Embedded Files
MODULE 3 - DATA MANAGEMENT
GATHERING, REPRESENTING AND INTERPRETING DATA
Statistics is the science of collecting, organizing, and summarizing data in such a way that valid conclusions and meaningful predictions can be drawn from them. Statistics has two types, namely, descriptive and inferential statistics.
Statistics is the science of collecting, organizing, and summarizing data in such a way that valid conclusions and meaningful predictions can be drawn from them. Statistics has two types, namely, descriptive and inferential statistics.
- Descriptive Statistics - is the branch of statistics that involves the collection, organization, summarization, and presentation of data.
- Inferential Statistics - is the branch of statistics that interprets and draws conclusions from the data.
VARIABLES
Variable is the characteristic that is being studied. It varies across individuals or objects. It includes age, race, gender, intelligence, personality type, attitudes, political or religious affiliation, height, weight, marital status, eye color, etc.
QUALITATIVE VS. QUANTITATIVE
DEPENDENT VS. INDEPENDENT
Variable is the characteristic that is being studied. It varies across individuals or objects. It includes age, race, gender, intelligence, personality type, attitudes, political or religious affiliation, height, weight, marital status, eye color, etc.
QUALITATIVE VS. QUANTITATIVE
- Qualitative Variables - represent differences in quality, character, or kind but not in amount. Examples: gender; religion; marital status; eye color; brand of computer purchased; birthplace or geographic locations
- Quantitative Variables - numerical in nature and can be ordered or ranked. Examples: height; weight; household size; age; test scores; speed and body temperature; grades
- Discrete Variables - data that can be counted. Examples: number of days; number of siblings; number of enrollees
- Continuous Variables - variables that can assume any numerical value over an interval or intervals. It can yield decimals or fractions. These are data that can be measured. Examples: height; weight; time; temperature
DEPENDENT VS. INDEPENDENT
- Dependent Variable - the value is being predicted.
- Independent Variable - the predictor.
POPULATION VS SAMPLE
A population is the entire group that you want to draw conclusions about while a sample is the specific group that you will collect data from. The size of the sample is always less than the total size of the population. In research, a population doesn’t always refer to people. It can mean a group containing elements of anything you want to study, such as objects, events, organizations, countries, species, organisms, etc. In a nutshell, population is the set of all objects under study while a sample is any subset of the population.
A population is the entire group that you want to draw conclusions about while a sample is the specific group that you will collect data from. The size of the sample is always less than the total size of the population. In research, a population doesn’t always refer to people. It can mean a group containing elements of anything you want to study, such as objects, events, organizations, countries, species, organisms, etc. In a nutshell, population is the set of all objects under study while a sample is any subset of the population.
DATA
Data is a collection of observation on one or more variables. It is the raw material which the statistician works. It can be found through surveys, experiments, numerical records, and other modes of research. Data has two types, namely, primary and secondary data.
Data is a collection of observation on one or more variables. It is the raw material which the statistician works. It can be found through surveys, experiments, numerical records, and other modes of research. Data has two types, namely, primary and secondary data.
- Primary Data - Refer to information which are gathered directly from the original source or which are based on direct or first hand experience. Examples: surveys; interview registration; observations; diaries; autobiographies
- Secondary Data - Refers to information which are taken from published or unpublished data which are previously gathered by other individuals or agencies. Examples; books; magazines and news paper; internet
LEVEL OF MEASUREMENTS
- Nominal or Categorical Level - is characterized by data that consists of names, labels, or categories only. Examples: gender; most preferred color; usual sleeping time
- Ordinal Level - involves data that arranged in some order, but differences between data. Examples: grades; socioeconomic status; intelligence; contest
- Interval Level - does not only include “ greater than” and “less than” relationships, but also has a limit of measurement that permits us to describe how much more or less one object possesses than another. It has no true zero which means zero is not really nothing. Example: Fahrenheit temperature scale (0°F is colder than 5°F)
- Ratio Level - similar to interval data, but has an absolute zero multiples are meaningful. Examples: election votes; grades of engineering students in Calculus
SAMPLING METHOD
Sampling is a method that allows researchers to infer information about a population based on results from a subset of the population, without having to investigate every individual. Reducing the number of individuals in a study reduces the cost and workload, and may make it easier to obtain high quality information, but this has to be balanced against having a large enough sample size with enough power to detect a true association. If a sample is to be used, by whatever method it is chosen, it is important that the individuals selected are representative of the whole population. This may involve specifically targeting hard to reach groups. Here are the four basic sampling techniques.
Sampling is a method that allows researchers to infer information about a population based on results from a subset of the population, without having to investigate every individual. Reducing the number of individuals in a study reduces the cost and workload, and may make it easier to obtain high quality information, but this has to be balanced against having a large enough sample size with enough power to detect a true association. If a sample is to be used, by whatever method it is chosen, it is important that the individuals selected are representative of the whole population. This may involve specifically targeting hard to reach groups. Here are the four basic sampling techniques.
- Random Sampling - This is done by using chance or random numbers.
- Systematic Sampling - This is done by numbering each subject of the population and then selecting nth number.
- Stratified Sampling - If a population has a distinct groups, it is possible to divide the population into these groups and to draw SRS’s from each of the groups.
- Cluster Sampling - This method uses intact groups called clusters.
DATA PRESENTATION
Data Presentation is the mere gathering of the information or data is not a small task. A greater task is to make the data comprehensible and meaningful. There are three ways of representing data.
Data Presentation is the mere gathering of the information or data is not a small task. A greater task is to make the data comprehensible and meaningful. There are three ways of representing data.
- Textual Form - The data are incorporated in the text of the report.
- Tabular Form - The data are presented in rows and columns.
- Graphical Form - The data are presented in graphics form for an “easy to digest” information.
ORGANIZING RAW DATA
Raw Data is the data collected in an investigation and are not organized systematically. There are different methods of organizing raw data.
Raw Data is the data collected in an investigation and are not organized systematically. There are different methods of organizing raw data.
- Array - ordering of the observations from smallest to largest or vice versa. It has advantages because the low and high values can be readily perceived. The process is tedious especially if the raw data are numerous.
- Frequency Distribution - table that lists observed events and the frequency of occurrence of each observed event. This is often used to organize raw data. Here are some of the terms used in frequency distribution:
- Single values - raw data consist of only a few distinct values.
- Grouped data - raw data consist of many non repeated data points.
- Relative Frequency - The relative frequency of a data is found by dividing its frequency by the total number of data in the data set.
- Histogram - a bar chart that shows how the data are distributed in each interval.
- Pie Chart - one of the easiest ways to summarize categorical data. It shows how various categories of a set of data account for certain proportions of the whole.
CONSTRUCTING A FREQUENCY DISTRIBUTION TABLE
1. If the raw data consist of many different values, create intervals and work with grouped data. If not, list each distinct data point. [When working with grouped data, choose from four to eight intervals. Divide the range (high minus low) by the desired number of intervals, round off this answer to be consistent with the data, and then add the result to the lowest data point to find the beginning of the second group.]2. Tally the number of data points in each interval or the number of times each individual data point occurs.3. List the frequency of each interval or each individual data point.4. Find the relative frequency by dividing the frequency of each interval or each individual data point by the total number of data points in the distribution. The resulting decimal can be expressed as a percent.
Furthermore, here are two terms used in frequency distribution table.
1. If the raw data consist of many different values, create intervals and work with grouped data. If not, list each distinct data point. [When working with grouped data, choose from four to eight intervals. Divide the range (high minus low) by the desired number of intervals, round off this answer to be consistent with the data, and then add the result to the lowest data point to find the beginning of the second group.]2. Tally the number of data points in each interval or the number of times each individual data point occurs.3. List the frequency of each interval or each individual data point.4. Find the relative frequency by dividing the frequency of each interval or each individual data point by the total number of data points in the distribution. The resulting decimal can be expressed as a percent.
Furthermore, here are two terms used in frequency distribution table.
- True Limits or Class Boundary - a point that represents the halfway point between successive classes/group. It is obtained by adding the upper limit of one class and the lower limit of the next class and then dividing by 2.
- Class Mark - a point that represents the halfway between the lower limit and the upper limit. It is obtained by adding the lower limit and the upper limit of the same class and then dividing by 2.
MEASURES OF CENTRAL TENDENCY
The arithmetic mean of a set of numbers is often referred to as simply the mean. If the data are collected from a sample, then the mean is denoted by x ; if the data are collected from an entire population, then the mean is denoted by μ.
- MEAN
The arithmetic mean of a set of numbers is often referred to as simply the mean. If the data are collected from a sample, then the mean is denoted by x ; if the data are collected from an entire population, then the mean is denoted by μ.
MEASURES OF CENTRAL TENDENCY
Median Is the middle number or the mean of the two middle numbers in a list of numbers that have been arranged in numerical order from smallest to largest or from largest to smallest. Any list of numbers that is arranged in numerical order from smallest to largest or from largest to smallest is called a ranked list. Note that the median of a ranked list of n numbers is: the middle number if n is odd; the mean of the two middle numbers if n is even.
- MEDIAN
Median Is the middle number or the mean of the two middle numbers in a list of numbers that have been arranged in numerical order from smallest to largest or from largest to smallest. Any list of numbers that is arranged in numerical order from smallest to largest or from largest to smallest is called a ranked list. Note that the median of a ranked list of n numbers is: the middle number if n is odd; the mean of the two middle numbers if n is even.
MEASURES OF CENTRAL TENDENCY
The mode of a list of numbers is the number that occurs most frequently.
- MODE
The mode of a list of numbers is the number that occurs most frequently.
WEIGHTED MEAN
Weighted mean is often used when some data values are more important than others.
Weighted mean is often used when some data values are more important than others.
MEASURES OF DISPERSION
- Range - A set of data values is the difference between the greatest data value and the least data value.
- Standard Deviation - A measure of dispersion that is less sensitive to extreme values. The standard deviation of a set of numerical data makes use of the individual amount that each data value deviates from the mean.
- Variance - The variance for a given set of data is the square of the standard deviation of the data. The formula for population and sample variance is almost the same with the standard deviation's formula, only that it has no square root. Nonetheless, you can always get it after squaring the standard deviation.
MEASURES OF RELATIVE POSITION
PERCENTILE FOR A GIVEN DATA VALUE
FINDING QUARTILES
The three numbers Q1, Q2, and Q3 that partition a ranked data set into four (approximately) equal groups are called the quartiles of the data. We can use the Median Procedure for Finding Quartiles. First, rank the data. Second, find the median of the data. This is the second quartile, Q2. Lastly, the first quartile, Q1, is the median of the data values less than Q2. The third quartile, Q3, is the median of the data values greater than Q2.
The three numbers Q1, Q2, and Q3 that partition a ranked data set into four (approximately) equal groups are called the quartiles of the data. We can use the Median Procedure for Finding Quartiles. First, rank the data. Second, find the median of the data. This is the second quartile, Q2. Lastly, the first quartile, Q1, is the median of the data values less than Q2. The third quartile, Q3, is the median of the data values greater than Q2.
BOX-AND-WHISKER PLOTS
Box-and-Whisker Plot (sometimes called a box plot) is often used to provide a visual summary of a set of data shows the median, the first and third quartiles, and the minimum and maximum values of a data set. Here are the steps on construction of a Box-and-Whisker Plot:1. Draw a horizontal scale that extends from the minimum data value to the maximum data value.2. Above the scale, draw a rectangle (box) with its left side at Q1 and its right side at Q3.3. Draw a vertical line segment across the rectangle at the median, Q2.4. Draw a horizontal line segment, called a whisker, that extends from Q1 to the minimum and another whisker that extends from Q3 to the maximum.
Box-and-Whisker Plot (sometimes called a box plot) is often used to provide a visual summary of a set of data shows the median, the first and third quartiles, and the minimum and maximum values of a data set. Here are the steps on construction of a Box-and-Whisker Plot:1. Draw a horizontal scale that extends from the minimum data value to the maximum data value.2. Above the scale, draw a rectangle (box) with its left side at Q1 and its right side at Q3.3. Draw a vertical line segment across the rectangle at the median, Q2.4. Draw a horizontal line segment, called a whisker, that extends from Q1 to the minimum and another whisker that extends from Q3 to the maximum.
STEM-AND-LEAF DIAGRAMS
The relative position of each data value in a small set of data can be graphically displayed by using a stem-and-leaf diagram. Here are the Steps in Construction of a Stem-and-Leaf Diagram:1. Determine the stems and list them in a column from smallest to largest or largest to smallest.2. List the remaining digit of each stem as a leaf to the right of the stem.3. Include a legend that explains the meaning of the stems and the leaves. Include a title for the diagram.
The relative position of each data value in a small set of data can be graphically displayed by using a stem-and-leaf diagram. Here are the Steps in Construction of a Stem-and-Leaf Diagram:1. Determine the stems and list them in a column from smallest to largest or largest to smallest.2. List the remaining digit of each stem as a leaf to the right of the stem.3. Include a legend that explains the meaning of the stems and the leaves. Include a title for the diagram.
BACK TO BACK STEM-AND-LEAF DIAGRAMS
A back to back stem-and-leaf diagram is use to compare two sets of data, in which common stems are listed in the middle column of the diagram. Leaves from one data set are displayed to the right of the stems, and leaves from the other data set are displayed to the left. The steps in constructing a back to back stem-and-leaf diagram are almost the same with a normal stem-and-leaf diagram, only that the stem is on the middle of the diagram with the leaves on both sides.
A back to back stem-and-leaf diagram is use to compare two sets of data, in which common stems are listed in the middle column of the diagram. Leaves from one data set are displayed to the right of the stems, and leaves from the other data set are displayed to the left. The steps in constructing a back to back stem-and-leaf diagram are almost the same with a normal stem-and-leaf diagram, only that the stem is on the middle of the diagram with the leaves on both sides.
PROBABILITY AND NORMAL DISTRIBUTION
Normal Distribution Forms a bell-shaped curve that is symmetric about a vertical line through the mean of the data. Properties of a Normal Distribution:
Normal Distribution Forms a bell-shaped curve that is symmetric about a vertical line through the mean of the data. Properties of a Normal Distribution:
- The graph is symmetric about a vertical line through the mean of the distribution.
- The mean, median, and mode are equal.
- The y-value of each point on the curve is the percent (expressed as a decimal) of
- Areas under the curve that are symmetric about the mean are equal.
- The total area under the curve is 1.
EMPIRICAL RULE FOR A NORMAL DISTRIBUTION
- 68% of the data lie within 1 standard deviation of the mean.
- 95% of the data lie within 2 standard deviations of the mean.
- 99.7% of the data lie within 3 standard deviations of the mean.
AREA UNDER NORMAL DISTRIBUTION
STANDARD NORMAL DISTRIBUTION
Area Under Standard Normal Curve .pdfAREAS UNDER THE NORMAL CURVE
The areas under the normal curve is useful especially when the z-score is not on the exact 1, 2, or 3 standard deviation from the mean. Here are other terms used in solving normal distribution:
- Tail region - a region of the standard normal distribution to the right of a positive z-value or to the left of a negative z-value.
- Cut-off scores - score that separates data into two groups such that the data in one group satisfy a certain requirement and the data in the other group do not satisfy the requirement.
LINEAR REGRESSION AND CORRELATION
Linear Regression is one method of determining a linear relationship for bivariate data (bivariate data is the relationship between paired data). Meanwhile, he least-squares regression line for a set of bivariate data is the line that minimizes the sum of the squares of the vertical deviations from each data point to the line.
Linear Regression is one method of determining a linear relationship for bivariate data (bivariate data is the relationship between paired data). Meanwhile, he least-squares regression line for a set of bivariate data is the line that minimizes the sum of the squares of the vertical deviations from each data point to the line.
LINEAR CORRELATION COEFFICIENT
To determine the strength of a linear relationship between two variables, statisticians use a statistic called the linear correlation coefficient, which is denoted by the variable r and is defined on the figure at the left.Meanwhile, interpolation made use of an equation to determine a point between given data points while extrapolation is the process of using an equation to determine a point to the right or left of given data points.
To determine the strength of a linear relationship between two variables, statisticians use a statistic called the linear correlation coefficient, which is denoted by the variable r and is defined on the figure at the left.Meanwhile, interpolation made use of an equation to determine a point between given data points while extrapolation is the process of using an equation to determine a point to the right or left of given data points.
PROPERTIES OF LINEAR CORRELATION COEFFICIENT
1. The linear correlation coefficient r is always a real number between 1 and −1, inclusive. In the case in which
1. The linear correlation coefficient r is always a real number between 1 and −1, inclusive. In the case in which
- all of the ordered pairs lie on a line with positive slope, r is 1.
- all of the ordered pairs lie on a line with negative slope, r is −1.
Salazar-SummativeQuiz-BSCE1B.pdfSUMMATIVE QUIZ DATA MANAGEMENT
REFLECTION
In this module, I was able to review the topics taught to us in the subject Statistics and Probability during Senior High School. It was like a summary of the subject. Somehow, I enjoyed this module especially when we were asked to construct a frequency distribution table, answer problems regarding normal distribution such as drawing normal curve and finding areas considering a z-score. Overall, I found the topics in this module to be not so easy yet not so difficult, somewhere in between because as I have said, some topics served as a review and some had addition of extra challenges. During the summative assessment, I was pressured by the time since every number of the 10-item quiz was really time-consuming. I had to analyze the problem first before computing to arrive to a reasonable answer. Same in the previous modules, our teacher really did a great job in teaching the lessons in a way that every student could understand plus she was always punctual in attending our 8 am class.
In this module, I was able to review the topics taught to us in the subject Statistics and Probability during Senior High School. It was like a summary of the subject. Somehow, I enjoyed this module especially when we were asked to construct a frequency distribution table, answer problems regarding normal distribution such as drawing normal curve and finding areas considering a z-score. Overall, I found the topics in this module to be not so easy yet not so difficult, somewhere in between because as I have said, some topics served as a review and some had addition of extra challenges. During the summative assessment, I was pressured by the time since every number of the 10-item quiz was really time-consuming. I had to analyze the problem first before computing to arrive to a reasonable answer. Same in the previous modules, our teacher really did a great job in teaching the lessons in a way that every student could understand plus she was always punctual in attending our 8 am class.
REFERENCES:
https://www.scienceworld.ca/wp-content/uploads/science-world-patterns-fractals-leaf-scaled.jpghttps://i.pinimg.com/originals/67/93/26/6793268b1edd7e0f85b7fe4c6319811b.jpghttps://wallpaperaccess.com/full/3280804.jpghttps://res.cloudinary.com/jerrick/image/upload/v1581025680/5e3c898fc935ad001e25fc42.jpghttps://cutewallpaper.org/21/color-background/Free-photo-color-background-Abstract-Bright-Closeup-.pnghttps://i.pinimg.com/564x/24/b7/31/24b7317b0cbfb62e564ee191fa24e887.jpghttps://24wallpapers.com/app-gateway/wallpaper-uploads/wallpapers/legacyUploads/wi89124833a91-caf7-4c3e-aad5-42da99b7dba92079665946.jpghttps://lh3.googleusercontent.com/proxy/jOT6eGe0azY36ry726BJ4TlMCLpezc9n9QoWT16GtlvXH8xxAcAwrd5Pq616kSuEHSAOREO75NgAZ8Wn_nCnxMwhPzK95pH4mhUL3k7OQQCOGGM6qQRyLI-xD3b9zUHY_UAil5C_rLf49LvqOcH0tAC-QcfQn3330B8JxAGK1bpjzKwarhmkySr-RnrFtu3adQhttps://www.statology.org/wp-content/uploads/2020/09/qual1.pnghttps://sciencenotes.org/wp-content/uploads/2020/05/IndependentDependent.pnghttps://thumbs.dreamstime.com/z/research-process-sampling-target-population-business-marketing-social-methods-selecting-sample-elements-to-81702898.jpghttps://www.kdnuggets.com/wp-content/uploads/image3-3.pnghttps://conjointly.com/img/kb/Assets/images/measlev2.gifhttps://www.scribbr.com/methodology/population-vs-sample/https://image1.slideserve.com/1979694/slide9-l.jpghttps://images.slideplayer.com/24/7496686/slides/slide_4.jpghttps://www.healthknowledge.org.uk/public-health-textbook/research-methods/1a-epidemiology/methods-of-sampling-populationhttps://d138zd1ktt9iqe.cloudfront.net/media/seo_landing_files/sample-standard-deviation-formula-1612256392.pnghttps://www.exceltip.com/wp-content/uploads/2020/03/Capture-103.jpghttps://images.slideplayer.com/16/5095680/slides/slide_5.jpghttps://www.mathematics-monster.com/images3/quartiles_cut_offs.jpghttps://ecdn.teacherspayteachers.com/thumbitem/Box-and-Whisker-Plot-Printable-Poster-4048135-1602016215/original-4048135-1.jpghttps://www.lbq.org/filestore/questionsupplement/884dd293-d1fa-45d6-92da-85153559d99c.pnghttps://peterstatistics.com/Ultimate/Session4/S04E02-B2BStem/ExampleB2Bstem.jpghttps://study.com/cimages/multimages/16/properties_of_nd.PNGhttps://s3-us-west-2.amazonaws.com/courses-images-archive-read-only/wp-content/uploads/sites/1298/2015/10/03182600/Figure5_3_1.pnghttps://cdn.scribbr.com/wp-content/uploads/2020/10/standard-normal-distribution-1024x633.pnghttps://www.j-pcs.org/articles/2018/4/2/images/JPractCardiovascSci_2018_4_2_116_240962_f1.jpg
Page updated
Report abuse