Solved 2025: FYUG Even Semester Exam, 2025 STATISTICS (2nd Semester) Course No.: STASEC-151

UNIT-I

Question 1 [1 x 3 = 3]

• (a) Who developed R-programming? R was developed by Ross Ihaka and Robert Gentleman at the University of Auckland, New Zealand.
• (b) Feature of R: R is an open-source language with extensive packages for statistical modeling and high-quality graphics.
• (c) Note on CRAN: The Comprehensive R Archive Network (CRAN) is a network of ftp and web servers around the world that store identical, up-to-date versions of code and documentation for R.
• (d) Remove duplicates: The unique() function is used to remove duplicate observations.

Question 2(a) [2]

R-code for min and max of: 2, 4, 7, 9, 5, 1, 15, 20

data <- c(2, 4, 7, 9, 5, 1, 15, 20)
min_val <- min(data)
max_val <- max(data)

Question 3(b) [5]

Define R. Mention three advantages and disadvantages.

Definition: R is a programming language and free software environment designed specifically for statistical computing and graphics

.

Advantages:

• Open-source and free to use.
• Strong graphical capabilities for data visualization.
• Large community support and over 15,000+ packages.

Disadvantages:

• High memory consumption as it stores all objects in RAM.
• Steeper learning curve compared to some other tools.
• Slower execution speed for some complex computations compared to C++ or Python.

UNIT-II

Question 4 [1 x 3 = 3]

• (a) xlim=c(0,20): This indicates the limits of the x-axis, setting the scale from 0 to 20.
• (c) Logical operators: Operators used include & (AND), | (OR), and ! (NOT).
• (d) xlab and ylab: These are used to provide labels for the x-axis and y-axis respectively.

Question 6(b) [5]

How to draw various diagrams in R:

• (i) Bar diagram: Use barplot(height). Labels and colors can be added using names.arg and col.
• (ii) Histogram: Use hist(x) to visualize the distribution of a continuous variable.
• (iii) Pie diagram: Use pie(x) to show proportions of a whole.
• (iv) Line diagram: Use plot(x, y, type="l") where "l" specifies a line plot.
• (v) Frequency polygon: This can be drawn using plot(density(x)) or by connecting the midpoints of a histogram.

UNIT-III

Question 7(d) [1]

R-code to compute square root of 29:

sqrt(29)

Question 8(a) [2]

Relationship between mean, median, and mode:

• Symmetrical: Mean = Median = Mode.
• Positively Skewed: Mean > Median > Mode.
• Negatively Skewed: Mean < Median < Mode.

Question 9(b) [5]

R-code for mean, median, variance, and SD of: 31, 27, 29, 45, 27, 19, 25

x <- c(31, 27, 29, 45, 27, 19, 25)
mean_val <- mean(x)
median_val <- median(x)
var_val <- var(x)
sd_val <- sd(x)

UNIT-IV

Question 10 [1 x 3 = 3]

• (a) Package for skewness/kurtosis: The moments package is commonly used.
• (c) Transpose of a matrix: Use the t(matrix_name) function.
• (d) Correlation: Use cor(x, y).

Question 11(a) [2]

Note on Kurtosis:

Kurtosis measures the "peakedness" of a distribution relative to a normal distribution

.
• Leptokurtic: Sharply peaked with heavy tails.
• Mesokurtic: Normal distribution.
• Platykurtic: Flat-topped with thin tails.

Question 12(b) [5]

R-code for Spearman's rank correlation:

X <- c(10, 15, 17, 21, 37, 41, 45)
Y <- c(9, 12, 21, 11, 17, 23, 41)
cor(X, Y, method = "spearman")

UNIT-V

Question 13 [1 x 3 = 3]

• (a) R²: The coefficient of determination, representing the proportion of variance in the dependent variable predictable from the independent variable.
• (c) Polynomial degree 2: model <- lm(y ~ poly(x, 2)).
• (d) summary() command: It provides a comprehensive statistical summary of an object, such as coefficients and p-values of a regression model.

Question 15(a) [5]

Simple Linear Regression Equation and R-code:

Equation: Y = β₀ + β₁X + ε

R-code for provided data:

matches <- 1:10
runs <- c(7, 11, 23, 27, 31, 45, 55, 67, 69, 71)
fit <- lm(runs ~ matches)
summary(fit)

Exam Focus Enhancements

Exam Tips

• When asked for R-code, always include the assignment of data to a vector (e.g., x <- c(...)) before the function call.
• In regression questions, mentioning the summary() function is vital as it outputs the results examiners look for.

Common Mistakes

• Confusing var() (variance) with sd() (standard deviation). SD is the square root of variance.
• Forgetting the method = "spearman" argument in the cor() function, which defaults to Pearson correlation.

Important Functions List

• lm(): Linear Models (Regression)
• poly(x, n): Polynomials of degree n
• t(): Transpose of a matrix

Answer Presentation Strategy

For R-programming questions, present code in a clear, monospaced format. [span_49](start_span)When defining statistical terms (like Kurtosis or R²), always pair the mathematical definition with its practical interpretation in data analysis[span_49](end_span).