungrouped and grouped data. It defines quartiles as values that divide a data distribution into four equal parts (Q1, Q2, Q3). The quartile deviation is half the difference between the first (Q1) and third (Q3) quartiles. It provides the steps to find Q1, Q3, and quartile deviation from ungrouped data by ranking scores and using quartile locators. For grouped data, it uses formulas involving class limits and cumulative frequencies to determine Q1 and Q3, then takes half their difference. An example calculation is shown.
lesson 3 presentation of data and frequency distribution
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.
Practice test1 solution
This document provides a summary of key statistical concepts and practice test questions. It covers topics such as types of variables, populations and samples, measures of central tendency and variation, frequency distributions, and levels of measurement. Several questions from a practice test on introductory statistics are presented and answered, involving calculations of mean, median, mode, variance, standard deviation, and interpreting frequency tables and distributions. Examples of different sampling methods and types of studies are also defined.
Similar to Fdt (20)
Frequency Distribution (Class-interval- Tally).pptx
Frequency Distribution (Class-interval- Tally).pptx
DATA ANALYSIS FOR BUSINESS ch02-Discriptive Statistics_Tabular and Graphical ...
DATA ANALYSIS FOR BUSINESS ch02-Discriptive Statistics_Tabular and Graphical ...
lesson 3 presentation of data and frequency distribution
lesson 3 presentation of data and frequency distribution
Fdt
- 2. FDT Shut Down Relative Freq. & Cumulative Frequency Start
- 5. Steps in Constructing a (FDT) Step 1 Step 2 Step 3 Step 4 Step 5 Step 6 Step 7
- 9. Step 4: List the lower and upper class limits of the first interval. Class Interval 20 – 41 42 – 63 64 – 85 86 – 107 108 – 129 130 – 151 152 - 173 Back Step 1 Step 2 Step 3 Step 5 Step 6 Step 7
- 13. Average Monthly Kilowatt-hours of Households in Barangay Santiago 20 – (1/2)(1.0) 41 + (1/2)(1.0) Class Interval Tally Frequency Class boundary 20 – 41 IIII-II 7 19.5 – 41.5 42 – 63 IIII-IIII 8 41.5 – 63.5 64 – 85 IIII-II 7 63.5 – 85.5 86 – 107 IIII 4 85.5 – 107.5 108 – 129 I 1 107.5 – 129.5 130 – 151 IIII 4 129.5 – 151.5 152 - 173 I 1 151.5 – 173.5 Back Step 1 Step 2 Step 3 Step 4 Step 5 Step 6 Step 7: