Mathematics · Quantitative Aptitude

Statistics and Dispersion

515 Questions

Statistics and dispersion involve the calculation of mean, standard deviation, variance, and coefficient of variation for data sets. These questions also cover probability distributions and cumulative frequency analysis. Such quantitative aptitude topics are heavily featured in banking and SSC examinations.

Standard deviationNormal distributionMean calculationCumulative frequencyCoefficient of variation

Statistics and Dispersion Questions

Multiple choice

What is the formula for calculating the margin of error in a confidence interval?

  1. Margin of Error = (Critical Value) * (Standard Error)

  2. Margin of Error = (Confidence Level) * (Standard Error)

  3. Margin of Error = (Sample Size) * (Standard Error)

  4. Margin of Error = (Standard Deviation) * (Critical Value)
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A Correct answer
Explanation

The margin of error is calculated by multiplying the critical value, which is based on the level of confidence and degrees of freedom, by the standard error of the mean.

Multiple choice

In a confidence interval for a population proportion, what is the formula for calculating the standard error?

  1. Standard Error = (Sample Proportion) * (1 - Sample Proportion) / Sample Size

  2. Standard Error = (Sample Mean) / Sample Size

  3. Standard Error = (Standard Deviation) / Sample Size

  4. Standard Error = (Sample Proportion) * (Sample Size)
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A Correct answer
Explanation

For a confidence interval for a population proportion, the standard error is calculated using the formula: Standard Error = sqrt((Sample Proportion) * (1 - Sample Proportion) / Sample Size).

Multiple choice

What is the expected value of a random variable?

  1. The average value of the random variable.

  2. The median value of the random variable.

  3. The mode value of the random variable.

  4. None of the above.
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A Correct answer
Explanation

The expected value of a random variable is the average value of the random variable. It is calculated by multiplying each possible value of the random variable by its probability and then summing the results.

Multiple choice

In a normal distribution, what percentage of data falls within one standard deviation of the mean?

  1. 68%

  2. 95%

  3. 99.7%

  4. 50%
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

In a normal distribution, approximately 68% of the data falls within one standard deviation of the mean.

Multiple choice

What is the standard deviation of a random variable?

  1. The square root of the variance of the random variable

  2. The average value of the random variable

  3. The most likely value of the random variable

  4. The median value of the random variable
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A Correct answer
Explanation

The standard deviation of a random variable is the square root of the variance of the random variable. It is a measure of how spread out the values of the random variable are.

Multiple choice

In a normal population with mean (\mu) and standard deviation (\sigma), the sampling distribution of the sample mean (\overline{X}) for samples of size n is:

  1. Normal with mean \(\mu\) and standard deviation \(\sigma\)
  2. Normal with mean \(\mu\) and standard deviation \(\sigma/\sqrt{n}\)
  3. Normal with mean \(\mu\) and standard deviation \(\sigma\sqrt{n}\)
  4. Normal with mean \(\mu/n\) and standard deviation \(\sigma\)
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The sampling distribution of the sample mean follows a normal distribution with mean (\mu) and standard deviation (\sigma/\sqrt{n}), where n is the sample size.

Multiple choice

What is the average HDI of the world?

  1. 0.7

  2. 0.8

  3. 0.9

  4. 1.0
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A Correct answer
Explanation

The average HDI of the world is 0.7, according to the 2020 Human Development Report.

Multiple choice

What is the formula for calculating the average order value?

  1. (Total Revenue / Number of Orders)

  2. (Total Revenue / Number of Website Visitors)

  3. (Total Revenue / Number of Page Views)

  4. (Total Revenue / Number of Leads)
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A Correct answer
Explanation

The average order value is calculated by dividing the total revenue by the number of orders.

Multiple choice

What is the formula for calculating the optimal portfolio weights using the mean-variance optimization approach?

  1. w = (Σ^-1 μ) / (μ^T Σ^-1 μ)

  2. w = (Σ μ) / (μ^T Σ μ)

  3. w = (Σ^-1 μ) / (μ^T Σ μ)

  4. w = (Σ μ) / (μ^T Σ^-1 μ)
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A Correct answer
Explanation

The optimal portfolio weights using the mean-variance optimization approach are calculated using the formula w = (Σ^-1 μ) / (μ^T Σ^-1 μ), where Σ is the covariance matrix of the asset returns, μ is the vector of expected asset returns, and w is the vector of optimal portfolio weights.

Multiple choice

What is the formula for calculating the Sharpe ratio of a portfolio?

  1. Sharpe ratio = (Expected return of portfolio - Risk-free rate) / Standard deviation of portfolio returns

  2. Sharpe ratio = (Expected return of portfolio + Risk-free rate) / Standard deviation of portfolio returns

  3. Sharpe ratio = (Expected return of portfolio - Risk-free rate) / Variance of portfolio returns

  4. Sharpe ratio = (Expected return of portfolio + Risk-free rate) / Variance of portfolio returns
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A Correct answer
Explanation

The Sharpe ratio of a portfolio is a measure of its risk-adjusted return. It is calculated by dividing the difference between the expected return of the portfolio and the risk-free rate by the standard deviation of the portfolio returns.

Multiple choice

What is the formula for calculating the Information ratio of a portfolio?

  1. Information ratio = (Expected return of portfolio - Benchmark return) / Standard deviation of portfolio returns

  2. Information ratio = (Expected return of portfolio + Benchmark return) / Standard deviation of portfolio returns

  3. Information ratio = (Expected return of portfolio - Benchmark return) / Variance of portfolio returns

  4. Information ratio = (Expected return of portfolio + Benchmark return) / Variance of portfolio returns
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A Correct answer
Explanation

The Information ratio of a portfolio is a measure of its excess return over and above a benchmark return per unit of risk. It is calculated by dividing the difference between the expected return of the portfolio and the benchmark return by the standard deviation of the portfolio returns.

Multiple choice

The range of a dataset is calculated by:

  1. Maximum value - Minimum value

  2. Maximum value + Minimum value

  3. Mean - Median
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A Correct answer
Explanation

The range is the difference between the maximum and minimum values in a dataset.

Multiple choice

The median of a dataset is:

  1. The middle value when the data is arranged in ascending order

  2. The average of the two middle values when the data is arranged in ascending order

  3. The value that occurs most frequently
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A Correct answer
Explanation

The median is the middle value when the data is arranged in ascending order. If there are an even number of observations, the median is the average of the two middle values.

Multiple choice

The empirical rule states that, in a normal distribution, approximately what percentage of data falls within one standard deviation of the mean?

  1. 68%

  2. 95%

  3. 99.7%
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The empirical rule states that, in a normal distribution, approximately 68% of data falls within one standard deviation of the mean.

Multiple choice

In a normal distribution, the mean, median, and mode are all equal. True or False?

  1. True

  2. False
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A Correct answer
Explanation

In a normal distribution, the mean, median, and mode are all equal to the same value.