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## Free AIOU Solved Assignment Code 4689 Spring 2021

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**Course: Social Statistics (4689)
**

**Semester: Spring, 2021**

**ASSIGNMENT No. 1**

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**Define research process and give its different steps. Elaborate each steps with the help of examples.**

Any research done without documenting the study so that others can review the process and results is not an investigation using the scientific research process. The scientific research process is a multiple-step process where the steps are interlinked with the other steps in the process. If changes are made in one step of the process, the researcher must review all the other steps to ensure that the changes are reflected throughout the process. Parks and recreation professionals are often involved in conducting research or evaluation projects within the agency. These professionals need to understand the eight steps of the research process as they apply to conducting a study. Table 2.4 lists the steps of the research process and provides an example of each step for a sample research study.

**Step 1: Identify the Problem**

The first step in the process is to identify a problem or develop a research question. The research problem may be something the agency identifies as a problem, some knowledge or information that is needed by the agency, or the desire to identify a recreation trend nationally. In the example in table 2.4, the problem that the agency has identified is childhood obesity, which is a local problem and concern within the community. This serves as the focus of the study.

**Step 2: Review the Literature**

Now that the problem has been identified, the researcher must learn more about the topic under investigation. To do this, the researcher must review the literature related to the research problem. This step provides foundational knowledge about the problem area. The review of literature also educates the researcher about what studies have been conducted in the past, how these studies were conducted, and the conclusions in the problem area. In the obesity study, the review of literature enables the programmer to discover horrifying statistics related to the long-term effects of childhood obesity in terms of health issues, death rates, and projected medical costs. In addition, the programmer finds several articles and information from the Centers for Disease Control and Prevention that describe the benefits of walking 10,000 steps a day. The information discovered during this step helps the programmer fully understand the magnitude of the problem, recognize the future consequences of obesity, and identify a strategy to combat obesity (i.e., walking).

**Step 3: Clarify the Problem**

Many times the initial problem identified in the first step of the process is too large or broad in scope. In step 3 of the process, the researcher clarifies the problem and narrows the scope of the study. This can only be done after the literature has been reviewed. The knowledge gained through the review of literature guides the researcher in clarifying and narrowing the research project. In the example, the programmer has identified childhood obesity as the problem and the purpose of the study. This topic is very broad and could be studied based on genetics, family environment, diet, exercise, self-confidence, leisure activities, or health issues. All of these areas cannot be investigated in a single study; therefore, the problem and purpose of the study must be more clearly defined. The programmer has decided that the purpose of the study is to determine if walking 10,000 steps a day for three days a week will improve the individual’s health. This purpose is more narrowly focused and researchable than the original problem.

**Step 4: Clearly Define Terms and Concepts**

Terms and concepts are words or phrases used in the purpose statement of the study or the description of the study. These items need to be specifically defined as they apply to the study. Terms or concepts often have different definitions depending on who is reading the study. To minimize confusion about what the terms and phrases mean, the researcher must specifically define them for the study. In the obesity study, the concept of “individual’s health” can be defined in hundreds of ways, such as physical, mental, emotional, or spiritual health. For this study, the individual’s health is defined as physical health. The concept of physical health may also be defined and measured in many ways. In this case, the programmer decides to more narrowly define “individual health” to refer to the areas of weight, percentage of body fat, and cholesterol. By defining the terms or concepts more narrowly, the scope of the study is more manageable for the programmer, making it easier to collect the necessary data for the study. This also makes the concepts more understandable to the reader.

**Step 5: Define the Population**

Research projects can focus on a specific group of people, facilities, park development, employee evaluations, programs, financial status, marketing efforts, or the integration of technology into the operations. For example, if a researcher wants to examine a specific group of people in the community, the study could examine a specific age group, males or females, people living in a specific geographic area, or a specific ethnic group. Literally thousands of options are available to the researcher to specifically identify the group to study. The research problem and the purpose of the study assist the researcher in identifying the group to involve in the study. In research terms, the group to involve in the study is always called the population. Defining the population assists the researcher in several ways. First, it narrows the scope of the study from a very large population to one that is manageable. Second, the population identifies the group that the researcher’s efforts will be focused on within the study. This helps ensure that the researcher stays on the right path during the study. Finally, by defining the population, the researcher identifies the group that the results will apply to at the conclusion of the study. In the example in table 2.4, the programmer has identified the population of the study as children ages 10 to 12 years. This narrower population makes the study more manageable in terms of time and resources.

**Step 6: Develop the Instrumentation Plan**

The plan for the study is referred to as the instrumentation plan. The instrumentation plan serves as the road map for the entire study, specifying who will participate in the study; how, when, and where data will be collected; and the content of the program. This plan is composed of numerous decisions and considerations that are addressed in chapter 8 of this text. In the obesity study, the researcher has decided to have the children participate in a walking program for six months. The group of participants is called the sample, which is a smaller group selected from the population specified for the study. The study cannot possibly include every 10- to 12-year-old child in the community, so a smaller group is used to represent the population. The researcher develops the plan for the walking program, indicating what data will be collected, when and how the data will be collected, who will collect the data, and how the data will be analyzed. The instrumentation plan specifies all the steps that must be completed for the study. This ensures that the programmer has carefully thought through all these decisions and that she provides a step-by-step plan to be followed in the study.

**Step 7: Collect Data**

Once the instrumentation plan is completed, the actual study begins with the collection of data. The collection of data is a critical step in providing the information needed to answer the research question. Every study includes the collection of some type of data—whether it is from the literature or from subjects—to answer the research question. Data can be collected in the form of words on a survey, with a questionnaire, through observations, or from the literature. In the obesity study, the programmers will be collecting data on the defined variables: weight, percentage of body fat, cholesterol levels, and the number of days the person walked a total of 10,000 steps during the class.

The researcher collects these data at the first session and at the last session of the program. These two sets of data are necessary to determine the effect of the walking program on weight, body fat, and cholesterol level. Once the data are collected on the variables, the researcher is ready to move to the final step of the process, which is the data analysis.

**Step 8: Analyze the Data**

All the time, effort, and resources dedicated to steps 1 through 7 of the research process culminate in this final step. The researcher finally has data to analyze so that the research question can be answered. In the instrumentation plan, the researcher specified how the data will be analyzed. The researcher now analyzes the data according to the plan. The results of this analysis are then reviewed and summarized in a manner directly related to the research questions. In the obesity study, the researcher compares the measurements of weight, percentage of body fat, and cholesterol that were taken at the first meeting of the subjects to the measurements of the same variables at the final program session. These two sets of data will be analyzed to determine if there was a difference between the first measurement and the second measurement for each individual in the program. Then, the data will be analyzed to determine if the differences are statistically significant. If the differences are statistically significant, the study validates the theory that was the focus of the study. The results of the study also provide valuable information about one strategy to combat childhood obesity in the community.** **

## AIOU Solved Assignment Code 4689 Spring 2021

**Discuss the applicability of statistics with examples.**

The scope of statistics is confined to two main aspects – the classification and application of statistics. In this article, we will explore the application of statistics in important areas of our economy.

## Application of Statistics

In the age of information technology, statistics has a wide range of applications. Let’s look at some important areas of application of statistics:

State

For the effective functioning of the State, Statistics is indispensable. Different department and authorities require various facts and figures on different matters. They use this data to frame policies and guidelines in order to perform smoothly.

Traditionally, people used statistics to collect data pertaining to manpower, crimes, wealth, income, etc. for the formation of suitable military and fiscal policies.

Over the years, with the change in the nature of functions of the State from maintaining law and order to promoting human welfare, the scope of the application of statistics has changed too.

Today, the State authorities collect statistics through their agencies on multiple aspects like population, agriculture, defense, national income, oceanography, natural resources, space research, etc.

Further, nearly all ministries at the Central as well as State level, rely heavily on statistics for their smooth functioning. Also, the availability of statistical information enables the government to frame policies and guidelines to improve the overall working of the system.

Economics

Economics is about allocating limited resources among unlimited ends in the most optimal manner. Statistics offers information to answer some basic questions in economics –

- What to produce?
- How to produce?
- For whom to produce?

Statistical information helps to understand the economic problems and formulation of economic policies. Traditionally, the application of statistics was limited since the economic theories were based on deductive logic. Also, most statistical techniques were not developed enough for application in all disciplines.

However, today, with computers and information technology, statistical data and advanced techniques of statistical analysis are a boon to many.

In economics, many scholars have now shifted their stand from deductive logic to inductive logic in order to explain any economic proposition. This inductive logic requires the observation of economic behavior of a large number of units. Hence, it needs strong statistical support in the form of data and techniques.

Applications of statistics and its techniques

**Test and Verification of Economic Theories or Principles or Hypothesis**

Economists have developed various theories and principles based on deductive reasoning in the areas of production, distribution, exchange, consumption, business cycles, taxation, etc.

These theories are for academic interest only unless they are put through an empirical test or verification. Statistics enables us to compare these theories in real-life situations.

**The understanding and study of Economic Problems**

Statistics also help us in understanding various economic problems with precision and clarity. Further, it enables us to frame policies in relevant areas for better results.

To give you an example, wealth and income statistics help in the framing of policies for reducing disparities of income. On the other hand, price statistics help us in understanding the problem of inflation and the cost of living in the economy.

**Economic Planning**

Economic planning is an important aspect of a country. For effective economic planning, the authorities require information regarding different components of the economy.

This allows them to plan for the future efficiently. Statistics help in providing data as well as tools to analyze the data. Some powerful techniques are index numbers, time series analysis, and also forecasting. These are immensely useful in the analysis of data in economic planning.

Further, statistical techniques help in framing planning models too. In India, the five-year plans extensively use statistical tools.

**Measurement of National Income and Components**

Statistics also allows the study and measure of various national income components and their compilations. It collects information on income, investment, saving, expenditure, etc and establishes the relationships between them.

Business Management and Industry

In today’s world, business management is a complex process. This is due to a change in:

- Size
- Technical know-how
- Quantum of production
- Number of employees
- Capital deployed
- Competition levels, etc.

Also, while planning, organizing, controlling, and communicating, the management is confronted with many alternative courses of action. The trial and error method is not a great way of making decisions.

Therefore, statistical data and powerful statistical techniques of probability, expectations, sampling, significance test, estimation theory, forecasting, etc. play an important role.

According to **Chao**, “Statistics is a method of decision-making in the face of uncertainty on the basis of numerical data and calculated risks.” Hence, statistics provides information to businesses which help them in making critical decisions. Further, in Industry, Statistics helps in the field of Quality Control.

Social Sciences and Natural Science

In social sciences, especially sociology, statistics are used in the field of demography for studying mortality, fertility, marriage, population, and growth. Also, in psychology and education, the intelligence quotient (IQ) is determined using statistics.

Biology and Medicine

In biology and medical sciences, there is regular use of statistical tools for collecting, presenting, and also analyzing the observed data pertaining to the causes of the incidence of diseases.

For example, the statistical pulse rate, body temperature, blood pressure, etc. of the patients helps the physician in diagnosing the disease properly. Additionally, statistics help in testing the efficacy of manufacturing drugs or injections or medicines for controlling or curing certain diseases.

## AIOU Solved Assignment 1 Code 4689 Spring 2021

**What is frequency distribution? Name the steps to be followed, whole making a frequency distribution for continuous data.**

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In statistics, the frequency (or absolute frequency) of an event is the number of times the event occurred in an experiment or study. These frequencies are often graphically represented in histograms. The relative frequency (or empirical probability) of an event refers to the absolute frequency normalized by the total number of events. The values of all events can be plotted to produce a frequency distribution.

A histogram is a graphical representation of tabulated frequencies, shown as adjacent rectangles, erected over discrete intervals (bins), with an area equal to the frequency of the observations in the interval. The height of a rectangle is also equal to the frequency density of the interval, i.e., the frequency divided by the width of the interval. The total area of the histogram is equal to the number of data. An example of the frequency distribution of letters of the alphabet in the English language is shown in the histogram in.

A histogram may also be normalized displaying relative frequencies. It then shows the proportion of cases that fall into each of several categories, with the total area equaling 1. The categories are usually specified as consecutive, non-overlapping intervals of a variable. The categories (intervals) must be adjacent, and often are chosen to be of the same size. The rectangles of a histogram are drawn so that they touch each other to indicate that the original variable is continuous.

There is no “best” number of bins, and different bin sizes can reveal different features of the data. Some theoreticians have attempted to determine an optimal number of bins, but these methods generally make strong assumptions about the shape of the distribution. Depending on the actual data distribution and the goals of the analysis, different bin widths may be appropriate, so experimentation is usually needed to determine an appropriate width.

A relative frequency is the fraction or proportion of times a value occurs. To find the relative frequencies, divide each frequency by the total number of data points in the sample. Relative frequencies can be written as fractions, percents, or decimals.

Constructing a relative frequency distribution is not that much different than from constructing a regular frequency distribution. The beginning process is the same, and the same guidelines must be used when creating classes for the data. Recall the following:

- Each data value should fit into one class only (classes are mutually exclusive).
- The classes should be of equal size.
- Classes should not be open-ended.
- Try to use between 5 and 20 classes.

Create the frequency distribution table, as you would normally. However, this time, you will need to add a third column. The first column should be labeled Class or Category. The second column should be labeled Frequency. The third column should be labeled Relative Frequency. Fill in your class limits in column one. Then, count the number of data points that fall in each class and write that number in column two.

Next, start to fill in the third column. The entries will be calculated by dividing the frequency of that class by the total number of data points. For example, suppose we have a frequency of 5 in one class, and there are a total of 50 data points. The relative frequency for that class would be calculated by the following:

5 / 50=0.10

You can choose to write the relative frequency as a decimal (0.10), as a fraction (1/10), or as a percent (10%). Since we are dealing with proportions, the relative frequency column should add up to 1 (or 100%). It may be slightly off due to rounding.

Relative frequency distributions is often displayed in histograms and in frequency polygons. The only difference between a relative frequency distribution graph and a frequency distribution graph is that the vertical axis uses proportional or relative frequency rather than simple frequency.

A plot is a graphical technique for representing a data set, usually as a graph showing the relationship between two or more variables. Graphs of functions are used in mathematics, sciences, engineering, technology, finance, and other areas where a visual representation of the relationship between variables would be useful. Graphs can also be used to read off the value of an unknown variable plotted as a function of a known one. Graphical procedures are also used to gain insight into a data set in terms of:

- testing assumptions,
- model selection,
- model validation,
- estimator selection,
- relationship identification,
- factor effect determination, or
- outlier detection.

Plots play an important role in statistics and data analysis. The procedures here can broadly be split into two parts: quantitative and graphical. Quantitative techniques are the set of statistical procedures that yield numeric or tabular output. Some examples of quantitative techniques include:

- hypothesis testing,
- analysis of variance,
- point estimates and confidence intervals, and
- least squares regression.

There are also many statistical tools generally referred to as graphical techniques which include:

- scatter plots,
- histograms,
- probability plots,
- residual plots,
- box plots, and
- block plots.

Below are brief descriptions of some of the most common plots:

Scatter plot: This is a type of mathematical diagram using Cartesian coordinates to display values for two variables for a set of data. The data is displayed as a collection of points, each having the value of one variable determining the position on the horizontal axis and the value of the other variable determining the position on the vertical axis. This kind of plot is also called a scatter chart, scattergram, scatter diagram, or scatter graph.

Histogram: In statistics, a histogram is a graphical representation of the distribution of data. It is an estimate of the probability distribution of a continuous variable or can be used to plot the frequency of an event (number of times an event occurs) in an experiment or study.

Box plot: In descriptive statistics, a boxplot, also known as a box-and-whisker diagram, is a convenient way of graphically depicting groups of numerical data through their five-number summaries (the smallest observation, lower quartile (Q1), median (Q2), upper quartile (Q3), and largest observation). A boxplot may also indicate which observations, if any, might be considered outliers.

## AIOU Solved Assignment 2 Code 4689 Spring 2021

**What is a Pie Diagram? Construct a Pie Diagram for the following data: Total production of urea is 300 thousand kg and its consumption for different crops rice, wheat, sugarcane and maize is 90, 105, 70 and 35 thousand kg respectively. What results can you deduce form the diagram? **

A **pie chart** (or a **circle chart**) is a circular statistical graphic, which is divided into slices to illustrate numerical proportion. In a pie chart, the arc length of each slice (and consequently its central angle and area), is proportional to the quantity it represents. While it is named for its resemblance to a pie which has been sliced, there are variations on the way it can be presented. The earliest known pie chart is generally credited to William Playfair‘s Statistical Breviary of 1801.

Pie charts are very widely used in the business world and the mass media. However, they have been criticized, and many experts recommend avoiding them, as research has shown it is difficult to compare different sections of a given pie chart, or to compare data across different pie charts. Pie charts can be replaced in most cases by other plots such as the bar chart, box plot, dot plot, etc.

From diagram, urea is most important for wheat.

## AIOU Solved Assignment Code 4689 Autumn 2021

**What is a bar graph? When do we use a multi-bar graph and a sub-divided bar graph? Give examples of each. **

A** bar chart** is a graph with rectangular bars. The graph usually compares different categories. Although the graphs can be plotted vertically (bars standing up) or horizontally (bars laying flat from left to right), the most usual type of bar graph is vertical.

The horizontal (x) axis represents the categories; The vertical (y) axis represents a value for those categories. In the graph below, the values are percentages.

A bar graph is useful for looking at a set of data and making comparisons. For example, it’s easier to see which items are taking the largest chunk of your budget by glancing at the above chart rather than looking at a string of numbers. They can also shows trends over time, or reveal patterns in periodic sequences.

Bar charts can also represent more **complex categories** with stacked bar charts or grouped bar charts. For example, if you had two houses and needed budgets for each, you could plot them on the same x-axis with a grouped bar chart, using different colors to represent each house.

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## Bar Graph Examples (Different Types)

A bar graph **compares different categories**. The bars can be vertical or horizontal. It doesn’t matter which type you use—it’s a matter of choice (and perhaps how much room you have on your paper!).

A bar chart with vertical bars. Categories are on the x-axis.

Bar chart with horizontal bars. Categories are on the y-axis. Image: SAMHSA.gov.

# Bar Chart / Bar Graph: Examples, Excel Steps & Stacked Graphs**Contents**:

## What is a Bar Chart?

A** bar chart** is a graph with rectangular bars. The graph usually compares different categories. Although the graphs can be plotted vertically (bars standing up) or horizontally (bars laying flat from left to right), the most usual type of bar graph is vertical.

The horizontal (x) axis represents the categories; The vertical (y) axis represents a value for those categories. In the graph below, the values are percentages.

A bar graph is useful for looking at a set of data and making comparisons. For example, it’s easier to see which items are taking the largest chunk of your budget by glancing at the above chart rather than looking at a string of numbers. They can also shows trends over time, or reveal patterns in periodic sequences.

Bar charts can also represent more **complex categories** with stacked bar charts or grouped bar charts. For example, if you had two houses and needed budgets for each, you could plot them on the same x-axis with a grouped bar chart, using different colors to represent each house. See types of bar graphs below.

## Difference Between a Histogram and a Bar Chart

Although they look the same, bar charts and histograms have one important difference: **they plot different types of data.** Plot discrete data on a bar chart, and plot continuous data on a histogram *What’s the difference between discrete and continuous data?*).

A bar chart is used for when you have **categories of data:** Types of movies, music genres, or dog breeds. It’s also a good choice when you want to compare things between different groups. You *could* use a bar graph if you want to track change over time as long as the changes are significant (for example, decades or centuries). If you have** continuous data**, like people’s weights or IQ scores, a histogram is best.

## Bar Graph Examples (Different Types)

A bar graph **compares different categories**. The bars can be vertical or horizontal. It doesn’t matter which type you use—it’s a matter of choice (and perhaps how much room you have on your paper!).

A bar chart with vertical bars. Categories are on the x-axis.

Bar chart with horizontal bars. Categories are on the y-axis. Image: SAMHSA.gov.

## AIOU Solved Assignment Code 4689 Autumn 2021

## List of Types

## 1. Grouped Bar Graph

A grouped bar graph is a way to show information about sub-groups of the main categories.

In the above image, the categories are issues that senior citizens face (hearing loss and mobility issues); the sub-groups are age. A separate colored bar represents each sub-group: blue for age 70-79 and red for age 80-100.

A key or legend is usually included to let you know what each sub-category is. Like regular bar charts, grouped bar charts can also be drawn with horizontal bars.

When there are only two sub-groups (as in the above image), the graph is called a** double bar graph.** It’s possible to have as many sub-groups as you like, although too many can make the graph look cluttered.

## 2. Stacked Bar Chart

A stacked bar chart also shows sub-groups, but the sub-groups are stacked on the same bar.

Stacked bar chart showing list price change announcements by company.

Each bar shows the total for sub-groups within each individual category.

Stacked bar chart showing list price change announcements by company.

Like the double bar chart, different colors represent different sub-groups. This type of chart is a good choice if you:

- Want to show the total size of groups.
- Are interested in showing how the proportions between groups related to each other, in addition to the total of each group.
- Have data that naturally falls into components, like:
- Sales by district.
- Book sales by type of book.

Stacked bar charts can also show** negative values**; negative values are displayed below the x-axis.

### 3. Segmented Bar Graph.

A type of stacked bar chart where each bar shows 100% of the discrete value. They should represent **100% on each of the bars** or else it’s going to be an ordinary stacked bar chart. For more on this particular type of graph, see: Segmented Bar Charts.

**Example problem:** Make a bar graph that represents exotic pet ownership in the United States. There are:

- 8,000,000 fish,
- 1,500,000 rabbits,
- 1,300,000 turtles,
- 1,000,000 poultry
- 900,000 hamsters.

Step 1: **Number the Y-axis** with the dependent variable. The dependent variable is the one being tested in an experiment. In this example question, the study wanted to know how many pets were in U.S. households. So the number of pets is the dependent variable. The highest number in the study is 8,000,000 and the lowest is 1,000,000 so it makes sense to label the Y-axis from 0 to 8.

Step 2: **Draw your bars.** The height of the bar should be even with the correct number on the Y-axis. Don’t forget to label each bar under the x-axis.

Step 3: **Label the X-axis** with what the bars represent. For this example problem, label the x-axis “Pet Types” and then label the Y-axis with what the Y-axis represents: “Number of pets (per 1,000 households).” Finally, give your graph a name. For this example, call the graph “Pet ownership (per 1,000 households).

**Optional:** In the above graph, I chose to write the actual numbers on the bars themselves. You don’t have to do this, but if you have numbers than don’t fall on a line (i.e. 900,000), then it can help make the graph clearer for a viewer.

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