Family Relations and Data Analysis Quiz

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Questions and Answers

How many female members are there in a family with a father, a mother, 3 married sons (two have 2 daughters each, one has a son), and one unmarried daughter?

  • 3
  • 5
  • 6
  • 9 (correct)

How is Vinit related to Rani, who remembers him as 'the brother of my grandfather's son'?

  • Aunt
  • Daughter
  • Niece (correct)
  • Sister

What is Bhima's relation to Shiva when Annanya is the mother of Satya, Shyam's mother, and Shiva is Annanya's brother?

  • Son-in-law
  • Brother-in-law (correct)
  • Cousin
  • Son

What is the relationship between Suman and Ramesh if Suman is the daughter-in-law of Rakesh and sister-in-law of Rajesh, while Ramesh is Rakesh's son?

<p>Wife (C)</p> Signup and view all the answers

How is Khushi's husband related to the man in the photograph, if Khushi states, 'This man's son's sister is my mother-in-law'?

<p>Grandson (D)</p> Signup and view all the answers

Which of the following is considered a source of primary data?

<p>Questionnaire filled by Enumerators (C)</p> Signup and view all the answers

In a table, what is the term for the left part that provides the description of the rows?

<p>Stub (B)</p> Signup and view all the answers

What is the suitable formula for computing the number of class intervals?

<p>1 + 3.322 logN (D)</p> Signup and view all the answers

What type of price index should be employed when adding a new commodity?

<p>Shifted price index (D)</p> Signup and view all the answers

Which index is not used for adding a new commodity in price calculations?

<p>Inflation-adjusted price index (A)</p> Signup and view all the answers

Among the following, which price index method is inappropriate for adapting to new products?

<p>Weighted price index (D)</p> Signup and view all the answers

If you need to incorporate a new commodity in price indexing, which index would you prioritize?

<p>Shifted price index (A)</p> Signup and view all the answers

What is an example of an index that would not be suitable for integrating a new item?

<p>Cyclic price index (B)</p> Signup and view all the answers

If the variance of random variable 'x' is 17, what is the variance of y = 2x + 5?

<p>68 (D)</p> Signup and view all the answers

What is the coefficient of variation (C.V) if the variance is 12 and the mean value is 40?

<p>8.65% (C)</p> Signup and view all the answers

In a data set where all values are the same, what is the variance?

<p>0 (A)</p> Signup and view all the answers

Given that the Arithmetic Mean (A.M) is 5 and the Geometric Mean (G.M) is 4, what is the Harmonic Mean (H.M)?

<p>3.2 (B)</p> Signup and view all the answers

What is the average of the remaining 2 students if the average age of 15 students is 9 years, the average age of 5 students is 13 years, and that of 8 students is 5 years?

<p>10 years (D)</p> Signup and view all the answers

If the standard deviation of a random variable x is equal to 5, what is the variance?

<p>25 (B)</p> Signup and view all the answers

What is the correct formula for the probability of the intersection of two independent events A and B?

<p>P(A) * P(B) (D)</p> Signup and view all the answers

For the theorem of compound probability, which of the following statements is true?

<p>P(A ∩ B) = P(A) * P(B/A) (B)</p> Signup and view all the answers

What happens to the variance of a dataset when the data points are all increased by the same constant value?

<p>It remains the same (A)</p> Signup and view all the answers

What is the probability of randomly selecting a number that is a multiple of both 3 and 4 from the first 50 natural numbers?

<p>2/25 (A)</p> Signup and view all the answers

Which of the following methods can be used to transform a dataset that needs normalization?

<p>Scaling to a range (B)</p> Signup and view all the answers

When tossing three coins, what is the probability of getting exactly two heads?

<p>3/8 (D)</p> Signup and view all the answers

What is the skewness of a normal distribution?

<p>Zero (D)</p> Signup and view all the answers

Which of the following statements about the addition of probabilities for independent events is false?

<p>P(A ∪ B) = P(A) + P(B) (B)</p> Signup and view all the answers

What is the annuity amount (A) calculated for a future value of ₹ 5,00,000 at a rate of 10% over 12 years?

<p>₹ 23,381.65 (D)</p> Signup and view all the answers

If events A and B are independent, which equation is always correct?

<p>P(A | B) = P(A) (A)</p> Signup and view all the answers

What is the effective annual rate of interest if the nominal rate is 6% per annum payable half yearly?

<p>6.09% (A)</p> Signup and view all the answers

How many outcomes are there when tossing three coins?

<p>8 (D)</p> Signup and view all the answers

How is the effective rate of interest calculated for a nominal rate of 3% payable semi-annually?

<p>E = (1 + R/2)^T - 1 (B)</p> Signup and view all the answers

If the earning per share (EPS) of a company was ₹ 5 ten years ago and is ₹ 22 now, what is the type of growth being measured?

<p>Annual growth rate (C)</p> Signup and view all the answers

What is the formula used to calculate future value in the annuity context?

<p>A = A * ((1 + i)^n - 1)/i (B)</p> Signup and view all the answers

What does 'n' represent in the context of annuities?

<p>The total period in years (B)</p> Signup and view all the answers

What was the nominal interest rate used in the calculation of future value?

<p>10% (D)</p> Signup and view all the answers

To find the effective interest rate, what constant is used in the half yearly calculation?

<p>3% (D)</p> Signup and view all the answers

What does the variable 'd' represent in the context of the provided table?

<p>The difference between the ranks of x and y (A)</p> Signup and view all the answers

What is the formula used to calculate the coefficient of rank correlation?

<p>rR = 1 - (6Σd²)/(n(n² - 1)) (B)</p> Signup and view all the answers

What does 'n' stand for in the correlation formula?

<p>The total number of observations (C)</p> Signup and view all the answers

What value was calculated for 'rR' based on the given data?

<p>-0.257 (C)</p> Signup and view all the answers

What does the term 'cov(x, y)' represent?

<p>The covariance between x and y (D)</p> Signup and view all the answers

How many squared differences (d²) were summed to obtain the value of 44?

<p>6 (D)</p> Signup and view all the answers

What is a possible interpretation of a negative rank correlation coefficient like -0.257?

<p>As x increases, y tends to decrease. (C)</p> Signup and view all the answers

What statistical method is being used to analyze the relationship between marks in Mathematics and Statistics?

<p>Rank correlation analysis (B)</p> Signup and view all the answers

Flashcards

Effective Annual Rate (EAR)

The rate of return on an investment considering the effect of compounding, which is a more accurate representation of the actual return compared to the nominal rate.

Nominal Rate

The stated, or quoted interest rate, without considering the effects of compounding. Normally, this is the rate per year.

Future Value of Annuity

The future value of an annuity, where the payments are received at the end of each period, considering a specific interest rate and number of periods.

Ordinary Annuity

A series of equal payments made at regular intervals, where the payments are received at the end of each period.

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EPS Growth Rate

The rate of increase in earnings per share (EPS) over a specific period.

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Earnings per Share (EPS)

Profit earned by a company per outstanding share of stock.

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Future Value

The estimated future price of a financial asset based on its current value and its expected rate of growth.

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Present Value

The amount of money that needs to be invested today to receive a specific future value, considering a specific interest rate and number of periods.

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Aunt

The sister of your father or mother.

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Cousin

The child of your uncle or aunt.

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Niece

The daughter of your brother or sister.

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Stepchild

A person's child who is not their spouse's child.

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Stepsibling

A person's sibling who is not their blood sibling.

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Nephew

The son of your brother or sister.

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Son-in-law

The person who is married to your child.

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Brother-in-law

The person who is married to your sibling.

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Variance Scaling Formula

The variance of a random variable 'x' scaled by a constant 'b' is equal to the square of 'b' multiplied by the original variance of 'x'.

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Linear Transformation and Variance

The change in variance of a random variable when it is linearly transformed, like 'y = 2x + 5', is only dependent on the coefficient of the variable 'x', not the constant term.

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Coefficient of Variation (C.V.)

It is the ratio of the standard deviation to the mean, expressed as a percentage. It helps understand the variability of data relative to its average.

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Variance of Identical Data

A dataset where all values are the same has zero variability, hence its standard deviation and variance are both zero.

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Relationship between Means

The harmonic mean can be calculated using the arithmetic mean and geometric mean of two numbers. It is especially useful for comparing rates or proportions.

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Mean of the Remaining Students

The average of the remaining two students is 15 years. This is calculated by finding the total age of all students and subtracting the ages of the first two groups.

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Conditional Probability: P(A|B)

The probability of event A occurring given that event B has already happened.

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Compound Probability Theorem

The probability of two events happening together, calculated by multiplying the probability of the first event by the conditional probability of the second event given that the first event has occurred.

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Independent Events

Two events are independent if the occurrence of one event does not affect the probability of the other event happening.

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Probability of Union of Events

The probability of either of two events happening is calculated by adding the individual probabilities of each event and subtracting the probability of both events happening together.

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Basic Probability Formula

The probability of an event happening is equal to the number of favorable outcomes divided by the total number of possible outcomes.

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Probability of Two Heads in Three Coin Toss

The probability of getting exactly two heads when tossing three coins.

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Skewness of Normal Distribution

A probability distribution where the skewness is zero, implying a symmetrical bell-shaped curve.

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Future Value of an Ordinary Annuity

The future value of an annuity where payments are received at the end of each period, considering a specific interest rate and number of periods.

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Shifted Price Index

A price index used when a new commodity is added to the basket of goods used for calculating the index.

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Splicing Price Index

A method used to combine price indices from different periods, allowing for the creation of a continuous price index.

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Deflating Price Index

A price index used to adjust values for changes in the overall price level, often used to compare real values over time.

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Value Price Index

A price index that reflects the total value of goods and services in a specific period.

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Adding New Commodites to a Price Index

The process of adding a new commodity to the basket of goods used for calculating a price index.

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Correlation Coefficient

A statistical measure that describes the strength and direction of the linear relationship between two variables.

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Rank Correlation Coefficient

A statistical measure that describes the strength and direction of the linear relationship between two variables, specifically focusing on their ranks.

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Spearman's Rank Correlation Coefficient

A statistical method used to calculate the correlation coefficient based on the ranks of the data, instead of the raw values.

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Pearson's Correlation Coefficient

A statistical measure that describes the strength and direction of the linear relationship between two variables, focusing on their deviations from their means.

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Variance

A statistical measure that quantifies the variability of a variable, calculated by summing squared deviations of each value from the mean, then dividing by the number of observations.

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Standard Deviation

A statistical measure that quantifies the spread of a variable, calculated as the square root of the variance.

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Correlation Coefficient

The measure of the degree to which two variables change together. It is calculated by dividing the covariance of the two variables by the product of their standard deviations.

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Covariance

A statistical concept that describes the tendency of two variables to change together.

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Study Notes

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