E - MATH NOTES
1st Quarter:
Collection of Data refers to the process of obtaining information.
Organization of data refers to the ascertaining manner of presenting data into tables, graphs or charts so that logical and statistical conclusions can be drawn from the collected measurements.
Analysis of Data refers to extracting relevant information from the given data from which numerical description can be formulated.
Interpretation of Data refers to the drawing of conclusions from the analyzed data.
Descriptive statistics is a statistical method concerned with describing a data set's properties and characteristics.
Examples: respondents profile such as gender, age, average family income
Inferential Statistics is a statistical method concerned with analyzing sample data, leading to predictions, inferences, interpretations or conclusions about the entire population.
Examples: sentiments of Filipinos on certain govt. issues, perception of
students towards existing concerns, etc.
Population refers to the totality of all elements or persons for which one has interest at a particular time. It is denoted by N.
Sample is a subset or portion of a population that estimates the characteristics of the study. It is denoted by n
Unit – is an individual object or person in the population. The units are often called subjects if the population consists of people.
Parameter refers to any statistical information or attribute taken from a population. It is a true value or actual statistic since its source is the population itself.
A statistic is any estimate of statistical attributes taken from a sample.
Variables are specific factor property or characteristic of a population or a sample that differentiates a sample or group of samples from another group. It can be discrete or continuous.
DISCRETE VARIABLE - obtained by counting (number of students, no. of books)
CONTINUOUS VARIABLE - obtained by measuring objects or attributes ( height and weight)
(for more examples check the book)
Data Collection is the process of gathering and measuring information on targeted variables in an established systematic fashion, which then enables one to answer relevant questions and evaluate outcomes.
Primary Data –are information gathered directly from the source. Those data can be obtained by doing an interview, observation or experimentation.
Secondary Data are information gathered from secondary sources, such as books, journals, magazines or thesis of other researchers.
Interview Method: referred to as the direct method of gathering data because this requires face-to-face inquiry with the respondent.
Questionnaire Method is referred to as the indirect method of gathering data because this makes use of written questions to be answered by the respondent.
Observation Method- This method makes use of the different human senses in gathering information.
Registration Method- This method requires the enactment of law to take effect because it needs the participation of a large , if not the entire population.
Experiment Method- This method is usually conducted in laboratories where specimens are subjected to some aspects of control to find out cause and effect relationship.
Probability Sampling- is a sampling procedure where every element of the population is given a nonzero chance of being selected as a sample.
Random Sampling - A technique that gives every individual or element in the population to be chosen in the study.
Systematic Sampling - A method of selecting every nth element in the list that represents the population.
Stratified sampling is a method of sampling where the population is divided into subgroups based on characteristics called the stratifying factors.
Cluster Sampling - The population is divided into groups
called the clusters in consideration of the geographical boundaries and accessibility.
2) Nonprobability Sampling- is a sampling procedure where not every element of the population is given a chance of being included in the sample. The drawing of samples is based purely on the researcher’s objectives.
Convenience Sampling- the researchers’ convenience is the primary concern in using this method.
Quota Sampling- If the desired quota is reached, the drawing of samples is terminated.
Purposive sampling- this is used when the specific objective under study
requires a particular sample based on certain characteristic which may not cover the entire population.
Presentation of Data:
Bar graph- used to show relative sizes of data discretely
Line Graph - used to show the trend of changes in the data over a given time.
Pie Graph - illustrates the relationship among parts or a part to a whole.
Pictograph - the most appealing presentation of data
2nd Quarter:
Measures of central tendency – a statistic that serves as representative of the data. It tends to lie within the center of the set of data
The mean is the most important measure of central tendency
The median is the middle value that separates the data set into 2 equal parts
Mode is the value that occurs the most frequent.
Mean of Grouped Data:
Median of Grouped Data:
Mode of Grouped Data:
Histogram – is a bar graph-like representation of a frequencydistribution where the rectangular bars doesn’t have spaces in between.
Frequency polygon is a line graph where the frequency of each class are plotted against the corresponding class mark.
An ogive( pronounced as o-jayv) is a line graph where the cumulative frequency is plotted against the corresponding class boundary.
3rd Quarter:
Measures of dispersion- a statistic that indicates how close or widespread the values are.
Range: HS - LS
Mean Deviation for Ungrouped Data:
Mean Deviation for Grouped Data:
The Standard Deviation is the most important measure of dispersion because it separates scores with equal averages
Standard Deviation of Ungrouped Data:
Standard Deviation of Grouped Data:
Variance is the square of standard deviation.
4th Quarter
(refer to the book for deciles, percentiles, and quartiles)
Measures of Position: number that tells where the score stands relative to the
others in a set of data.
1st Quarter:
Collection of Data refers to the process of obtaining information.
Organization of data refers to the ascertaining manner of presenting data into tables, graphs or charts so that logical and statistical conclusions can be drawn from the collected measurements.
Analysis of Data refers to extracting relevant information from the given data from which numerical description can be formulated.
Interpretation of Data refers to the drawing of conclusions from the analyzed data.
Descriptive statistics is a statistical method concerned with describing a data set's properties and characteristics.
Examples: respondents profile such as gender, age, average family income
Inferential Statistics is a statistical method concerned with analyzing sample data, leading to predictions, inferences, interpretations or conclusions about the entire population.
Examples: sentiments of Filipinos on certain govt. issues, perception of
students towards existing concerns, etc.
Population refers to the totality of all elements or persons for which one has interest at a particular time. It is denoted by N.
Sample is a subset or portion of a population that estimates the characteristics of the study. It is denoted by n
Unit – is an individual object or person in the population. The units are often called subjects if the population consists of people.
Parameter refers to any statistical information or attribute taken from a population. It is a true value or actual statistic since its source is the population itself.
A statistic is any estimate of statistical attributes taken from a sample.
Variables are specific factor property or characteristic of a population or a sample that differentiates a sample or group of samples from another group. It can be discrete or continuous.
DISCRETE VARIABLE - obtained by counting (number of students, no. of books)
CONTINUOUS VARIABLE - obtained by measuring objects or attributes ( height and weight)
(for more examples check the book)
Data Collection is the process of gathering and measuring information on targeted variables in an established systematic fashion, which then enables one to answer relevant questions and evaluate outcomes.
Primary Data –are information gathered directly from the source. Those data can be obtained by doing an interview, observation or experimentation.
Secondary Data are information gathered from secondary sources, such as books, journals, magazines or thesis of other researchers.
Interview Method: referred to as the direct method of gathering data because this requires face-to-face inquiry with the respondent.
Questionnaire Method is referred to as the indirect method of gathering data because this makes use of written questions to be answered by the respondent.
Observation Method- This method makes use of the different human senses in gathering information.
Registration Method- This method requires the enactment of law to take effect because it needs the participation of a large , if not the entire population.
Experiment Method- This method is usually conducted in laboratories where specimens are subjected to some aspects of control to find out cause and effect relationship.
Probability Sampling- is a sampling procedure where every element of the population is given a nonzero chance of being selected as a sample.
Random Sampling - A technique that gives every individual or element in the population to be chosen in the study.
Systematic Sampling - A method of selecting every nth element in the list that represents the population.
Stratified sampling is a method of sampling where the population is divided into subgroups based on characteristics called the stratifying factors.
Cluster Sampling - The population is divided into groups
called the clusters in consideration of the geographical boundaries and accessibility.
2) Nonprobability Sampling- is a sampling procedure where not every element of the population is given a chance of being included in the sample. The drawing of samples is based purely on the researcher’s objectives.
Convenience Sampling- the researchers’ convenience is the primary concern in using this method.
Quota Sampling- If the desired quota is reached, the drawing of samples is terminated.
Purposive sampling- this is used when the specific objective under study
requires a particular sample based on certain characteristic which may not cover the entire population.
Presentation of Data:
Bar graph- used to show relative sizes of data discretely
Line Graph - used to show the trend of changes in the data over a given time.
Pie Graph - illustrates the relationship among parts or a part to a whole.
Pictograph - the most appealing presentation of data
2nd Quarter:
Measures of central tendency – a statistic that serves as representative of the data. It tends to lie within the center of the set of data
The mean is the most important measure of central tendency
The median is the middle value that separates the data set into 2 equal parts
Mode is the value that occurs the most frequent.
Mean of Grouped Data:
Median of Grouped Data:
Mode of Grouped Data:
Histogram – is a bar graph-like representation of a frequencydistribution where the rectangular bars doesn’t have spaces in between.
Frequency polygon is a line graph where the frequency of each class are plotted against the corresponding class mark.
An ogive( pronounced as o-jayv) is a line graph where the cumulative frequency is plotted against the corresponding class boundary.
3rd Quarter:
Measures of dispersion- a statistic that indicates how close or widespread the values are.
Range: HS - LS
Mean Deviation for Ungrouped Data:
Mean Deviation for Grouped Data:
The Standard Deviation is the most important measure of dispersion because it separates scores with equal averages
Standard Deviation of Ungrouped Data:
Standard Deviation of Grouped Data:
Variance is the square of standard deviation.
4th Quarter
(refer to the book for deciles, percentiles, and quartiles)
Measures of Position: number that tells where the score stands relative to the
others in a set of data.
