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 standard deviation of a normal distribution with a mean of 5 and a standard deviation of 2?

  1. 1

  2. 2

  3. 3

  4. 4
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The standard deviation of a normal distribution is a measure of how spread out the distribution is. In this case, the standard deviation is 2.

Multiple choice

What is the probability of getting a sample mean of 100 or higher from a population with a mean of 100 and a standard deviation of 10, if the sample size is 100?

  1. 0.5

  2. 0.68

  3. 0.95

  4. 0.99
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The sampling distribution of the sample mean is a normal distribution with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size. In this case, the sampling distribution of the sample mean has a mean of 100 and a standard deviation of 10 / sqrt(100) = 1. So, the probability of getting a sample mean of 100 or higher is 0.99.

Multiple choice

What is the standard error of the mean?

  1. The standard deviation of the population

  2. The standard deviation of the sample

  3. The standard deviation of the sampling distribution of sample means

  4. The standard deviation of the sampling distribution of sample proportions
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The standard error of the mean is the standard deviation of the sampling distribution of sample means.

Multiple choice

What is the probability density function of a standard normal distribution?

  1. $f(x) = \frac{1}{\sqrt{2\pi}} e^{-\frac{x^2}{2}}$
  2. $f(x) = \frac{1}{\sqrt{2\pi}} e^{-x^2}$
  3. $f(x) = \frac{1}{2\pi} e^{-\frac{x^2}{2}}$
  4. $f(x) = \frac{1}{2\pi} e^{-x^2}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The probability density function of a standard normal distribution is given by $f(x) = \frac{1}{\sqrt{2\pi}} e^{-\frac{x^2}{2}}$.

Multiple choice

What is the average HDI of the world?

  1. 0.5

  2. 0.6

  3. 0.7

  4. 0.8
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The average HDI of the world is 0.7, which indicates a high level of human development.

Multiple choice

How is the MPI calculated?

  1. By averaging the scores of each individual on the three dimensions of the index

  2. By multiplying the scores of each individual on the three dimensions of the index

  3. By taking the minimum of the scores of each individual on the three dimensions of the index

  4. By taking the maximum of the scores of each individual on the three dimensions of the index
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The MPI is calculated by averaging the scores of each individual on the three dimensions of the index. Each dimension is given equal weight, and the overall score is expressed as a percentage. A score of 0% indicates that an individual is not poor, while a score of 100% indicates that an individual is extremely poor.

Multiple choice

The central limit theorem states that the distribution of sample means will be:

  1. Normal

  2. Skewed

  3. Uniform

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

The central limit theorem states that the distribution of sample means will be approximately normal, regardless of the shape of the population distribution.

Multiple choice

What is the average IQ score?

  1. 85

  2. 100

  3. 115

  4. 130
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The average IQ score is 100. IQ scores are distributed according to a normal distribution, with the majority of people scoring between 85 and 115.

Multiple choice

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

  1. Margin of error = (Critical value) * (Standard error of the mean)

  2. Margin of error = (Critical value) * (Sample standard deviation)

  3. Margin of error = (Critical value) * (Population standard deviation)

  4. Margin of error = (Critical value) * (Sample mean)
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The margin of error is calculated by multiplying the critical value from the appropriate distribution (t-distribution or z-distribution) by the standard error of the mean.

Multiple choice

What is the standard error of the mean?

  1. The standard deviation of the sample mean

  2. The standard deviation of the population mean

  3. The average of the sample means

  4. The difference between the sample mean and the population mean
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The standard error of the mean is a measure of the variability of the sample mean and is calculated by dividing the population standard deviation by the square root of the sample size.

Multiple choice

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

  1. 34.1%

  2. 68.2%

  3. 95.4%

  4. 99.7%
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

In a normal distribution, approximately 68.2% of the data falls within one standard deviation of the mean.

Multiple choice

What is the expected value of a random variable?

  1. The average value of a random variable

  2. The median value of a random variable

  3. The mode value of a random variable

  4. The range of a random variable
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The expected value of a random variable is the average value of a random variable.

Multiple choice

In a normal distribution with mean 'μ' and standard deviation 'σ', what is the probability of obtaining a value less than 'μ'?

  1. 0.5

  2. 1

  3. Cannot be determined

  4. Depends on the values of 'μ' and 'σ'
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

In a normal distribution, the probability of obtaining a value less than the mean 'μ' is 0.5. This is because the normal distribution is symmetric around the mean, so the probability of obtaining a value less than 'μ' is the same as the probability of obtaining a value greater than 'μ'.

Multiple choice

What is the probability of obtaining a value greater than 'μ + σ' in a normal distribution with mean 'μ' and standard deviation 'σ'?

  1. 0.1587

  2. 0.3413

  3. 0.5

  4. Cannot be determined
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

In a normal distribution, the probability of obtaining a value greater than 'μ + σ' is approximately 0.1587. This can be calculated using the standard normal distribution (z-distribution) and the cumulative distribution function (CDF).

Multiple choice

What is the formula for calculating the standard deviation of a random variable?

  1. σ = √(E(X^2) - (E(X))^2)

  2. σ = E(X) - E(X^2)

  3. σ = E(X^2) / E(X)

  4. σ = (E(X))^2 - E(X^2)
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The standard deviation of a random variable X is calculated by taking the square root of the variance, which is the expected value of the squared deviation of X from its mean.