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 purpose of a scatter plot?

  1. To show the distribution of a variable across a region

  2. To show the relationship between two variables

  3. To show the movement of people or goods

  4. To show the physical features of a region
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Scatter plots are used to show the relationship between two variables by plotting the values of one variable on the x-axis and the values of the other variable on the y-axis.

Multiple choice

What is the purpose of a line graph?

  1. To show the distribution of a variable across a region

  2. To show the relationship between two variables

  3. To show the movement of people or goods

  4. To show the physical features of a region
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Line graphs are used to show the movement of people or goods over time by plotting the values of the variable on the y-axis and the time on the x-axis.

Multiple choice

Which of the following is a continuous data type?

  1. Age

  2. Gender

  3. Height

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

Continuous data types can take on any value within a range, such as height or weight.

Multiple choice

Which of the following is a discrete data type?

  1. Age

  2. Gender

  3. Height

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

Discrete data types can only take on specific values, such as gender or occupation.

Multiple choice

Which of the following mathematics journals is published by the Institute of Mathematical Statistics?

  1. The Annals of Statistics

  2. The Annals of Probability

  3. The Journal of the American Statistical Association

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

The Annals of Statistics is published by the Institute of Mathematical Statistics.

Multiple choice

A company claims that their product has a mean lifespan of 1000 hours. A sample of 50 products is tested and the sample mean lifespan is found to be 950 hours. If the population standard deviation is known to be 100 hours, what is the p-value for the hypothesis test that the population mean lifespan is equal to 1000 hours?

  1. 0.01

  2. 0.05

  3. 0.10

  4. 0.15
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The p-value is the probability of obtaining a sample mean lifespan as extreme as or more extreme than the observed sample mean, assuming that the population mean lifespan is equal to 1000 hours. Using a z-test, the p-value is calculated as P(Z < -2.5) = 0.01.

Multiple choice

A company uses a control chart to monitor the quality of their products. The control limits are set at 3 standard deviations above and below the mean. If the sample mean is 100 and the sample standard deviation is 10, what are the control limits?

  1. (70, 130)

  2. (80, 120)

  3. (90, 110)

  4. (100, 140)
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The control limits are calculated as the mean plus or minus 3 standard deviations. Therefore, the control limits are 100 +/- 3 * 10 = (70, 130).

Multiple choice

A company claims that their product has a mean lifespan of 500 hours. A sample of 100 products is tested and the sample mean lifespan is found to be 480 hours. If the population standard deviation is known to be 50 hours, what is the p-value for the hypothesis test that the population mean lifespan is equal to 500 hours?

  1. 0.01

  2. 0.05

  3. 0.10

  4. 0.15
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The p-value is the probability of obtaining a sample mean lifespan as extreme as or more extreme than the observed sample mean, assuming that the population mean lifespan is equal to 500 hours. Using a z-test, the p-value is calculated as P(Z < -2) = 0.05.

Multiple choice

A company uses a control chart to monitor the quality of their products. The control limits are set at 2 standard deviations above and below the mean. If the sample mean is 100 and the sample standard deviation is 10, what are the control limits?

  1. (80, 120)

  2. (90, 110)

  3. (100, 140)

  4. (110, 130)
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The control limits are calculated as the mean plus or minus 2 standard deviations. Therefore, the control limits are 100 +/- 2 * 10 = (80, 120).

Multiple choice

A company claims that their product has a mean lifespan of 1000 hours. A sample of 50 products is tested and the sample mean lifespan is found to be 900 hours. If the population standard deviation is known to be 100 hours, what is the p-value for the hypothesis test that the population mean lifespan is equal to 1000 hours?

  1. 0.01

  2. 0.05

  3. 0.10

  4. 0.15
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The p-value is the probability of obtaining a sample mean lifespan as extreme as or more extreme than the observed sample mean, assuming that the population mean lifespan is equal to 1000 hours. Using a z-test, the p-value is calculated as P(Z < -3) = 0.01.

Multiple choice

A company uses a control chart to monitor the quality of their products. The control limits are set at 4 standard deviations above and below the mean. If the sample mean is 100 and the sample standard deviation is 10, what are the control limits?

  1. (60, 140)

  2. (70, 130)

  3. (80, 120)

  4. (90, 110)
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The control limits are calculated as the mean plus or minus 4 standard deviations. Therefore, the control limits are 100 +/- 4 * 10 = (60, 140).

Multiple choice

What is the formula for calculating MAE?

  1. MAE = (1/n) * Σ|y_i - y_hat_i|

  2. MAE = (1/n) * Σ(y_i - y_hat_i)^2

  3. MAE = (1/n) * Σy_i * y_hat_i

  4. MAE = (1/n) * Σ(y_i + y_hat_i)
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

MAE is calculated by taking the average of the absolute differences between the predicted values (y_hat_i) and the observed values (y_i).

Multiple choice

Find the mean of the following numbers: 5, 7, 9, 11, 13

  1. 7

  2. 8

  3. 9

  4. 10
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The mean of a set of numbers is the sum of the numbers divided by the number of numbers. In this case, the mean is (5 + 7 + 9 + 11 + 13) / 5 = 45 / 5 = 9.

Multiple choice

What is the formula for calculating mean squared error?

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

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

  3. Mean squared error = Σ(y_i - μ_i)^2

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

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

Multiple choice

What is the formula for calculating root mean squared error?

  1. Root mean squared error = √sqrt((1/n) * Σ(y_i - μ_i)^2)

  2. Root mean squared error = √sqrt((1/n) * Σ(y_i - μ_i))

  3. Root mean squared error = √sqrt(Σ(y_i - μ_i)^2)

  4. Root mean squared error = √sqrt(Σ(y_i - μ_i))
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Root mean squared error is calculated by taking the square root of the mean squared error.