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 formula for calculating mean absolute error?

  1. Mean absolute error = (1/n) * Σ|y_i - μ_i|

  2. Mean absolute error = (1/n) * Σ(y_i - μ_i)

  3. Mean absolute error = Σ|y_i - μ_i|

  4. Mean absolute error = Σ(y_i - μ_i)
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Mean absolute error is calculated by taking the average of the absolute differences between the predicted values and the actual values.

Multiple choice

What is the probability of obtaining a yield of at least 100 bushels per acre if the yield distribution is normally distributed with a mean of 120 bushels per acre and a standard deviation of 20 bushels per acre?

  1. 0.8413

  2. 0.9772

  3. 0.1587

  4. 0.0228
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The probability of obtaining a yield of at least 100 bushels per acre can be calculated using the standard normal distribution. The z-score for a yield of 100 bushels per acre is (100 - 120) / 20 = -1.00. The probability of obtaining a z-score of -1.00 or higher is 0.8413.

Multiple choice

A farmer is considering two different crop varieties, A and B. Variety A has a yield distribution with a mean of 100 bushels per acre and a standard deviation of 20 bushels per acre. Variety B has a yield distribution with a mean of 120 bushels per acre and a standard deviation of 30 bushels per acre. Which variety has the lower risk of yield loss?

  1. Variety A

  2. Variety B

  3. Both varieties have the same risk of yield loss

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

The risk of yield loss is measured by the variance of the yield distribution. The variance of Variety A is 20^2 = 400, while the variance of Variety B is 30^2 = 900. Therefore, Variety A has the lower risk of yield loss.

Multiple choice

What is the expected value of a random variable $X$?

  1. The average value of $X$
  2. The sum of all possible values of $X$
  3. The probability of $X$ taking on a particular value
  4. The standard deviation of $X$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The expected value of a random variable $X$ is the average value of $X$ over all possible outcomes.

Multiple choice

What is the variance of a random variable $X$?

  1. The average value of $X$
  2. The sum of all possible values of $X$
  3. The probability of $X$ taking on a particular value
  4. The standard deviation of $X$ squared
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The variance of a random variable $X$ is the expected value of the squared deviation of $X$ from its mean.

Multiple choice

If the expected value of a random variable $X$ is 5 and its variance is 4, what is the standard deviation of $X$?

  1. 2

  2. 4

  3. 6

  4. 8
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The standard deviation of $X$ is the square root of the variance of $X$, which is 4. Therefore, the standard deviation of $X$ is 2.

Multiple choice

What is the formula for calculating the mean of a dataset?

  1. Mean = Sum of all values / Number of values

  2. Mean = Median + Mode

  3. Mean = Range / 2

  4. Mean = Sum of all values * Number of values
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The mean is calculated by adding up all the values in a dataset and dividing the sum by the number of values.

Multiple choice

What is the formula for calculating the median of a dataset?

  1. Median = Sum of all values / Number of values

  2. Median = Mean + Mode

  3. Median = Range / 2

  4. Median = Middle value of a dataset when assorted in numerical order
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The median is the middle value of a dataset when assorted in numerical order.

Multiple choice

What are the steps involved in conducting a hypothesis test?

  1. State the null and alternative hypotheses.

  2. Collect data from a sample.

  3. Calculate the test statistic.

  4. Determine the p-value.

  5. Make a decision about the null hypothesis.

  6. All of the above.
Reveal answer Fill a bubble to check yourself
F Correct answer
Explanation

The steps involved in conducting a hypothesis test include stating the null and alternative hypotheses, collecting data from a sample, calculating the test statistic, determining the p-value, and making a decision about the null hypothesis.

Multiple choice

What is a Type I error?

  1. A Type I error is rejecting the null hypothesis when it is true.

  2. A Type I error is accepting the null hypothesis when it is false.

  3. A Type I error is making a false positive decision.

  4. A Type I error is making a false negative decision.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

A Type I error is rejecting the null hypothesis when it is true, also known as a false positive decision.

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. The range of the 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 the random variable, weighted by their probabilities.

Multiple choice

What is the standard deviation of a random variable?

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

  2. The square of the variance of the random variable

  3. The reciprocal of the variance of the random variable

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

The standard deviation of a random variable is the square root of the variance of the random variable, indicating the typical deviation of the values from the expected value.

Multiple choice

What is a good SSIM score?

  1. 0

  2. 1

  3. 0.5

  4. 0.75
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

A good SSIM score is 1. This indicates that the two images are identical. A score of 0 indicates that the two images are completely different. A score between 0 and 1 indicates that the two images are similar, but not identical.

Multiple choice

What is the mathematical equation that represents a linear regression model?

  1. y = mx + b

  2. y = mx^2 + b

  3. y = mx^3 + b

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

The linear regression model is expressed as 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 least squares method used for in linear regression?

  1. To find the best-fit line that minimizes the sum of squared errors

  2. To calculate the slope and y-intercept of the line

  3. To predict the value of the dependent variable for a given value of the independent variable

  4. To measure the strength of the relationship between variables
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The least squares method is an optimization technique used in linear regression to find the best-fit line that minimizes the sum of squared errors between the predicted values and the actual values of the dependent variable.