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

Paper Name: Statistical Data Analysis Using R

Course No: STASEC-151

Year: 2025

Subject: Statistics (Skill Enhancement Course)

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).