IGNOU BECC 107 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).

Answer the following Descriptive Category questions in about 500 words each. Each question carries 20 marks. Word limit does not apply in case of numerical questions in Assignment One.

Answer the following Middle Category questions in about 250 words each. Each question carries 10 marks. Word limit does not apply in case of numerical questions in Assignment Two.

Answer the following Short Category questions in about 100 words each. Each question carries 6 marks in Assignment Three.

Answer all the questions.

Assignment One

1) (a) Bring out the salient features of normal distribution. What is the need for a
standard normal distribution?

In a normal distribution, data is symmetrically distributed with no skew. When plotted on a graph, the data follows a bell shape, with most values clustering around a central region and tapering off as they go further away from the center.

Normal distributions are also called Gaussian distributions or bell curves because of their shape.

All kinds of variables in natural and social sciences are normally or approximately normally distributed. Height, birth weight, reading ability, job satisfaction, or SAT scores are just a few examples of such variables.

Because normally distributed variables are so common, many statistical tests are designed for normally distributed populations.

Understanding the properties of normal distributions means you can use inferential statistics to compare different groups and make estimates about populations using samples.

Normal distributions have key characteristics that are easy to spot in graphs:

The mean, median and mode are exactly the same.
The distribution is symmetric about the mean—half the values fall below the mean and half above the mean.
The distribution can be described by two values: the mean and the standard deviation.

The mean is the location parameter while the standard deviation is the scale parameter.

The mean determines where the peak of the curve is centered. Increasing the mean moves the curve right, while decreasing it moves the curve left.

The standard deviation stretches or squeezes the curve. A small standard deviation results in a narrow curve, while a large standard deviation leads to a wide curve.

Empirical rule

The empirical rule, or the 68-95-99.7 rule, tells you where most of your values lie in a normal distribution:

Around 68% of values are within 1 standard deviation from the mean.
Around 95% of values are within 2 standard deviations from the mean.
Around 99.7% of values are within 3 standard deviations from the mean.

(b) Find out the area under the standard normal curve for each of the following
(use z-table). Sketch each one of them.
(i) between z = 0 and z = – 0.78
(ii) between z = – 0.62 and z = 0
(iii) between z = – 0.45 and z = 0.87
(iv) between z = 0.5 and z = 1.5
(v) to the right of z = – 1.33.

2) Differentiate between seasonal variation and cyclical fluctuations in time series data. Outline the steps of the ratio-to-trend method.

Time series refers to an arrangement and presentation of statistical data in chronological order. The statistical data is collected over a period of time. According to Spiegel, “A time series is a set of observations taken at specified times, usually at equal intervals.” There exist various forces that affect the values of the phenomenon in a time series. These are also the components of the time series analysis. Learn the definition of Time Series Analysis here.

Definition of Time Series Analysis

Following are the various components of the time series:

Secular Trend or Simple trend or Long term movement: Secular trend refers to the general tendency of data to increase or decrease or stagnate over a long period of time. Time series relating to Economic, Business, and Commerce may show an upward or increasing tendency. Whereas, the time series relating to death rates, birth rates, share prices, etc. may show a downward or decreasing tendency.
Seasonal variations: Seasonal variations refer to the changes that take place due to the rhythmic forces which operate in a regular and periodic manner. These forces usually have the same or most similar pattern year after year. When we record data weekly, monthly or quarterly, we can see and calculate seasonal variations. Thus, when a time series consists of data only based on annual figures, there will be seen no seasonal variations. These variations may be due to seasons, weather conditions, habits, customs or traditions. For example, in summers the sale of ice-cream increases and at the time of Diwali the sale of diyas, crackers, etc. go up.
Cyclical variations: Cyclical variations are due to the ups and downs recurring after a period from time to time. These are due to the business cycle and every organization has to phase all the four phases of a business cycle some time or the other. Prosperity or boom, recession, depression, and recovery are the four phases of a business cycle.
Random or irregular variations: Random variations are fluctuations which are a result of unforeseen and unpredictable forces. These forces operate in an absolutely random or erratic manner and do not have any definite pattern. Thus, these variations may be due to floods, famines, earthquakes, strikes, etc.

Assignment Two

3) Bring out the major properties of binomial distribution. Mention certain important uses
of this distribution.

4) a) Define correlation coefficient. What are its properties?
b) Find out the correlation coefficient from the following data.
X 5 8 10 12 13 15 17 16
Y 8 12 14 10 13 16 14 17

5) Describe the factor reversal test and time reversal test in the context of index number.
Does any index number formula satisfy both the above tests?

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Assignment Three

6) Write short notes on the following in about 100 words each:
(a) Contingency table and chi-squared test
(b) Properties of a good estimator
(c) Measurement of skewness

7) Differentiate between the following:
(a) Estimator and estimate
(b) Type I and Type II errors in hypothesis testing
(c) Sampling error and non-sampling error.

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