Procedure for Determining Median | Merits of Median | Demerits of Median | Educational Statistics | 8614 |

 

QUESTION

How do we calculate the median? Also, mention its merits and demerits.

Course: Educational Statistics

Course code 8614

Level: B.Ed Solved Assignment 

ANSWER

Median

The median is the middle value of rank order data. It divides the distribution into two halves (i.e. 50% of scores or observations on either side of the median value). It means that this value separates the higher half of the data set from the lower half. The goal of the median is to determine the precise midpoint of the distribution. The median is appropriate for describing ordinal data.

Procedure for Determining Median

When the number of scores is odd, simply arrange the scores in order (from lower to higher or from higher to lower). The median will be the middle score in the list. Consider the set of scores 2, 5, 7, 10, 12. The score “7” lies in the middle of the scores, so it is the median. When there is an even number of scores in the distribution, arrange the scores in order (from lower to higher or from higher to lower). The median will be the average of the middle two scores in the list. Consider the set of scores 4, 6, 9, 14 16, 20. The average of the middle two scores 11.5 (i.e. 9+14/2 = 23/2 = 11.5) is the median of the distribution.

The median is less affected by outliers and skewed data and is usually the preferred measure of central tendency when the distribution is not symmetrical. The median cannot be determined for categorical or nominal data.

Merits of Median

i)  It is rigidly defined.

ii)  It is easy to understand and calculate.

iii)  It is not affected by extreme values.

iv)  Even if the extreme values are not known median can be calculated.

v)  It can be located just by inspection in many cases.

vi)  It can be located graphically.

vii)  It is not much affected by sampling fluctuations.

viii)  It can be calculated by data based on an ordinal scale.

ix)  It is suitable for skewed distribution.

x)  It is easily located in individual and discrete classes.

Demerits of Median

i)  It is not based on all values of the given data.

ii)  For larger data sizes the arrangement of the data in increasing order is

a somewhat difficult process.

iii)  It is not capable of further mathematical treatment.

iv)  It is not sensitive to some change in the data value.

v)  It cannot be used for further mathematical processing.

Related Topics

ANOVA and its Logics

Median (Procedure of Determination, Merits, Demerits)

Measures of Dispersion

Descriptive and Inferential Statistics

What is data Cleaning? Importance and Benefits of Data Cleaning 

Explain the terms Degree of Freedom,Spread of Score,Sample,Z Score,Confidence Interval 

What is measure of difference? Explain different types of test

Concept of Reliability, Types and methods of Reliability

Level of Measurement

Types of Variable in Stats 

Measures of Central Tedency and Dispersion, 

Role of Normal Distribution, and also note on Skewness and Kurtosis. 

Methods of Effective Presentation

Measures of Dispersion | Educational Statistics | 8614 |

QUESTION

Explain different measures of dispersion used in educational research.

• Course: Educational Statistics
• Course code 8614
• Level: B.Ed Solved Assignment

ANSWER

Introduction to Measures of Dispersion

Measures of central tendency focus on what is an average or in the middle of the distribution of scores. Often the information provided by these measures does not give us a clear picture of the data and we need something more. It means that knowing the mean, median, and mode of a distribution does allow us to differentiate between two or more than two distributions; and we need additional information about the distribution. This additional information is provided by a series of measures which are commonly known as measures of dispersion.

There is dispersion when there is dissimilarity among the data values. The greater the dissimilarity, the greater the degree of dispersion will be.

Measures of dispersion are needed for four basic purposes.

i)  To determine the reliability of an average.

ii)  To serve as a basis for the control of the variability.

iii)  To compare two or more series about their variability.

iv)  To facilitate the use of other statistical measures.

 

The measure of dispersion enables us to compare two or more series concerning their variability. It is also looked at as a means of determining uniformity or consistency. A high degree would mean little consistency or uniformity whereas a low degree of variation would mean greater uniformity or consistency among the data set. Commonly used measures of dispersion are range, quartile deviation, mean deviation, variance, and standard deviation.

Range

The range is the simplest measure of spread and is the difference between the highest and lowest scores in a data set. In other words, we can say that the range is the distance between the largest score and the smallest score in the distribution. We can calculate the range as:

Range = Highest value of the data – The lowest value of the data

For example, if the lowest and highest marks scored in a test are 22 and 95 respectively, then

Range = 95 – 22 = 73

The range is the easiest measure of dispersion and is useful when you wish to evaluate the whole of a dataset. However, it is not considered a good measure of dispersion as it does not utilize the other information related to the spread. The outliers, either extremely low or extremely high value, can considerably affect the range.

Quartiles

The values that divide the given set of data into four equal parts are called quartiles and are denoted by Q₁, Q₂, and Q_3. Q₁  is called the lower quartile and Q₃ is called the upper quartile. 25% of scores are less than Q₁and 75% scores are less than Q₃. Q₂ is the median. The formulas for the quartiles are:

Quartile Deviation (QD)

Quartile deviation or semi inter-quartile range is one-half the difference between the first and the third quartile, i.e.

Q D = Q₃ – Q₁

Where Q₁ = the first quartile (lower quartile)

Q₃ = third quartile (upper quartile)

Calculating quartile deviation from ungrouped date:

To calculate quartile deviation from ungrouped data, the following steps are used.

i)  Arrange the test scores from highest to lowest

ii)  Assign a serial number to each score. The first serial number is assigned to the lowest score.

Determine the first quartile (Q₁) by using the formula

Use the obtained value to locate the serial number of the score that falls under Q₁.

iv  Determine the third (Q₃), by using the formula

Locate the serial number corresponding to the obtained answer. Opposite to this number is the test score corresponding to Q₃.

v)  Subtract the Q₁ from Q₃, and divide the difference by 2.

Mean Deviation or Average Deviation

The mean or the average deviation is defined as the arithmetic mean of the deviations of the scores from the mean or the median. The deviations are taken as positive. Mathematically, 

Standard Deviation

Standard deviation is the most commonly used and the most important measure of variation. It determines whether the scores are generally near or far from the mean, i.e. are the scores clustered together or scattered. In simple words, standard deviation tells how tightly all the scores are clustered around the mean in a data set. When the scores are close to the mean, the standard deviation is small. And large standard deviation tells that the scores are spread apart. Standard deviation is simply the square root of variance, i.e.

 Variance

Related Topics

Chi-Square, and independent test.

ANOVA and its Logics

Median (Procedure of Determination, Merits, Demerits)

Measures of Dispersion

Descriptive and Inferential Statistics

What is data Cleaning? Importance and Benefits of Data Cleaning 

Explain the terms Degree of Freedom,Spread of Score,Sample,Z Score,Confidence Interval 

What is measure of difference? Explain different types of test

Concept of Reliability, Types and methods of Reliability

Level of Measurement

Types of Variable in Stats 

Measures of Central Tedency and Dispersion, 

Role of Normal Distribution, and also note on Skewness and Kurtosis. 

Methods of Effective Presentation

Non-Probability Sampling | Educational Statistics |

 

QUESTION

Explain non-probability sampling techniques used in educational research. 

Course: Educational Statistics

Course code 8614

Level: B.Ed Solved Assignment 

ANSWER

Non-Probability Sampling

This technique depends on subjective judgment. It is a process where probabilities cannot  be assigned to the individuals objectively. It means that in this technique samples are gathered in a way that does not give all individuals in the population equal chances of being selected. Choosing these methods could result in biased data or a limited ability to make general inferences based on the findings. But there are also many situations in which choosing this kind of sampling technique is the best choice for a particular research question or the stage of research.

There are four kinds of non-probability sampling techniques.

i)  Convenience Sampling

In this technique a researcher relies on available subjects, such as stopping people in the markets or on street corners as they pass by. This method is extremely risky and does not allow the researcher to have any control over the representativeness of the sample. It is useful when the researcher wants to know the opinion of the masses on a current issue; or the characteristics of people passing by on streets at a certain point of time; or if time and resources are limited in such a way that the research would not be possible otherwise. What may be the reason for selecting convenience samples, it is not possible to use the results from a convenience sampling to generalize to a wider population.

ii)  Purposive or Judgmental Sampling

In this technique, a sample is selected on the basis of the knowledge of the population and the purpose of the study. For example, when an educational psychologist wants to study the emotional and psychological effects of corporal punishment, he will create a sample that will include only those students who ever had received corporal punishment.  In this case, the researcher used a purposive sample because those being selected fit a specific purpose or description that was necessary to conduct the research.

Snowball Sample

This type of sampling is appropriate when the members of the population are difficult to locate, such as homeless industry workers, undocumented immigrants, etc. A snowball sample is one in which the researcher collects data on a few members of the target population he or she can locate, then asks to locate those individuals to provide the information needed to locate other members of that population whom they know. For example, if a researcher wants to interview undocumented immigrants from Afghanistan, he might interview a few undocumented individuals he knows or can locate, and would then rely on those subjects to help locate more undocumented individuals. This process continues until the researcher has all the interviews he needs and all contacts have been exhausted. This technique is useful when studying a sensitive topic that people might not openly talk about, or if talking about the issue under investigation could jeopardize their safety.

iv)  Quota Sample

A quota sample is one in which units are selected into a sample on the basis of pre-specified characteristics so that the total sample has the same distribution of characteristics assumed to exist in the population. For example, if a researcher wants a national quota sample, he might need to know what proportion of the population is male and what proportion is female, as well as what proportion of each gender fall into different age category and educational category. The researcher would then collect a sample with the same proportion as the national population.

Descriptive and Inferential Statistics | Educational Statistics |

 QUESTION

How do descriptive and inferential statistics help a teacher? Explain. 

Course: Educational Statistics
Course code 8614
Level: B.Ed Solved Assignment 

ANSWER 

Descriptive and Inferential Statistics 

Researchers use a variety of statistical procedures to organize and interpret data. These procedures can be classified into two categories – Descriptive Statistics and Inferential Statistics. The starting point for dealing with a collection of data is to organize, display, and summarize it effectively. It is the major objective of descriptive statistics.

Descriptive Statistics, as the name implies, describes the data. Descriptive statistics consist of methods for organizing and summarizing information. These are statistical procedures that are used to organize, summarize, and simplify data. In these techniques, raw scores are taken, and some statistical techniques to obtain a more manageable form. These techniques allow the researcher to describe a large amount of information or scores in a few indices such as mean, median, standard deviation, etc. When these indices are calculated for a sample, they are called statistics; and when they are calculated from the entire population, they are called parameters (Fraenkel, Wallen, & Hyun, 2012). Descriptive statistics organizes scores in the form of a table or a graph. It is especially useful when the researcher finds it necessary to handle interrelationships among more than two variables.

Only summarizing and organizing data is not the whole purpose of a researcher. He often wishes to make inferences about a population based on data he has obtained from a sample. For this purpose, he uses inferential statistics. Inferential Statistics are techniques that allow a researcher to study samples and then make generalizations about the populations from which they are selected.

The population of a research study is typically too large and it is difficult for a researcher to observe each individual. Therefore a sample is selected. By analyzing the results obtained from a sample, a researcher hopes to make a general conclusion about the population. One problem with using a sample is that a sample provides only limited information about the population. To address this problem the notion that the sample should be representative of the population. That is, the general characteristics of the sample should be consistent with the characteristics of the population             

Related Topics

Chi-Square, and independent test.

ANOVA and its Logics

Median (Procedure of Determination, Merits, Demerits)

Measures of Dispersion

Descriptive and Inferential Statistics

What is data Cleaning? Importance and Benefits of Data Cleaning 

Explain the terms Degree of Freedom,Spread of Score,Sample,Z Score,Confidence Interval 

What is measure of difference? Explain different types of test

Concept of Reliability, Types and methods of Reliability

Level of Measurement

Types of Variable in Stats 

Measures of Central Tedency and Dispersion, 

Role of Normal Distribution, and also note on Skewness and Kurtosis. 

Methods of Effective Presentation

                     

Calculating CGPA and Assigning Letter Grades|Educational Assessment and Evaluation|

 

QUESTION

Discuss the methods of calculating CGPA and assigning letter grades.

Course: Educational Assessment and Evaluation

Course code 8602

Level: B.Ed Solved Assignment 

ANSWER  

Calculating CGPA and Assigning Letter Grades

CGPA stands for Cumulative Grade Point Average. It reflects the grade point average of all subjects/courses regarding a student’s performance in a composite way. To calculate CGPA, we should have the following information.

Marks in each subject/course

 • Grade point average in each subject/course

• Total credit hours (by adding credit hours of each subject/course)

Calculating CGPA is very simple the total grade point average is divided by total credit hours. For example, if a student's MA Education program has studied 12 courses, each of 3 credits. The total credit hours will be 36. The CGPA will be 36/12 = 3.0

Assigning letter grades

The letter grade system is the most popular in the world including Pakistan. Most teachers face problems while assigning grades. There are four core problems or issues in this regard; 

1) what should be included in a letter grade,

 2) how should achievement data be combined in assigning letter grades?

 3) what frame of reference should be used in grading, and 

4) how should the distribution of letter grades be determined?

Determining what to include in a grade Letter grades are likely to be most meaningful and useful when they represent achievement only. If they are communicated with other factors or aspects such as effort of work completed, personal conduct, and so on, their interpretation will become hopelessly confused. For example, a letter grade of C may represent average achievement with extraordinary effort and excellent conduct and behavior or vice versa. If letter grades are to be valid indicators of achievement, they must be based on valid measures of achievement. This involves defining objectives as intended learning outcomes and developing or selecting tests and assessments that can measure these learning outcomes.

Combining data in assigning grades

 One of the key concerns while assigning grades is to be clear about what aspects of a student are to be assessed or what will be the tentative weightage to each learning outcome. For example, if we decide that 35 percent weightage is to be given to mid-term assessments, 40 percent final term tests or assessments, and 25% to assignments, presentations, classroom participation, and conduct and behavior; we have to combine all elements by assigning appropriate weights to each element, and then use these composite scores as a basis for grading.

Selecting the proper frame of reference for grading

 Letter grades are typically assigned based on one of the following frames of reference.

a)      Performance of other group members (relative grading)

b)      Performance concerning specified standards (absolute grading)

c)       Performance concerning learning ability (amount of improvement)

 

Assigning grades on a relative basis involves comparing a student’s performance with that of a reference group, mostly class fellows. In this system, the grade is determined by the student’s relative position or ranking in the total group. Although relative grading has the disadvantage of a shifting frame of reference (i.e. grades depend upon the group’s ability), it is still widely used in schools, as most of the time our system of testing is ‘norm-referenced’.

 

Assigning grades on an absolute basis involves comparing a student’s performance to specified standards set by the teacher. This is what we call ‘criterion-referenced’ testing. If all students show a low level of mastery consistent with the established performance standard, all will receive low grades. The student performance about the learning ability is inconsistent with a standard[1]based system of evaluating and reporting student performance. The improvement over a short period is difficult. Thus lack of reliability in judging achievement about ability and in judging degree of improvement will result in grades of low dependability. Therefore such grades are used as supplementary to other grading systems.

 

Determining the distribution of grades

 

 The assigning of relative grades is essentially a matter of ranking the student in order of overall achievement and assigning letter grades based on each student’s rank in the group. This ranking might be limited to a single classroom group or might be based on the combined distribution of several classroom groups taking the same course. If grading on the curve is to be done, the most sensible approach in determining the distribution of letter grades in a school is to have the school staff set general guidelines for introductory and advanced courses.

All staff members must understand the basis for assigning grades, and this basis must be clearly communicated to users of the grades. If the objectives of a course are clearly mentioned and the standards for mastery appropriately set, the letter grades in an absolute system may be defined as the degree to which the objectives have been attained, as follows. A = Outstanding (90 to 100%) B = Very Good (80-89%) C = Satisfactory (70-79%) D = Very Weak (60-69%) F = Unsatisfactory (Less than 60%)

Related Topics 

• Calculating CGPA and Assigning Letter Grades 

• Interpreting Test Scores by ordering and ranking 

• Content Validity and Content Construct Validity 

• Extended Response Essay Type Item 

• Intelligence tests (Advantages and Disadvantages), Why Intelligence Tests are Used 

• What is classroom assessment and its characteristics  

• Difference among sociograms, social distance scale 

• The procedure for development of multiple choice tests items and assembling the test prepare ten multiple choice items 

• Blooms taxonomy with SOLO Taxonfomy of educational objectives. 

• Cognitive Domain of blooms Taxonomy  

• Importance of Table of Specification, and How to Develop  

• Validity of a Test and its Type 

• Significance and Scope of Establishment of Partnership between the Teacher Training Institutions

Interpreting Test Scores by ordering and ranking|Educational Assessment and Evaluation

QUESTION

Write how to interpret test scores by ordering and ranking?

Course: Educational Assessment and Evaluation

Course code 8602

Level: B.Ed Solved Assignment 

ANSWER  

Interpreting Test Scores by ordering and ranking

Organizing and reporting students’ scores starts with placing the scores in ascending or descending order. Teachers can find the smallest, largest, range, and some other facts like the variability of scores associated with scores from ranked scores. Teacher may use ranked scores to see the relative position of each student within the class but ranked scores does not yield any significant numerical value for result interpretation or reporting.

Measurement Scales

 Measurement is the assignment of numbers to objects or events in a systematic fashion. Measurement scales are critical because they relate to the types of statistics you can use to analyze your data. An easy way to have a paper rejected is to have used either an incorrect scale/statistic combination or to have used a low-powered statistic on a high-powered set of data. The following four levels of measurement scales are commonly distinguished so that the proper analysis can be used on the data a number can be used merely to label or categorize a response.

Nominal Scale.

Nominal scales are the lowest scales of measurement. A nominal scale, as the name implies, is simply some placing of data into categories, without any order or structure. You are only allowed to examine if a nominal scale datum is equal to some particular value or to count the number of occurrences of each value. For example, the categorization of blood groups of classmates into A, B AB, O, etc. The only mathematical operation we can perform with nominal data is to count. Variables assessed on a nominal scale are called categorical variables; Categorical data are measured on nominal scales which merely assign labels to distinguish categories. For example, gender is a nominal scale variable. Classifying people according to gender is a common application of a nominal scale.

Nominal Data

 • classification or categorization of data, e.g. male or female

• no ordering, e.g. it makes no sense to state that male is greater than female (M > F), etc

• arbitrary labels, e.g., pass=1 and fail=2, etc

Ordinal Scale.

 Something measured on an "ordinal" scale does have an evaluative connotation. You are also allowed to examine if an ordinal scale datum is less than or greater than another value. For example rating of job satisfaction on a scale from 1 to 10, with 10 representing complete satisfaction. With ordinal scales, we only know that 2 is better than 1 or 10 is better than 9; we do not know by how much. It may vary. Hence, you can 'rank' ordinal data, but you cannot 'quantify' differences between two ordinal values. Nominal scale properties are included in the ordinal scale.

Ordinal Data

• ordered but differences between values are not important. Differences between values may or may not same or equal.

 • e.g., political parties on left to right spectrum given labels 0, 1, 2

• e.g., Likert scales, rank on a scale of 1..5 your degree of satisfaction

 • e.g., restaurant ratings

 

Interval Scale

An ordinal scale has quantifiable differences between values and becomes an interval scale. You are allowed to quantify the difference between two interval scale values but there is no natural zero. A variable measured on an interval scale gives information about more or better than ordinal scales do, but interval variables have an equal distance between each value. The distance between 1 and 2 is equal to the distance between 9 and 10. For example, temperature scales are interval data with 25C warmer than 20C and a 5C difference has some physical meaning. Note that 0C is arbitrary so it does not make sense to say that 20C is twice as hot as 10C but there is the exact same difference between 100C and 90C as there is between 42C and 32C. Students’ achievement scores are measured on an interval scale

Interval Data

• ordered, constant scale, but no natural zero

• differences make sense, but ratios do not (e.g., 30°-20°=20°-10°, but 20°/10° is not twice as hot!

 • e.g., temperature (C, F), dates

Ratio Scale

Something measured on a ratio scale has the same properties that an interval scale has except, with a ratio scaling, there is an absolute zero point. Temperature measured in Kelvin is an example. There is no value possible below 0 degrees Kelvin, it is absolute zero. Physical measurements of height, weight, and length are typically ratio variables. Weight is another example, 0 lbs. is a meaningful absence of weight. This ratio holds true regardless of which scale the object is being measured in (e.g. meters or yards). This is because there is a natural zero.

Ratio Data

• ordered, constant scale, natural zero

 • e.g., height, weight, age, length One can think of nominal, ordinal, interval, and ratio as being ranked in their relation to one another. Ratio is more sophisticated than interval, interval is more sophisticated than ordinal, and ordinal is more sophisticated than nominal.

Related Topics 

• Calculating CGPA and Assigning Letter Grades 

• Interpreting Test Scores by ordering and ranking 

• Content Validity and Content Construct Validity 

• Extended Response Essay Type Item 

• Intelligence tests (Advantages and Disadvantages), Why Intelligence Tests are Used 

• What is classroom assessment and its characteristics  

• Difference among sociograms, social distance scale 

• The procedure for development of multiple choice tests items and assembling the test prepare ten multiple choice items 

• Blooms taxonomy with SOLO Taxonfomy of educational objectives. 

• Cognitive Domain of blooms Taxonomy  

• Importance of Table of Specification, and How to Develop  

• Validity of a Test and its Type 

• Significance and Scope of Establishment of Partnership between the Teacher Training Institutions

What is a consideration while planning a test|Educational Assessment and Evaluation|

 

QUESTION

What is a consideration while planning a test?

Course: Educational Assessment and Evaluation

Course code 8602

Level: B.Ed Solved Assignment 

ANSWER  

Planning a Test

The main objective of classroom assessment is to obtain valid, reliable, and useful data regarding student learning achievement. This requires determining what is to be measured and then defining it precisely so that assessment tasks to measure desired performance can be developed. Classroom tests and assessments can be used for the following instructional objectives:

 i. Pre-testing

 Tests and assessments can be given at the beginning of an instructional unit or course to determine:-

• whether the students have the prerequisite skills needed for the instruction (readiness, motivation, etc)

• to what extent the students have already achieved the objectives of planned instruction (to determine placement or modification of instruction)

 ii. During the Instruction Testing

 • provides bases for formative assessment

• monitor learning progress

 • detect learning errors

 • provide feedback for students and teachers

 iii. End of Instruction Testing

 • measure intended learning outcomes

 • used for formative assessment

 • provides bases for grades, promotion, etc

 Prior to developing an effective test, one needs to determine whether or not a test is the appropriate type of assessment. If the learning objectives are primarily types of procedural knowledge (how to perform a task) then a written test may not be the best approach. Assessment of procedural knowledge generally calls for a performance demonstration assessed using a rubric. Where a demonstration of a procedure is not appropriate, a test can be an effective assessment tool.

The first stage of developing a test is planning the test content and length. Planning the test begins with the development of a blueprint or test specifications for the test structured on the learning outcomes or instructional objectives to be assessed by the test instrument. For each learning outcome, a weight should be assigned based on the relative importance of that outcome in the test. The weight will be used to determine the number of items related to each of the learning outcomes.

 

Test Specifications

 When an engineer prepares a design to construct a building and chooses the materials, he intends to use in construction, he usually knows what a building is going to be used for, and therefore designs it to meet the requirements of its planned inhabitants. Similarly, in testing, the table of specification is the blueprint of the assessment which specifies percentages and weightage of test items and measuring constructs. It includes constructs and concepts to be measured, the tentative weightage of each construct, a specific number of items for each concept, and a description of item types to be constructed. It is not surprising that specifications are also referred to as ‘blueprints’, for they are literally architectural drawings for test construction. Fulcher & Davidson (2009) divided test specifications into the following four elements:

 

Item specifications:

 Item specifications describe the items, prompts or tasks, and any other material such as texts, diagrams, and charts that are used as stimuli. Typically, a specification at this sub-level contains two key elements: samples of the tasks to be produced, and guiding language that details all information necessary to produce the task.

Presentation Model:

The presentation model provides information on how the items and tasks are presented to the test takers.

Assembly Model: 

The assembly model helps the test developer combine test items and tasks to develop a test format.

Delivery Model:

The delivery Model tells how the actual test is delivered. It includes information regarding test administration, test security/confidentiality, and time constraints.