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

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)
Reveal answer Fill a bubble to check yourself
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 formula for calculating the odds ratio?

  1. Odds Ratio = (Odds of disease in exposed / Odds of disease in unexposed)

  2. Odds Ratio = (Risk Ratio - 1) / Risk Ratio

  3. Odds Ratio = (Relative Risk - 1) / Relative Risk

  4. Odds Ratio = (Attributable Risk / (1 - Attributable Risk))
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Odds Ratio is calculated by dividing the odds of disease in exposed individuals by the odds of disease in unexposed individuals.

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.
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. 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
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. It is a measure of how spread out the values of the random variable are.

Multiple choice

In a simple random sample of size n, the probability of selecting any specific individual from the population is:

  1. 1/n

  2. n/N

  3. 1/N

  4. N/n
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

In a simple random sample, each individual in the population has an equal chance of being selected, so the probability of selecting any specific individual is 1/N, where N is the population size.

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
Reveal answer Fill a bubble to check yourself
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 range of values for a validity coefficient?

  1. 0 to 1

  2. -1 to 1

  3. 0 to infinity

  4. -1 to infinity
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

A validity coefficient can range from -1 to 1, with -1 indicating perfect negative correlation, 0 indicating no correlation, and 1 indicating perfect positive correlation.

Multiple choice

The range of a dataset is calculated by:

  1. Maximum value - Minimum value

  2. Maximum value + Minimum value

  3. Mean - Median
Reveal answer Fill a bubble to check yourself
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
Reveal answer Fill a bubble to check yourself
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 interquartile range (IQR) is calculated as:

  1. Q3 - Q1

  2. Q3 + Q1

  3. Q2 - Q1
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The interquartile range (IQR) is the difference between the third quartile (Q3) and the first quartile (Q1).

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
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

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

Multiple choice

Find the mean of the following numbers: 12, 15, 18, 21, 24.

  1. 16

  2. 17

  3. 18

  4. 19
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The mean of a set of numbers is calculated by adding all the numbers and dividing the sum by the number of numbers. In this case, we have (12 + 15 + 18 + 21 + 24) ÷ 5 = 90 ÷ 5 = 18.