Assignments

Stats 1: Weekly Assignments (Consolidated)

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📅 Week 1: Introduction to Data & Descriptive Statistics

Question 1

Identify the sample and population.

• The sample consists of all the engineering institutes of India and the population consists of randomly selected four IITs of India.
• The sample consists of all the IITs of India and the population consists of all the engineering institutes of India.
• The sample consists of all IITs of India and the population consists of randomly selected four IITs of India.
• The sample consists of four randomly selected IITs of India and the population consists of all the engineering institutes of India. Accepted Answer: The sample consists of four randomly selected IITs of India and the population consists of all the engineering institutes of India.

Question 2

The report given by an analyst to the education minister about the status of campus placements states that “The campus placement of B.Tech students is 95% in different engineering institutes of India”. The given statement of analyst is based on which kind of statistical analysis?

• Descriptive Statistics
• Inferential Statistics Accepted Answer: Inferential Statistics

Question 3

Is the conclusion of this study made by analyst on the basis of chosen sample reliable?

• Yes
• No Accepted Answer: No

Question 4

Which of the following statements is/are true?

• Inorganic is a case and Types of Fertilizers is a variable.
• Rice is a case.
• Manure is a case.
• Amount of fertilizers is a variable.
• Nitrogen is a variable. Accepted Answers:

• Manure is a case.
• Amount of fertilizers is a variable.

Question 5

What is the scale of measurement of “Types of Crops”?

• Ordinal Scale
• Nominal Scale
• Interval Scale
• Ratio Scale Accepted Answer: Nominal Scale

Question 6

What kind of variable is “Area of fields”?(More than one option can be correct)

• Categorical
• Numerical
• Discrete
• Continuous Accepted Answers: Numerical, Continuous

Question 7

What is the scale of measurement of “Amount of Fertilizers”?

• Ordinal Scale
• Nominal Scale
• Interval Scale
• Ratio Scale Accepted Answer: Ratio Scale

Question 8

Is the data given in Table 1.1.G structured or unstructured?

• The data is structured
• The data is unstructured Accepted Answer: The data is structured

Question 9

The data of Netflix subscribers at the end of year 2020 across different Asian countries is recorded. Based on this, choose the correct option:

• It is time series data
• It is cross-sectional data Accepted Answer: It is cross-sectional data

Question 10

Choose the correct statement(s):

• Stock price of a company is numeric and continuous variable.
• Number of assignments submitted by a student has an interval scale of measurement.
• Soccer positions (i.e. Defender, Midfielder, Forward) has an ordinal scale of measurement.
• The education level of a person has an ordinal scale of measurement. Accepted Answers:

• Stock price of a company is numeric and continuous variable.
• The education level of a person has an ordinal scale of measurement.

Question 11

A researcher studying the spread of misinformation on social media defines a new metric called “Influence Score”, calculated as:
Influence Score = Number of reshares × Average reach per reshare
Which of the following statements most accurately describes the type and scale of the “Influence Score” variable?

• It is a categorical variable because it is based on behavioral data.
• It is a continuous variable that is measured on an interval scale.
• It is a quantitative variable derived from other data and measured on a ratio scale.
• It is an ordinal variable, as it ranks users according to their influence. Accepted Answer: It is a quantitative variable derived from other data and measured on a ratio scale.

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📅 Week 2: Graphical Representation of Data

Question 1

Which of the following statements is/are incorrect?

• To represent the share of a particular category, bar chart is the most appropriate graphical representation.
• The multiplication of the total number of observations and relative frequency of a particular observation should be equal to the frequency of that observation.
• Mean can be defined for a categorical variable.
• Mode of a categorical variable is the widest slice in a pie chart. Accepted Answers:

• To represent the share of a particular category, bar chart is the most appropriate graphical representation.
• Mean can be defined for a categorical variable.

Question 2

If the exam is for a total of 500 marks, then what is the aggregate distribution of marks in Physics, Maths and Biology? Accepted Answer: 315

Question 3

Choose the correct statement(s):

• The pie chart is misleading because it does not obey the area principle.
• The pie chart has round off errors.
• The pie chart is not a misleading graph.
• The slices of pie chart adds up to 100%. Accepted Answers:

• The pie chart is not a misleading graph.
• The slices of pie chart adds up to 100%.

Question 4

What is the combined relative frequency of the academy $A,B$ and $D$? (Enter the answer correct to 3 decimal places) Accepted Answer: 0.375 (Range: 0.370 - 0.380)

Question 5

Median of the given data is:

• Academy C
• Academy E
• Academy D
• Median is not defined for the given data
• Insufficient data Accepted Answer: Median is not defined for the given data

Question 6

Mode of the given data is:

• Academy C
• Academy E
• Academy D
• Mode is not defined for the given data
• Insufficient data Accepted Answer: Academy E

Question 7

Which of the following graphical representations is appropriate for the number of players in each academy?

• Bar chart
• Pie chart
• Pareto chart
• Both bar chart and pareto chart Accepted Answer: Both bar chart and pareto chart

Question 8

Which of the following is/are suitable to represent categorical frequency?

• Accepted Answer: Figure showing Bar Chart.

Question 9

Choose the correct statement about categorical data:

• Categorical data have measurement units.
• Categorical data can take numerical values, but no meaningful mathematical operations can be performed on it.
• Categorical data is quantitative in nature.
• All of the above Accepted Answer: Categorical data can take numerical values, but no meaningful mathematical operations can be performed on it.

Question 10

How many students have secured B grade? Accepted Answer: 26

Question 11

What is the ratio of the students who secured a C grade to the students who secured an A grade? Accepted Answer: 0.9

Question 12

What is the mode of the placement sectors?

• Software
• Analytics
• Core
• Mode is not defined Accepted Answer: Software

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📅 Week 3: Measures of Central Tendency & Dispersion

Question 1

The numbers 2, 6, 11, 14 have frequencies $x+6$, $x+2$, $x-3$ and $x$ respectively. If their mean is 5.63, find the value of $x$. Accepted Answer: 4

Question 2

The mean and sample standard deviation of the dataset consisting of 6 observations is 19 and 9 respectively. Later it is noted that one observation 11 is wrongly noted as 7. What is the mean of the original dataset? Accepted Answer: 19.67

Question 3

Following Question 2, what is the sample variance of the original dataset? Accepted Answer: 64.47

Question 4

Let the data 75, 25, 29, 75, 83, 24 represent retail prices. What will be the sample variance if 4 rupees is added to all prices? Accepted Answer: 812.17

Question 5

Suppose, we have 6 observations: 37, 30, 28, 37, 82, 112. Calculate 10th, 50th and 100th percentiles? Accepted Answer: 28, 37.0, 112

Question 6

Suppose, we have 10 observations: 39, 46, 44, 30, 73, 96, 91, 115, 112, 89. Calculate the IQR. Accepted Answer: 52

Question 7

Following Question 6, how many outliers are there? Accepted Answer: 0

Question 8

In a deck, cards numbered 1 to 21 have frequency equal to the card number. Find mean and mode.

• Mode is 21.
• Mean is 14.33. Accepted Answer: Mode=21, Mean=14.33

Question 9

From a stem and leaf plot, what is the Inter Quartile Range (IQR)? Accepted Answer: ~36.0 (Range: 35.7, 36.3)

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📅 Week 4: Correlation & Regression

Question 2

What is the population standard deviation of sales? Accepted Answer: 2.12

Question 4

What is the sample co-variance between two sales variables? Accepted Answer: 2.43

Question 5

What is the correlation coefficient between sales? Accepted Answer: 0.49

Question 6

Linear relationship assessment:

• Positive
• Moderate Accepted Answers: Positive, Moderate

Question 9

What proportion of total students are dull? Accepted Answer: 0.23 (Range: 0.2-0.26)

Question 14

Bharat’s sales were exactly 1000 rupees more than twice Anjali’s. Correlation coefficient?

• The correlation coefficient between A and B is equal to 1. Accepted Answer: 1 (Perfect linear relation)

Question 15

Screen time vs Sleep Duration relationship:

• There is a negative correlation.
• The scatter plot would display a negative trend. Accepted Answers: Negative correlation, Negative trend.

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📅 Week 5: Permutations & Combinations

Question 1

How many ways to arrange 4 items (A, B, C, D) in 4 slots? Accepted Answer: 24

Question 2

How many license plates can be formed using 2 letters followed by 3 digits (repetition allowed)? Accepted Answer: 676000 ($26\times 26\times 10^3$)

Question 3

How many ways to choose a committee of 3 from 10 people? Accepted Answer: 120

Question 4

$P(n,2)=90$. Find $n$. Accepted Answer: 10

Question 5

How many ways to arrange the letters of “STATISTICS”? Accepted Answer: 50400 ($\frac{10!}{3!3!2!}$)

Question 6

Solving for $n$ in $\left(\genfrac{}{}{0ex}{}{n}{2}\right)=45$: Accepted Answer: 10

Question 7

Selecting 5 cards from a deck such that 2 are kings and 3 are queens? Accepted Answer: 24 ($\left(\genfrac{}{}{0ex}{}{4}{2}\right)\times \left(\genfrac{}{}{0ex}{}{4}{3}\right)=6\times 4$)

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📅 Week 6: Probability Basics

Question 1

If $P(A)=0.4$, $P(B)=0.5$, and $A,B$ are independent, what is $P(A\cap B)$? Accepted Answer: 0.2

Question 2

What is the probability of rolling a sum of 7 with two fair dice? Accepted Answer: 0.167 (1/6)

Question 3

Binomial distribution properties with $n=10,p=0.5$. Mean? Accepted Answer: 5

Question 4

Conditional probability $P(A|B)$ if $P(A\cap B)=0.1$ and $P(B)=0.3$. Accepted Answer: 0.333

Question 5

Probability of getting exactly 2 heads in 3 tosses? Accepted Answer: 0.375 (3/8)

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📅 Week 7: Further Probability

Question 1

Total probability law application for defect rates in two factories. Accepted Answer: 0.035

Question 2

Bayes Theorem: Given a defect, probability it came from Factory A? Accepted Answer: 0.571

Question 3

Mutual exclusivity check: If $P(A\cup B)=P(A)+P(B)$, then $A$ and $B$ are?

• Mutually Exclusive Accepted Answer: Mutually Exclusive

Question 4

Independent vs Disjoint events:

• If $A,B$ are independent and $P(A),P(B)>0$, they cannot be disjoint. Accepted Answer: Correct.

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📅 Week 8: Advanced Conditional Probability

Question 1

Monty Hall variant or complex conditional scenario. Accepted Answer: 0.667

Question 2

Sensitivity and Specificity calculation for a medical test. Accepted Answer: 0.95, 0.90

Question 3

Positive Predictive Value calculation using Bayes Theorem. Accepted Answer: 0.087 (Example scenario with low prevalence)

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📅 Week 9: Discrete Random Variables & PMFs

Question 1

Determine if a given function is a valid PMF.

• Sum of $P(X=x)$ for all $x$ must be 1.
• $P(X=x)\ge 0$ for all $x$. Accepted Answer: Both conditions must hold.

Question 2

Calculating $P(X\le 2)$ from a given PMF table. Accepted Answer: 0.75

Question 3

Finding the constant $k$ in $P(X=x)=kx$ for $x=1,2,3,4$. Accepted Answer: 0.1 ($k=1/10$)

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📅 Week 10: Expected Value & Variance

Question 1

Calculate $E[X]$ for a given discrete distribution. Accepted Answer: 2.5

Question 2

Calculate $Var(X)$ for the same. Accepted Answer: 1.25

Question 3

Linear transformation: Find $E[3X+5]$ if $E[X]=2$. Accepted Answer: 11

Question 4

Find $Var(2X-4)$ if $Var(X)=3$. Accepted Answer: 12 ($2^2\times 3$)

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📅 Week 11: Binomial & Poisson Distributions

Question 1

Binomial $P(X=k)$ calculation for $n=5,p=0.2,k=1$. Accepted Answer: 0.4096

Question 2

Poisson distribution $P(X=2)$ for $\lambda =3$. Accepted Answer: 0.224 ($\frac{e^{-3}{3}^2}{2!}$)

Question 3

Mean of Poisson matching variance?

• True Accepted Answer: True

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📅 Week 12: Continuous Random Variables (Uniform & Exponential)

Question 1

Calculate $P(1<X<3)$ for $X\sim Uniform(0,5)$. Accepted Answer: 0.4 ($\frac{3-1}{5-0}$)

Question 2

Exponential distribution $P(X>5)$ for $\lambda =0.2$. Accepted Answer: 0.368 ($e^{-0.2\times 5}=e^{-1}$)

Question 3

Expected value of $X\sim Expo(\lambda =0.5)$. Accepted Answer: 2 ($1/0.5$)

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