Quantitative Aptitude

Statistics

606 Questions
All Ungrouped data dispersion and consistency 209 Unknown terms from given average 124 Grouped data central tendencies 101 Merging means and variances of groups 53 Replacement change in average 27 Alligation and weighted average 21 Data interpretation from tables and charts 20 Net successive percentage change 19 Grouped data variance via step deviation 18 Combination of multiple ratios 1

Statistics Questions

Multiple choice

Directions: Type in your answer in the input box provided below the question. Five positive integers have their mean, median and mode each equal to 10. If their range is equal to 15, how many possible values can the least of the five integers assume?

  1. 4

  2. 1

  3. 2

  4. 9
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let the integers be a, b, c, d, e in increasing order. Median = c = 10. Mean = (a+b+10+d+e)/5 = 10, so a+b+d+e = 40. Range = e - a = 15, so e = a + 15. Mode = 10, so at least two numbers must be 10. Since median is 10, either b=10 or d=10. If b=10, then a+10+10+d+e = 50, so a+d+e = 30. Since e=a+15, a+d+a+15 = 30, 2a+d = 15. Possible values for a: if a=1, d=13 (e=16, set: 1, 10, 10, 13, 16); if a=2, d=11 (e=17, set: 2, 10, 10, 11, 17); if a=3, d=9 (invalid, d must be >= 10); if a=4, d=7 (invalid). If d=10, then a+b+10+10+e = 50, a+b+e = 30. e=a+15, so 2a+b+15 = 30, 2a+b = 15. If a=1, b=13 (invalid, b must be <= 10); if a=2, b=11 (invalid); if a=3, b=9 (set: 3, 9, 10, 10, 18); if a=4, b=7 (set: 4, 7, 10, 10, 19); if a=5, b=5 (set: 5, 5, 10, 10, 20). Total 4 valid sets.

Multiple choice

Directions: Select the correct alternative from the given choices. A data set comprises five natural numbers, 15, 4, 42, 23 and x. How many values of x exist such that the median of the above set of numbers is equal to its mean?

  1. 0

  2. 3

  3. 1

  4. 2
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Sorted set: 4, 15, 23, 42, x. Mean = (4+15+23+42+x)/5 = (84+x)/5. If x is between 15 and 23, median is x. So x = (84+x)/5 => 5x = 84+x => 4x = 84 => x = 21 (valid). If x > 42, median is 23. So 23 = (84+x)/5 => 115 = 84+x => x = 31 (not > 42, invalid). If x < 4, median is 15. So 15 = (84+x)/5 => 75 = 84+x => x = -9 (not < 4, invalid). Checking other positions reveals 2 solutions.

Multiple choice

If 15 is included in the series 7, 8, 13, 13, 9, 14, 15, 15, 15, 19, which will be affected the most?

  1. Mean

  2. Median

  3. Mode

  4. Both mean and mode

  5. Both mean and median
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Original series: 7, 8, 13, 13, 9, 14, 15, 15, 15, 19. Sorted: 7, 8, 9, 13, 13, 14, 15, 15, 15, 19. Median is (13+14)/2 = 13.5. Adding 15: 7, 8, 9, 13, 13, 14, 15, 15, 15, 15, 19. Median is 14. The median changed from 13.5 to 14. The mode was 15 and remains 15. The mean changes slightly. The median is affected significantly.

Multiple choice

A set of 20 numbers represents the height of 20 students of a particular class. The variance of the given 20 numbers is 8. Now, the height of each student is multiplied by 3. What is the new variance of the numbers?

  1. 64

  2. 72

  3. 87

  4. 65
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

When each value in a data set is multiplied by a constant k, the variance is multiplied by k^2. Here, the original variance is 8 and the constant is 3, so the new variance is 8 * 3^2 = 8 * 9 = 72.

Multiple choice

A scientist was weighing each of 30 fishes. Their mean weight worked out is 30 g and standard deviation is 2 g. Later, it was found that the measuring scale was misaligned and always under-reported every fish's weight by 2 g. The correct mean and standard deviation (in g) of fishes, are respectively

  1. 32 and 2

  2. 32 and 4

  3. 28 and 2

  4. 28 and 4
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Adding a constant to every value in a dataset increases the mean by that constant but does not change the standard deviation. Thus, the new mean is 30 + 2 = 32, and the standard deviation remains 2.

Multiple choice

The mean and standard deviations of 50 observations are 15 and 2 respectively. It was found that one incorrect observation was taken such that the sum of correct and incorrect observations is 70. If the correct mean is 16, then the correct variance is equal to

  1. 10

  2. 36

  3. 43

  4. 60
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Original sum of 50 observations = 50 * 15 = 750. The incorrect observation was replaced. Let the incorrect be x and correct be y. Given x + y = 70. New sum = 750 - x + y = 50 * 16 = 800. Solving x + y = 70 and y - x = 50 gives y = 60, x = 10. The new variance is calculated using the new sum of squares.

Multiple choice

Youtube views of a comedy video increase sharply. There were 20,000 views initially observed on Monday. The number of views gets doubled every 3 days. How many views will there be 15 days after the initial observation of Monday?

  1. 1,00,000

  2. 3,00,000

  3. 3,20,000

  4. 6,40,000
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The number of views doubles every 3 days. Over 15 days, there are 15/3 = 5 doubling periods. The calculation is 20,000 * 2^5 = 20,000 * 32 = 640,000.