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

The mean of eight positive values is 95. If the first value is two-thirds of the sum of the remaining seven values, what is the average of the last seven values?

  1. 64.26

  2. 65.14

  3. 66.34

  4. 67.36

  5. 68.56
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Sum of 8 values = 8 * 95 = 760. Let x be the first value and S_7 be the sum of the other seven. x = (2/3)S_7. x + S_7 = 760 => (2/3)S_7 + S_7 = 760 => (5/3)S_7 = 760 => S_7 = 760 * 3 / 5 = 456. Average of last seven = 456 / 7 = 65.14.

Multiple choice

If the mean of three variables x, y, and z is N, and the sum of the products xy, yz, and zx is zero, determine the value of K such that the mean of x2, y2, and z2 is KN2.

  1. 1

  2. 2

  3. 3

  4. 4

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

Mean of x, y, z is N, so x+y+z = 3N. We know (x+y+z)^2 = x^2+y^2+z^2 + 2(xy+yz+zx). Given xy+yz+zx = 0, we have (3N)^2 = x^2+y^2+z^2 + 0. So x^2+y^2+z^2 = 9N^2. The mean of x^2, y^2, z^2 is (x^2+y^2+z^2)/3 = 9N^2/3 = 3N^2. Thus K=3.

Multiple choice

The mean and variance of a data set comprising 15 observations are 15 and 5 respectively. If one of the observation 15 is deleted and two new observations 6, 8 added then resulting data have new variance is

  1. (1) 10.3715

  2. (2) 11.8125

  3. (3) 13.25

  4. (4) 5.7516
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Original sum = 15 * 15 = 225. Original sum of squares = 15 * (5 + 15^2) = 15 * 230 = 3450. After removing 15 and adding 6, 8: New sum = 225 - 15 + 6 + 8 = 224. New sum of squares = 3450 - 225 + 36 + 64 = 3325. New variance = (3325 / 16) - (224 / 16)^2 = 207.8125 - 196 = 11.8125.

Multiple choice

A test of five questions, each carrying 10 marks, was conducted in a school. Marks of two students Mary and Harry were tabulated as follows: Question Number 1 2 3 4 5 Mary's Score 10 8 9 8 7 Harry's Score 4 7 10 10 10 Choose the correct statement.

  1. The mean marks of Mary are greater than the mean marks of Harry.

  2. The mean marks of Mary are less than the mean marks of Harry.

  3. The mean marks of Mary and the mean marks of Harry are equal.

  4. There is not enough information to compare the means marks.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Mary's mean is (10+8+9+8+7)/5 = 42/5 = 8.4. Harry's mean is (4+7+10+10+10)/5 = 41/5 = 8.2. Since 8.4 > 8.2, Mary's mean is greater.

Multiple choice

The marks obtained by 10 students in a Statistics test are 24, 47, 18, 32, 19, 15, 21, 35, 50 and 41. What is the mean deviation of the largest five observations?

  1. 4.8

  2. 5.5

  3. 6

  4. 7.5
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Sorted observations: 15, 18, 19, 21, 24, 32, 35, 41, 47, 50. Largest five: 32, 35, 41, 47, 50. Mean = (32+35+41+47+50)/5 = 205/5 = 41. Mean deviation = (|32-41| + |35-41| + |41-41| + |47-41| + |50-41|) / 5 = (9 + 6 + 0 + 6 + 9) / 5 = 30 / 5 = 6.

Multiple choice

A dataset originally consists of 10 values with an average value of 50 each. After adding 3 new consecutive integral values, the average of the entire dataset increases to 53. What is the maximum value among these 3 consecutive integral values?

  1. 62

  2. 63

  3. 64

  4. 65

  5. 66
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Initial sum = 10 * 50 = 500. New sum = 13 * 53 = 689. The sum of the 3 new integers is 689 - 500 = 189. Let the integers be x-1, x, x+1. Their sum is 3x = 189, so x = 63. The values are 62, 63, 64. The maximum is 64.

Multiple choice

A data set of 27 different numbers has a mean of 33 and a median of 33. A new data set is created by adding 7 to each number in the original data set that is greater than the median and subtracting 7 from each number in the original data set that is less than the median. Which of the following measures does NOT have the same value in both the original and new data sets?

  1. Median

  2. Mean

  3. Sum of the numbers

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

Adding/subtracting a constant to values greater/less than the median changes the distribution spread, thus affecting the standard deviation. The mean, median, and sum remain unchanged because the changes are symmetric around the median.