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

Which NumPy function is used to calculate the mean of a given array?

  1. np.mean()

  2. np.average()

  3. np.median()

  4. np.sum()
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The np.mean() function in NumPy is used to calculate the mean (average) of a given array.

Multiple choice

Which NumPy function is used to calculate the standard deviation of an array?

  1. np.std()

  2. np.var()

  3. np.mean()

  4. np.median()
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The np.std() function in NumPy is used to calculate the standard deviation of an array, which measures the spread of data around the mean.

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.

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

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 average GII for the world?

  1. 0.46

  2. 0.52

  3. 0.58

  4. 0.64
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The average GII for the world is 0.46.

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 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

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.