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 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 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

The mean of a binomial distribution is given by:

  1. \(np\)
  2. \(nq\)
  3. \(np + nq\)
  4. \(np - nq\)
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The mean of a binomial distribution is given by (np).

Multiple choice

What is the mean of a normal distribution with a mean of 10 and a standard deviation of 2?

  1. 10

  2. 12

  3. 8

  4. 14
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The mean of a normal distribution is the center of the distribution, and it is equal to the expected value of the random variable. In this case, the mean is given as 10, so the mean of the normal distribution is 10.

Multiple choice

What is the standard deviation of a normal distribution with a mean of 10 and a variance of 4?

  1. 2

  2. 4

  3. 8

  4. 16
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The standard deviation of a normal distribution is the square root of the variance. In this case, the variance is given as 4, so the standard deviation is √4 = 2.

Multiple choice

What is the probability of getting a value between 8 and 12 from a normal distribution with a mean of 10 and a standard deviation of 2?

  1. 0.3413

  2. 0.6826

  3. 0.9545

  4. 0.9973
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The probability of getting a value between 8 and 12 from a normal distribution with a mean of 10 and a standard deviation of 2 can be calculated using the standard normal distribution (z-distribution). First, we need to convert the values 8 and 12 to z-scores using the formula z = (x - μ) / σ, where x is the value, μ is the mean, and σ is the standard deviation. Plugging in the values, we get z = (8 - 10) / 2 = -1 and z = (12 - 10) / 2 = 1. Then, we can use a standard normal distribution table or calculator to find the probability of getting a z-score between -1 and 1. The probability is 0.6826.

Multiple choice

What is the formula for calculating the Berger-Parker Index?

  1. D = \frac{N_{max}}{N}

  2. D = \frac{N}{N_{max}}

  3. D = \frac{1}{N_{max}}

  4. D = \frac{1}{N}
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The Berger-Parker Index is calculated by dividing the abundance of the most abundant species by the total abundance of all species in the community.

Multiple choice

What is the median of the following set of numbers: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19?

  1. 9

  2. 10

  3. 11

  4. 12
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The median of a set of numbers is the middle value when the numbers are arranged in ascending order. In this case, the numbers are 1, 3, 5, 7, 9, 11, 13, 15, 17, 19. The middle value is the 5th value. Therefore, the median of the set of numbers is 10.

Multiple choice

What is the standard deviation of the following set of numbers: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19?

  1. 5.66

  2. 6.66

  3. 7.66

  4. 8.66
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The standard deviation of a set of numbers is a measure of how spread out the numbers are. It is calculated by taking the square root of the variance. The variance is calculated by finding the average of the squared differences between each number and the mean. In this case, the mean of the set of numbers is 10. The variance is calculated as follows: [(1 - 10)^2 + (3 - 10)^2 + (5 - 10)^2 + (7 - 10)^2 + (9 - 10)^2 + (11 - 10)^2 + (13 - 10)^2 + (15 - 10)^2 + (17 - 10)^2 + (19 - 10)^2] / 10 = 44.44. The standard deviation is the square root of the variance, which is √44.44 = 6.66.

Multiple choice

In a normal distribution, what is the area under the curve between the mean and one standard deviation?

  1. 0.3413

  2. 0.6826

  3. 0.9545

  4. 0.9973
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

In a normal distribution, the area under the curve between the mean and one standard deviation is approximately 0.3413.