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Q. What are quartiles, deciles, and percentiles? State the general equation of computing the ith quartile, jth decile, and kth percentile.
Answer. Quartiles are measures like the median. Median divides the series into two equal parts. Extending this concept of median, we have quartiles. Quartiles can be classified into Q1, Q2 and Q3 This divided the series into four equal parts....... Deciles: The values which divides an ordered data set into 10 equal parts. The 5th decile is the median. The values of observations in a data set when arranged in an ordered sequence can be divided into ten equal parts, using nine deciles...... Percentiles The values of observations in a data when arranged in an ordered sequence can be divided into hundred equal parts using ninety nine percentiles, Pi (i = 1, 2,…, 99). In general, the ith percentile is a number that has i% of the data values at or below it and...........
Q. In a railway reservation office, two clerks are engaged in checking reservation forms. On an average, the first clerk (A1) checks 55 per cent of the forms, while the second (A2) checks the remaining. While A1 has an error rate of 0.03 that of A2 is 0.02. A reservation form is selected at random from the total number of forms checked during a day and is discovered to have an error. Find the probabilities that it was checked by A1, and A2, respectively.
Q.The weekly wages of 2000 workmen are normally distributed with mean wage of Rs 70 and wage standard deviation of Rs 5. Estimate the number of workers whose weekly wage are
a. between Rs 70 and Rs 71?
b. between Rs 69 and Rs 73
c. more than Rs 72, and
d. less than Rs 65
Q. A research organization claims that the monthly wages of industrial workers in district X exceeds that of those in district Y by more than Rs 150. Two different samples drawn independently from the two district yielded the following results:
District X: x1 = 648, s12 = 120, and n1 = 100
District Y: x2 = 495, s22 = 140, and n2 = 90
Verify at 0.05 level of significance whether the sample results support the claim of the organization.
Q. What do you mean by decomposition of a time series? State the essential characteristics of the additive and multiplicative models of time series analysis.
Answer. A time series is a sequence of data points, measured typically at successive points in time spaced at uniform time intervals........ Time series methods take into account possible internal structure in the data, Time series data often arise when monitoring..... The analysis of time series consists of two major steps: Identifying the various factors or influences which produce the variations in the time series, and Isolating, analysing and measuring the effect of these factors independently, by holding other things constant. The purpose of decomposition models is to break a time series into its components:
MS-08 Solved Assignment IGNOU MBA
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Q. Write a note on measures of central tendency.
Answer. Measures of central tendency are descriptive statistics that summarize the data with a single number that represents the most typical score within a set of data. We use measures of central tendency because we typically believe that most scores on a scale or responses to an item cluster around the typical or most common score or response in the data set. Consequently, a measure of central tendency is a convenient statistical tool for indicating the most typical score in a set of data. Selecting an appropriate measure of central tendency depends on the measurement scale used to represent a particular variable........... Measures of central tendency identify the middle or centre of a set of data. There are three types: Arithmetic average or mean – the total of items or scores in a set divided by the number of individual items in the set. It may give a distorted picture because of large items at either end of the scale. Median – the middle item in a range of items (often used in pay surveys when the arithmetic mean is likely to be distorted). Mode – the most commonly occurring item in a set of data......... The following are the few requirements to be satisfied by an average or a measure of central tendency: It should be rigidly defined The definition of an average should be clear and rigid so that there must be uniformity in its interpretation by different decision-makers or investigators. There should not be any chance for applying discretion; rather it should be defined by an algebraic formula.........