IGNOU BCA BCS 40 Statistical Techniques Solved Assignment ENGLISH

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BCS 040 (July 2026 - January 2027) - ENGLISH

Course Code: BCS-040
Course Title: Statistical Techniques
Assignment Number: BCA_NEW/BCAOL(III)040/Assign/2024-25
Maximum Marks: 100
Last Date of Submission:
31st October, 2024 (For July 2024 Session)
30th April, 2025 (For January 2025 Session)
Note: This assignment has 16 questions of 80 marks (each question carries equal marks). Answer all the questions. Rest 20 marks are for viva voce. You may use illustrations and diagrams to enhance explanations. Please go through the guidelines regarding assignments given in the Programme Guide for the format of presentation.
Q1: In a study on per capita income for a particular year in a city, the following weekly observations were made:
Per Capita Income: 14K—15K, 15K—16K, 16K—17K, 17K—18K, 18K—19K, 19K—20K
Number of Weeks: 5, 10, 20, 9, 6, 2
Draw a histogram and a frequency polygon on the same scale. Also explain the usefulness of both diagrams in representing grouped data.
Q2: The following data show the age groups of students and the number of regular players in each group:
Age Groups: 15—16, 16—17, 17—18, 18—19, 19—20, 20—21
Number of Students: 200, 270, 340, 360, 400, 300
Number of Regular Players: 150, 152, 170, 180, 180, 120
Apply Chi-Square Statistic and determine whether there is any relationship between age and playing habits of students. Interpret the result clearly.
Q3: The mean marks and standard deviations of students in two subjects are given below:
Subject A: Mean = 36, Standard Deviation = 11
Subject B: Mean = 85, Standard Deviation = 8
Coefficient of correlation between A and B = ±0.66
Determine the two equations of regression and calculate the expected marks in Subject A corresponding to 75 marks obtained in Subject B.
Q4: A drilling machine bores holes with a mean diameter of 0.5230 cm and standard deviation of 0.0032 cm. Calculate the 2-sigma and 3-sigma upper and lower control limits for samples of size 4. Also prepare and explain the control chart.

 

BCS 040 (July 2025 - January 2026) - ENGLISH

Course Code : BCS-040

Course Title  ; Statistical Techniques

Assignment Number : BCA_NEW(III)-040/Assignment/2025-26

Maximum Marks : 100

Weightage : 30%

Last Date of Submission : 31 October, 2025(For July 2025 Session)

30th April, 2026 (For January 2026 Session)

Note: This assignment has 8 questions of 80 marks (each question carries equal marks). Answer all the questions. The rest 20 marks are for viva voce. You may use illustrations and diagrams to enhance explanations.

Q1. The following table shows the distribution of response times (in milliseconds) for a web server over a period of 100 requests:

Response Time (ms)	0–10	10–20	20–30	30–40	40–50	50–60
Number of Requests	8	15	25	30	12	10

(a) Calculate the Mean and Median response time.

(b) Calculate the Standard Deviation of the response times.

(c) Draw a Histogram for the given data.

Q2. To study the relationship between the number of hours spent studying per week and the marks obtained in an examination, a sample of 10 students was taken. The data is as follows:

Study Hours (X)	5	8	10	12	15	4	7	9	11	14
Marks (Y)	55	70	75	80	90	50	65	72	78	85

(a) Calculate the Karl Pearson's coefficient of correlation between Study Hours and Marks.

(b) Determine the two regression equations (Y on X and X on Y).

(c) Predict the marks of a student who studies for 13 hours a week.

Q3. (a) A software company has two divisions, A and B, developing mobile apps. Division A develops 60% of the apps, and Division B develops 40%. It is known that 5% of apps from Division A have bugs, while 8% of apps from Division B have bugs. If an app selected at random is found to have a bug, what is the probability that it was developed by Division A?

(b) A call center receives an average of 4 calls per minute. Assuming a Poisson distribution, find the probability that in a given minute, the call center receives:

(i) Exactly 2 calls.

(ii) At most 1 call.

(Given e⁻⁴ ≈ 0.0183)

Q4. A manufacturer of LED bulbs claims that the average lifespan of their bulbs is 8000 hours. A random sample of 50 bulbs is tested, and it is found that their average lifespan is 7950 hours with a standard deviation of 120 hours.

Test the manufacturer's claim at a 5% level of significance. State your null and alternative hypotheses clearly. (Given Z₀.₀₂₅ = 1.96 for a two-tailed test).

Q5. A survey was conducted to determine if there is a relationship between a person's age group and their preferred mode of online payment. The results are tabulated below:

Age Group	UPI	Credit/Debit Card	Net Banking	Total
18–30	150	60	40	250
31–45	80	70	50	200
46–60	40	50	60	150
Total	270	180	150	600

Using the Chi-Square (χ²) test, determine whether the preferred mode of payment is independent of the age group at a 5% level of significance.

(Given χ² critical value for 4 degrees of freedom at α=0.05 is 9.488).

Q6. (a) Explain the key differences between Simple Random Sampling, Stratified Sampling, and Cluster Sampling. Provide a suitable example for each to illustrate its application.

(b) A random sample of size 100 is taken from a large population. The sample mean is found to be 150 and the population standard deviation is known to be 20. Construct a 95% confidence interval for the population mean. (Given Z₀.₀₂₅ = 1.96).

Q7. An e-commerce company wants to test three different website layouts (Layout A, Layout B, Layout C) to see if they have a significant effect on the average time (in minutes) a user spends on the site. The following data was collected from different user groups:

Layout A	Layout B	Layout C
8	12	13
10	11	15
9	10	14
11	13	16
7	9	12

Perform a one-way ANOVA to test the hypothesis that there is no significant difference between the mean user session times for the three layouts at a 5% level of significance.

(Given F-critical value F(2, 12) at α=0.05 is 3.89).

Q8. (a) The quarterly sales (in thousands of units) of a company from 2022 to 2024 are given below. Calculate the 4-quarterly moving averages to determine the trend.

Year	Q1	Q2	Q3	Q4
2022	30	40	36	44
2023	34	46	40	50
2024	38	52	46	56

(b) Explain the purpose of control charts in Statistical Quality Control (SQC). Differentiate between a pchart and a c-chart with respect to the type of data they monitor.

 

 

 

 

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