Decision Science December 2026
Q.1: A university wants to study the factors influencing the academic performance of postgraduate students. A researcher collects data on students’ specialization, socioeconomic status, satisfaction with the programme, CGPA, monthly family income, number of hours spent studying per week, and the distance travelled by students to reach the university. Students are also asked to rate the quality of teaching on a scale from 1 to 5.
As a researcher, identify and justify the level of measurement of each variable in the above study. Explain how the nature of these measurement levels affects the type of comparison and statistical analysis that can appropriately be performed on the variables.
Answer:
Introduction:
In research, the level of measurement is a classification that refers to the different ways in which a variable can be measured. It also includes the mathematical expressions that can be used to describe the data. In any study, it is essential to define the measurement level because it defines the comparisons and statistical operations that can be performed. In the proposed research, the university wants to determine the factors that may affect postgraduate students’ academic performance. The factors include specialization, socioeconomic status, program satisfaction, CGPA, family income per month, hours of study per week, distance from residence to university, and quality of teaching, which is marked from 1 to 5. All these variables can be measured using different levels of measurements. Some variables represent categories, while others are expressed as numbers. Because of this, the researcher must discuss the variables based on their levels of measurement, including nominal, ordinal, interval, and ratio.
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Q.2: The following distribution shows the monthly expenditure (Rs.) of 100 households:
Monthly Expenditure |
No. of Households |
0 - 2000 |
12 |
2000 - 4000 |
18 |
4000 - 6000 |
25 |
6000 - 8000 |
20 |
8000 - 10000 |
15 |
10000 - 12000 |
6 |
12000 - 14000 |
4 |
Calculate the median monthly expenditure using the appropriate formula for grouped data and interpret the result in the context of household expenditure.
Answer:
Introduction:
The median is a method used to identify the middle value of a set of ordered observations. In the case of grouped data, the values of the expenditure for each household are not known; instead, we know the ranges or classes of expenditure. Therefore, we use the median formula for continuous grouped frequency distribution to estimate the median expenditure for the data set of 100 households. The monthly expenditure of 100 households is divided into seven classes or ranges of ₹0-₹2,000, ₹2,000-₹4,000, ₹4,000-₹6,000, ₹6,000-₹8,000, ₹8,000- ₹10,000, ₹10,000- ₹12,000, ₹12,000- ₹14,000. The number of households in each range or class of expenditure is given by the frequencies below the respective classes. To compute the median, we will use the concept of cumulative frequencies. Using the cumulative frequency, we can identify the median class and then substitute the necessary values in the grouped-data median formula to obtain the median expenditure value for the households.
Q.3 (A): A speaks the truth in 75% cases and B in 80% cases. In what percentage of cases are they likely to contradict each other?
Answer:
Introduction:
The concept of probability is used to define the chance of an event occurring. The problem states that A speaks the truth in 75% of the cases whereas B speaks the truth in 80% of the cases. Therefore, it can be concluded that A lies in 25% of the cases and B lies in 20% of the cases. Contradiction occurs when one person speaks the truth and the other one lies. Therefore, to calculate the chances of contradiction we need to add up the probability of A speaking the truth and B lying to the probability of A lying and B speaking the truth. This will give us the percentage of cases in which A and B contradict each other.
Q.3 (B): The mean weight of 400 students at a college is 60 kgs. and standard deviation is 10 kgs. Assuming that weights are normally distributed, find out as to how many students, weight is Between 45 and 65 kgs.
The following values from the Standard Normal Distribution Table are provided.
Students are required to select the appropriate value(s) from the table.
0.50 |
0.1915 |
0.84 |
0.2995 |
1.00 |
0.3413 |
1.28 |
0.3997 |
1.50 |
0.4332 |
1.64 |
0.4495 |
1.96 |
0.475 |
2.00 |
0.4772 |
Answer:
Introduction:
The problem involves finding the number of college students that weigh between 45 kg and 65 kg out of a total of 400 students. It is given that the weights of the students are normally distributed with a mean 60 kg and a standard deviation of 10 kg. We have to first convert the weights 45 kg and 65 kg into Z-scores by using the standard normal distribution formula. The results obtained from the given Standard Normal Distribution Table values will be used to calculate the percentage of students that weigh between 45 kg and 65 kg. Finally, we multiply by the total number of students (400) to get the required number of students.