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## Free AIOU Solved Assignment Code 8614 Spring 2023

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**Course: Educational Statistics (8614)
**

**Semester: Spring, 2023**

**ASSIGNMENT No. 1**

**Q.1 What do you understand by statistics? What are the characteristics of statistics? Explain in detail.**

Statistics education is the practice of teaching and learning of statistics, along with the associated scholarly research. Statistics is both a formal science and a practical theory of scientific inquiry, and both aspects are considered in statistics education. Education in statistics has similar concerns as does education in other mathematical sciences, like logic, mathematics, and computer science. At the same time, statistics is concerned with evidence-based reasoning, particularly with the analysis of data. Therefore, education in statistics has strong similarities to education in empirical disciplines like psychology and chemistry, in which education is closely tied to “hands-on” experimentation. Mathematicians and statisticians often work in a department of mathematical sciences (particularly at colleges and small universities). Statistics courses have been sometimes taught by non-statisticians, against the recommendations of some professional organizations of statisticians and of mathematicians. Statistics education research is an emerging field that grew out of different disciplines and is currently establishing itself as a unique field that is devoted to the improvement of teaching and learning statistics at all educational levels.

Disposition has to do with the ways students question the data and approach a statistical problem. Dispositions are one of the four dimensions in Wild and Pfannkuch’ framework for statistical thinking, and contains the following elements:

**Curiosity and Awareness:**These traits are a part of the process of generating questions and generating ideas to explore and analyze data.**Engagement:**Students will be most observant and aware in the areas they find most interesting.**Imagination:**This trait is important for viewing a problem from different perspectives and coming up with possible explanations.**Skepticism:**Critical thinking is important for receiving new ideas and information and evaluating the appropriateness of study design and analysis.**Being logical:**The ability to detect when one idea follows from another is important for arriving at valid conclusions.**A propensity to seek deeper meaning:**This means not taking everything at face value and being open to consider new ideas and dig deeper for information.- The following points explain the functions of statistics in summary:
- It helps in collecting and presenting the data in a systematic manner.
- It helps to understand unwisely and complex data by simplifying it.
- It helps to classify the data.
- It provides basis and techniques for making comparison.
- It helps to study the relationship between different phenomena.
- It helps to indicate the trend of behavior.
- It helps to formulate the hypothesis and test it.
- It helps to draw rational conclusions.

### Statistics in Education:

Measurement and evaluation are essential part of teaching learning process. In this process we obtained scores and then interpret these score in order to take decisions. Statistics enables us to study these scores objectively. It makes the teaching learning process more efficient.

The knowledge of statistics helps the teacher in the following way:

- It helps the teacher to provide the most exact type of description:

When we want to know about the pupil we administer a test or observe the child. Then from the result we describe about the pupil’s performance or trait. Statistics helps the teacher to give an accurate description of the data.

- It makes the teacher definite and exact in procedures and thinking:

Sometimes due to lack of technical knowledge the teachers become vague in describing pupil’s performance. But statistics enables him to describe the performance by using proper language, and symbols. Which make the interpretation definite and exact.

- It enables the teacher to summarize the results in a meaningful and convenient form:

Statistics gives order to the data. It helps the teacher to make the data precise and meaningful and to express it in an understandable and interpretable manner.

- It enables the teacher to draw general conclusions:

Statistics helps to draw conclusions as well as extracting conclusions. Statistical steps also help to say about how much faith should be placed in any conclusion and about how far we may extend our generalization.

- It helps the teacher to predict the future performance of the pupils:

Statistics enables the teacher to predict how much of a thing will happen under conditions we know and have measured. For example the teacher can predict the probable score of a student in the final examination from his entrance test score. But the prediction may be erroneous due to different factors. Statistical methods tell about how much margin of error to allow in making predictions.

- Statistics enables the teacher to analyse some of the causal factors underlying complex and otherwise be-wildering events: It is a common factor that the behavioral outcome is a resultant of numerous causal factors. The reason why a particular student performs poor in a particular subject are varied and many. So with the appropriate statistical methods we can keep these extraneous variables constant and can observe the cause of failure of the pupil in a particular subject.

### Important Concepts in Statistics:

**Data:**

Data may be defined as information obtained from a survey, an experiment or an investigation.

**Score:**

Score is the numerical evaluation of the performance of an individual on a test.

**Continuous Series:**

Continuous series is a series of observations in which the various possible values of the variable may differ by infinitesimal amounts. In the series it is possible to occur at any intermediate value within the range of the series.

**Discrete Series:**

Discrete series is a series in which the values of a variable are arranged according to magnitude or to some ordered principles. In this series it is not possible to occur at any intermediate value within the range. The example of such is merit, number of persons or census data.

**Variable:**

Any trait or quality which has the ability to vary or has at least two points of measurement. It is the trait that changes from one case or condition to another.

**Variability:**

The spread of scores, usually indicated by quartile deviations, standard deviations, range etc.

**Frequency:**

Frequency may be defined as the number of occurrences of any given value or set of values. For example 8 students have scored 65. So that the score 65 has a frequency of 8.

**Frequency Distribution:**

It is a tabulation showing the frequencies of the values of a variable when these values are arranged in order of magnitude.

**Correlation:**

Correlation means the interdepended between two or more random variables. It may be stated as the tendency for corresponding observation in two or more series to vary together from the averages of their respective series, that is, to have similar relative position. If corresponding observations tend to have similar relative positions in their respective series, the correlation is positive; if the corresponding values tend to be divergent in position in their respective series, the correlation is negative; absence of any systematic tendency for the corresponding observations to be either similar or dissimilar in their relative positions indicated zero correlation.

**Coefficient:**

It is a statistical constant that is independent of the unit of measurement.

**Coefficient of correlation:**

It is a pure number, limited by the values + 1.00 and —1.00 that expresses the degree of relationship between two continuous variables.** **

## AIOU Solved Assignment 1 Code 8614 Spring 2023

**Q.2 What do you understand by the term “data”? Write in detail the types of data. **

Now, if we talk about data mainly in the field of science, then the answer to “what is data” will be that data is different types of information that usually is formatted in a particular manner. All the software is divided into two major categories, and those are programs and data. Programs are the collection made of instructions that are used to manipulate data. So, now after thoroughly understanding what is data and data science, let us learn some fantastic facts.

## Types and Uses of Data

Growth in the field of technology, specifically in smartphones has led to text, video, and audio is included under data plus the web and log activity records as well. Most of this data is unstructured.

The term Big Data is used in the data definition to describe the data that is in the petabyte range or higher. Big Data is also described as 5Vs: variety, volume, value, veracity, and velocity. Nowadays, web-based eCommerce has spread vastly, business models based on Big Data have evolved, and they treat data as an asset itself. And there are many benefits of Big Data as well, such as reduced costs, enhanced efficiency, enhanced sales, etc.

The meaning of data expands beyond the processing of data in computing applications. When it comes to what data science is, a body made of facts is called data science. Accordingly, finance, demographics, health, and marketing also have different meanings of data, which ultimately make up different answers for what is data.

Ideally, there are two ways to analyze the data:

- Data Analysis in Qualitative Research
- Data Analysis in Quantitative Research

Data analysis and research in subjective information work somewhat better than numerical information as the quality information consists of words, portrayals, pictures, objects, and sometimes images. Getting knowledge from such entangled data is a confounded procedure; thus, it is usually utilized for exploratory research as well as data analysis.

Although there are a few different ways to discover patterns in the printed data, a word-based strategy is the most depended and broadly utilized global method for research and analysis of data. Prominently, the process of data analysis in qualitative research is manual. Here the specialists, as a rule, read the accessible information and find monotonous or frequently utilized words.

The primary stage in research and analysis of data is to do it for the examination with the goal that the nominal information can be changed over into something important. The preparation of data comprises the following.

- Data Validation
- Data Editing
- Data Coding

For quantitative statistical research, the utilization of descriptive analysis regularly gives supreme numbers. However, the analysis is never adequate to show the justification behind those numbers. Still, it is important to think about the best technique to be utilized for research and analysis of data fitting your review survey and what story specialists need to tell.

Consequently, enterprises ready to make due in the hypercompetitive world must have a remarkable capacity to investigate complex research information, infer noteworthy bits of knowledge, and adjust to new market needs.

## AIOU Solved Assignment 2 Code 8614 Spring 2023

**Q.3 What types of characteristics a pictogram should have to successfully convey the meaning? Write down the advantages and drawbacks of using pictograms.**

In prehistoric art, the term “pictograph” or “pictogram” (derived from the Latin “pictus” meaning painting, and “graph/gram” meaning drawn or written) describes an image, sign or symbol which is created in order to express some idea or information. In addition, note that pictographic symbols that are cut or carved into the rock surface are known as “petroglyphs“, while those drawn or painted on rocks are called “petrograms”. A pictograph that represents one particular idea is usually referred to as an “ideogram”. The most obvious type of Stone Age pictograph were the prehistoric abstract signs (aviforms, circles, claviforms, cordiforms, quadrangles, tectiforms, triangles and the like) which, experts believe, functioned as pictographs or pictograms, in that they were intended to express some simple message. (A good example-site is Le Placard Cave, near La Rochefoucauld.) However, paintings of animals or hunting scenes may also have been carefully arranged to communicate some kind of message. Pictographs are characterized by their stereotyped execution which is standardized at least within their group or locality. This type of pictographic rock art served as an early forerunner of Neolithic written languages, such as Sumerian cuneiforms (wedge-shaped symbols) and Egyptian hieroglyphs. Few archeologists or anthropologists would agree on a specific starting date, or even period, for the first pictograph. It depends whether certain very early non-functional hemispherical indentations in the surface of rocks, known as “cupules“, can be said to constitute incised pictographs (petroglyphs). If so, then it is possible that Neanderthal humans (Homo neanderthalensis) were creating petroglyphs in the Lower Paleolithic, as far back as 700,000 BCE. See, for instance, the Bhimbetka Petroglyphs, discovered in Central India. Otherwise, the earliest known rock pictographs are likely to be the geometric Blombos Cave engravings, which date to the Middle Paleolithic, around 70,000 BCE. For more about the oldest works, see: Earliest Art.

The oldest known pictographs of the Upper Paleolithic are the red-ochre blobs among the El Castillo Cave paintings, which have been Uranium/Thorium dated to at least 39,000 BCE, about the time that anatomically modern man first set foot in Europe. During the Stone Age, most artworks including pictographs/pictograms were created inside rock shelters or deep caves. This parietal art consisted of four main types, listed here in order of age: abstract symbols (please see above), hand stencils (handprints or palm-prints), rock engravings (painted or unpainted), and cave painting (monochrome or polychrome). This cave art was not “art for art’s sake”, but a means of expression with a shamanistic, or ceremonial, or hunting function. If this is true then all these different types of imagery qualify as pictographs. As it happens, most of the abstract symbols are to be found around or actually inside the paintings of animal figures, almost as if they are providing a primitive commentary on the illustrations. Thus we may have to consider the art “as a whole” rather than separating it into types. Paleolithic scholars continue to debate the meaning of these early prehistoric pictographs. Probably these images had a variety of meanings, which varied from region to region. In any event, it is worth emphasizing that, as a rule, decorated caves were not occupied by domestic inhabitants. Indeed, judging by the lack of footprints and other signs of human presence, only a small group of artists and other decision-makers ever ventured inside. This leads credence to the idea of the prehistoric cave as a sanctuary or sacred place, and the paintings as an iconographic backdrop for whatever ceremony or ritual was performed therein. Unfortunately, no one knows exactly what kind of ceremonial activity might have occurred. But two basic possibilities suggest themselves.

First, given the overwhelming visual effect of the animal figures, engraved, drawn or painted in almost every cave, it is clear that Paleolithic art is essentially the art of the hunter. Thus the cave paintings might be interpreted as a primitive type of hunting “wish-list”. Dangerous predators (such as lions and bears) might have been pictorialized in order to demonize or cast spells upon them, in the way that voodoo dolls are first made then pierced with pins and the like. (See: Chauvet Cave paintings, for instance.) Game animals hunted for food might have been pictorialized in order to improve hunting prospects. (See: Lascaux Cave paintings, for example.)

Second, given the fact that these small groups of humans kept going into these (deep and dark) caves for thirty thousand years, not to live or shelter there, but to draw on the walls, something significant must have been going on. And since time immemorial, the dark – and especially the underground dark – has been seen as a sort of supernatural realm, harbouring any number of spirits in contact with higher powers. Furthermore, the influence of “shamans” – witchdoctor-type individuals in contact with the spirit world – was a widespread cultural phenomenon among Upper Paleolithic hunter-gatherer societies. (See, for instance, the extraordinary painted and engraved image of the “Sorcerer” in the Trois Freres Cave c.13,000 BCE.) Therefore it seems reasonable to agree with archeologists Jean Clottes and David Lewis-Williams (Clottes & Lewis-Williams, 1998) who suggest that Shamanism is at the root of this Stone Age art and that early humans may have regarded the cave as a bridge between this world and the next. This “supernatural” interpretation is the only one which explains the lack of visitors to the cave: people were probably too terrified by voodoo-type fears and superstitions to enter.

Among the less portentous explanations of ancient art inside caves, please note the recent extensive study into the meaning of hand stencils, conducted by Paul Pettitt of the University of Sheffield. Pettitt demonstrates that the handprints were quite often created in places that were difficult to reach. He suggests that a possible interpretation of this is that they represented navigational pictographs in dimly lit caves, giving advice such as “do not use this passageway”. See also: Gargas Cave Hand Stencils (25,000 BCE).

A pictograph is the representation of data using images. Pictographs represent the frequency of data while using symbols or images that are relevant to the data. This is one of the simplest ways to represent statistical data. And reading a pictograph is made extremely easy as well. The best way to explain a pictograph is through an example. So let us get started. Let us take an example. We must represent how many TV sets have been sold in the last few years via a pictograph. So we get started

**Collect Data**: First step is obviously collecting the data of the category you want to represent. Collect your data by appropriate means. And then make a list or table of the data. And one timefinally review the data.**Pick your symbol**: Pick a*symbol or picture*that accurately represents your data. If you are drawing a pictograph to represent TV sets sold then a symbol of a basketball would be highly confusing! So pick your symbol carefully.**Assign a Key**: Sometimes the frequency of the data is too high. Then one symbol cannot represent one frequency. You must set a numerical value that one symbol will represent. This numerical value must be written along with the pictograph. Example one symbol of a TV represents 500 TV sets. This is the*key of the pictograph.***Draw the pictograph**: Final step is drawing your pictograph. Draw the two columns that represent the category and the data. Then draw the actual symbols that represent the frequencies. Remember that the symbols can be drawn as fractionsas well if the frequency is not a whole number.**Review your Data**: And finally, review your pictograph and make sure it correctly represents the information that you wanted to relay. Don’t forget to check the labellingof your graph.

After you are done drawing the above pictograph it should look something similar to the following picture.

### Advantages of a Pictograph

- Express a large amount of information or data in a simple form
- Since they make the use of symbols, pictographs attract attention i,e, it is an attractive way to represent data
- Pictographs are easy to read since all the information is available at one glance
- And since pictographs are universally used they do not require a lot of explanation

## AIOU Solved Assignment Code 8614 Spring 2023

**Q.4 Define normal curve. Write down the properties of normal curve.**

Known characteristics of the normal curve make it possible to estimate the probability of occurrence of any value of a normally distributed variable. Suppose that the total area under the curve is defined to be 1. You can multiply that number by 100 and say there is a 100 percent chance that any value you can name will be somewhere in the distribution. ( **Remember **: The distribution extends to infinity in both directions.) Similarly, because half the area of the curve is below the mean and half is above it, you can say that there is a 50 percent chance that a randomly chosen value will be above the mean and the same chance that it will be below it.

It makes sense that the area under the normal curve is equivalent to the probability of randomly drawing a value in that range. The area is greatest in the middle, where the “hump” is, and thins out toward the tails. That is consistent with the fact that there are more values close to the mean in a normal distribution than far from it.

When the area of the standard normal curve is divided into sections by standard deviations above and below the mean, the area in each section is a known quantity (see Figure 1). As explained earlier, the area in each section is the same as the probability of randomly drawing a value in that range.

Figure 1.The normal curve and the area under the curve between σ units.

For example, 0.3413 of the curve falls between the mean and one standard deviation above the mean, which means that about 34 percent of all the values of a normally distributed variable are between the mean and one standard deviation above it. It also means that there is a 0.3413 chance that a value drawn at random from the distribution will lie between these two points.

Sections of the curve above and below the mean may be added together to find the probability of obtaining a value within (plus or minus) a given number of standard deviations of the mean (see Figure 2). For example, the amount of curve area between one standard deviation above the mean and one standard deviation below is 0.3413 + 0.3413 = 0.6826, which means that approximately 68.26 percent of the values lie in that range. Similarly, about 95 percent of the values lie within two standard deviations of the mean, and 99.7 percent of the values lie within three standard deviations.

Figure 2.The normal curve and the area under the curve between σ units.

In order to use the area of the normal curve to determine the probability of occurrence of a given value, the value must first be **standardized,** or converted to a **z‐score **. To convert a value to a z‐score is to express it in terms of how many standard deviations it is above or below the mean. After the z‐score is obtained, you can look up its corresponding probability in a table. The formula to compute a z‐score is

where x is the value to be converted, μ is the population mean, and σ is the population standard deviation.** **

## AIOU Solved Assignment Code 8614 Autumn 2023

**Q.5 Explain procedure for determining median, with one example each at least, if: **

**The number of scores is even****The number of scores is odd.**

The median is the middle score of a distribution. To calculate the median

- Arrange your numbers in numerical order.
- Count how many numbers you have.
- If you have an odd number, divide by 2 and round up to get the position of the median number.
- If you have an even number, divide by 2. Go to the number in that position and average it with the number in the next higher position to get the median.

Consider this set of numbers: 5, 7, 9, 9, 11. Since you have an odd number of scores, the median would be 9. You have five numbers, so you divide 5 by 2 to get 2.5, and round up to 3. The number in the third position is the median.

What happens when you have an even number of scores so there is no single middle score? Consider this set of numbers: 1, 2, 2, 4, 5, 7. Since there is an even number of scores, you need to take the average of the middle two scores, calculating their mean.

In this case, the mean would be 2 + 4 (add the two middle numbers), which equals 6. Then, you take 6 and divide it by 2 (the total number of scores you added together), which equals 3. So, for this example, the median is 3.

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