Mathematics · Quantitative Aptitude

Statistics and Dispersion

559 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 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

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 equation for a simple linear regression model?

  1. y = mx + b

  2. y = mx^2 + b

  3. y = ax^2 + bx + c

  4. y = a^x + b
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The equation for a simple linear regression model is y = mx + b, where y is the dependent variable, x is the independent variable, m is the slope of the line, and b is the y-intercept.

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.

Multiple choice

In a 95% confidence interval, what is the probability that the true population parameter falls within the interval?

  1. 95%

  2. 99%

  3. 90%

  4. 80%
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The level of confidence indicates the probability that the true population parameter falls within the interval. In a 95% confidence interval, there is a 95% chance that the true population parameter is captured within the interval.

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)
Reveal answer Fill a bubble to check yourself
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.