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

Find the average of the first 30 multiples of 9.

  1. 139.5

  2. 279

  3. 1395

  4. 270

  5. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Required average = 9(1 + 2 + 3 +.................. + 30)/30                                   = (9*30*31)/(30*2)                                   = 279/2                                   = 139.5

Multiple choice

The average of 7 results is 16, the average of the first three is 14 and that of the last three is 18. What is the fourth result?

  1. 16

  2. 48
    • 16
    • 8.4

  5. 6.8
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

If the average of 7 numbers is 16, then the sum of numbers must be,  112. If average of first 3 numbers is 14, then the sum of numbers must be 42. And if the average of the next 3 numbers is 18, the sum of numbers must be 54. Now, 112 - 42 - 54 = 16. Hence, the last number is 16.

Multiple choice

In a set of three numbers, the average of the first two numbers is 4, the average of the last two numbers is 5, and the average of the first and the last numbers is 6. What is the average of three numbers?

  1. 30

  2. 5

  3. 15

  4. 3

  5. 2
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

 Suppose the 3 numbers are A, B and C, so A + B = 2 x 4 = 8 ----------------- (1) B + C = 2 x 5 = 10 --------------- (2) A + C = 2 x 6 = 12 --------------- (3) On adding (1), (2) and (3), we get A + B + C = 15. Therefore, average = 15/3 = 5 

Multiple choice

The annual precipitation data of a city is normally distributed with mean and standard deviation as 1000 mm and 200 mm, respectively. The probability that the annual precipitation will be more than 1200 mm is

  1. < 50%

  2. 50%

  3. 75%

  4. 100%
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

In a normal distribution, the mean is 1000. 1200 is one standard deviation (200) above the mean. Since the distribution is symmetric, the area above the mean is 50%, and the area above one standard deviation is less than 50%.

Multiple choice

Which of the following assertions are CORRECT? P: Adding 7 to each entry in a list adds 7 to the mean of the list Q: Adding 7 to each entry in a list adds 7 to the standard deviation of the list R: Doubling each entry in a list doubles the mean of the list S: Doubling each entry in a list leaves the standard deviation of the list unchanged

  1. P, Q

  2. Q, R

  3. P, R

  4. R, S
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Adding a constant to each entry shifts the mean by that constant but does not change the standard deviation. Doubling each entry doubles the mean and doubles the standard deviation. Thus, P and R are correct.