IGNOU BPC 004 Solved Assignment 2022-23

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Submission Date :

31st March 2033 (if enrolled in the July 2033 Session)
30th Sept, 2033 (if enrolled in the January 2033 session).

All questions are compulsory.

Section A

Answer the following questions in 1000 words each. 3 x 15 = 45 marks

1. Define statistics and describe its types, scope and uses.

Statistics, the science of collecting, analyzing, presenting, and interpreting data. Governmental needs for census data as well as information about a variety of economic activities provided much of the early impetus for the field of statistics. Currently the need to turn the large amounts of data available in many applied fields into useful information has stimulated both theoretical and practical developments in statistics.

Data are the facts and figures that are collected, analyzed, and summarized for presentation and interpretation. Data may be classified as either quantitative or qualitative. Quantitative data measure either how much or how many of something, and qualitative data provide labels, or names, for categories of like items. For example, suppose that a particular study is interested in characteristics such as age, gender, marital status, and annual income for a sample of 100 individuals. These characteristics would be called the variables of the study, and data values for each of the variables would be associated with each individual. Thus, the data values of 28, male, single, and $30,000 would be recorded for a 28-year-old single male with an annual income of $30,000. With 100 individuals and 4 variables, the data set would have 100 × 4 = 400 items. In this example, age and annual income are quantitative variables; the corresponding data values indicate how many years and how much money for each individual. Gender and marital status are qualitative variables. The labels male and female provide the qualitative data for gender, and the labels single, married, divorced, and widowed indicate marital status.

Sample survey methods are used to collect data from observational studies, and experimental design methods are used to collect data from experimental studies. The area of descriptive statistics is concerned primarily with methods of presenting and interpreting data using graphs, tables, and numerical summaries. Whenever statisticians use data from a sample—i.e., a subset of the population—to make statements about a population, they are performing statistical inference. Estimation and hypothesis testing are procedures used to make statistical inferences. Fields such as health care, biology, chemistry, physics, education, engineering, business, and economics make extensive use of statistical inference.

Methods of probability were developed initially for the analysis of gambling games. Probability plays a key role in statistical inference; it is used to provide measures of the quality and precision of the inferences. Many of the methods of statistical inference are described in this article. Some of these methods are used primarily for single-variable studies, while others, such as regression and correlation analysis, are used to make inferences about relationships among two or more variables.

Descriptive statistics

Descriptive statistics are tabular, graphical, and numerical summaries of data. The purpose of descriptive statistics is to facilitate the presentation and interpretation of data. Most of the statistical presentations appearing in newspapers and magazines are descriptive in nature. Univariate methods of descriptive statistics use data to enhance the understanding of a single variable; multivariate methods focus on using statistics to understand the relationships among two or more variables. To illustrate methods of descriptive statistics, the previous example in which data were collected on the age, gender, marital status, and annual income of 100 individuals will be examined.

Tabular methods

The most commonly used tabular summary of data for a single variable is a frequency distribution. A frequency distribution shows the number of data values in each of several nonoverlapping classes. Another tabular summary, called a relative frequency distribution, shows the fraction, or percentage, of data values in each class. The most common tabular summary of data for two variables is a cross tabulation, a two-variable analogue of a frequency distribution.

For a qualitative variable, a frequency distribution shows the number of data values in each qualitative category. For instance, the variable gender has two categories: male and female. Thus, a frequency distribution for gender would have two nonoverlapping classes to show the number of males and females. A relative frequency distribution for this variable would show the fraction of individuals that are male and the fraction of individuals that are female.

Constructing a frequency distribution for a quantitative variable requires more care in defining the classes and the division points between adjacent classes. For instance, if the age data of the example above ranged from 22 to 78 years, the following six nonoverlapping classes could be used: 20–29, 30–39, 40–49, 50–59, 60–69, and 70–79. A frequency distribution would show the number of data values in each of these classes, and a relative frequency distribution would show the fraction of data values in each.

A cross tabulation is a two-way table with the rows of the table representing the classes of one variable and the columns of the table representing the classes of another variable. To construct a cross tabulation using the variables gender and age, gender could be shown with two rows, male and female, and age could be shown with six columns corresponding to the age classes 20–29, 30–39, 40–49, 50–59, 60–69, and 70–79. The entry in each cell of the table would specify the number of data values with the gender given by the row heading and the age given by the column heading. Such a cross tabulation could be helpful in understanding the relationship between gender and age.

Graphical methods

A number of graphical methods are available for describing data. A bar graph is a graphical device for depicting qualitative data that have been summarized in a frequency distribution. Labels for the categories of the qualitative variable are shown on the horizontal axis of the graph. A bar above each label is constructed such that the height of each bar is proportional to the number of data values in the category. A bar graph of the marital status for the 100 individuals in the above example is shown in Figure 1. There are 4 bars in the graph, one for each class. A pie chart is another graphical device for summarizing qualitative data.

A histogram is the most common graphical presentation of quantitative data that have been summarized in a frequency distribution. The values of the quantitative variable are shown on the horizontal axis. A rectangle is drawn above each class such that the base of the rectangle is equal to the width of the class interval and its height is proportional to the number of data values in the class.

Numerical measures

A variety of numerical measures are used to summarize data. The proportion, or percentage, of data values in each category is the primary numerical measure for qualitative data. The mean, median, mode, percentiles, range, variance, and standard deviation are the most commonly used numerical measures for quantitative data. The mean, often called the average, is computed by adding all the data values for a variable and dividing the sum by the number of data values. The mean is a measure of the central location for the data. The median is another measure of central location that, unlike the mean, is not affected by extremely large or extremely small data values. When determining the median, the data values are first ranked in order from the smallest value to the largest value. If there is an odd number of data values, the median is the middle value; if there is an even number of data values, the median is the average of the two middle values. The third measure of central tendency is the mode, the data value that occurs with greatest frequency.

Percentiles provide an indication of how the data values are spread over the interval from the smallest value to the largest value. Approximately p percent of the data values fall below the pth percentile, and roughly 100 − p percent of the data values are above the pth percentile. Percentiles are reported, for example, on most standardized tests. Quartiles divide the data values into four parts; the first quartile is the 25th percentile, the second quartile is the 50th percentile (also the median), and the third quartile is the 75th percentile.

The range, the difference between the largest value and the smallest value, is the simplest measure of variability in the data. The range is determined by only the two extreme data values. The variance (s²) and the standard deviation (s), on the other hand, are measures of variability that are based on all the data and are more commonly used. Equation 1 shows the formula for computing the variance of a sample consisting of n items. In applying equation 1, the deviation (difference) of each data value from the sample mean is computed and squared. The squared deviations are then summed and divided by n − 1 to provide the sample variance.

The standard deviation is the square root of the variance. Because the unit of measure for the standard deviation is the same as the unit of measure for the data, many individuals prefer to use the standard deviation as the descriptive measure of variability.

2. Calculate Spearman’s Rank Order Correlation for the following data:

ignou bpc 004 solved assignment 2022-23

3. The scores obtained by the two groups of employees on self concept scale are given as follows, compute t test and find if significant difference exists between the two groups:

ignou bpc 004 solved assignment 2022-23

Section B

Answer the following questions in 400 words each. 5 x 5 = 25 marks

4. Compute mean and standard deviation for the following data:
12,13,14,15,16, 23, 23,12,12,10

5. Describe tabulation of data.

6. What are linear and non-linear relationships? Explain the direction of correlation.

7. Compute Chi-square for the following data:

8. Explain the fundamental concepts in determining the significance of the difference
between means.

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Section C

Answer the following questions in 50 words each. 10 x 3 = 30 marks

9. Cumulative frequency curve
10. Point estimation
11. Frequency polygon
12. Dispersion
13. Properties of quartile deviation
14. Scatter diagram
15. Parametric statistics
16. Kendall’s tau
17. Test of goodness of fit
18. Types of probability

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