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 frequency of numbers 3, 5, 6, 4 is respectively x, x + 2, x - 8 and x. If their mean is 4, then value of x will be ________.

  1. 3

  2. 6

  3. 7

  4. 8
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The mean is calculated as the sum of (value * frequency) divided by the total frequency. Sum = 3x + 5(x+2) + 6(x-8) + 4x = 18x - 38. Total frequency = x + x+2 + x-8 + x = 4x - 6. Setting (18x-38)/(4x-6) = 4, we get 18x - 38 = 16x - 24, which simplifies to 2x = 14, so x = 7.

Multiple choice

If the mean of a data set a1, a2, ..., a2n is 99, and the sum of the deviations of the data set values measured from 100 is denoted by K, while the sum of the deviations of the values measured from 92 is 140, then what is the value of K?

  1. -30

  2. -20

  3. -10

  4. 10

  5. 20
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Mean = 99. Sum of 2n values = 99 * 2n = 198n. Sum of deviations from 100: sum(a_i - 100) = sum(a_i) - 200n = 198n - 200n = -2n = K. Sum of deviations from 92: sum(a_i - 92) = sum(a_i) - 184n = 198n - 184n = 14n = 140. So n = 10. Thus K = -2(10) = -20.

Multiple choice

For the past m days, the average daily production at a factory was 40 gadgets. If today's production of 100 gadgets increases the average to 45 gadgets per day, what is the value of m?

  1. 20

  2. 15

  3. 11

  4. 8

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

Let the total production for m days be 40m. After adding 100, the new total is 40m + 100, and the new count is m + 1. The equation (40m + 100) / (m + 1) = 45 gives 40m + 100 = 45m + 45, so 5m = 55, which means m = 11.

Multiple choice

A data set of 25 distinct numbers has a mean of 40 and a median of 40. A new data set is created by adding 5 to each number greater than the median and subtracting 5 from each number less than the median. Which of the following measures does NOT remain unchanged in both the original and new data sets?

  1. Median

  2. Mean

  3. Sum of the 25 numbers

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

Adding 5 to values above the median and subtracting 5 from values below the median changes the spread of the data, thereby increasing the standard deviation, while the mean and median remain unchanged due to symmetry.

Multiple choice

he mean and standard deviation of a normal distribution are 50 and 10 respectively. What percentage of observations lie between 30 and 70 (approx)?

  1. 35%

  2. 95%

  3. 82%

  4. 99.7%
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The interval from 30 to 70 is 20 units on either side of the mean 50. Since the standard deviation is 10, this interval is within 2 standard deviations of the mean. Approximately 95% of observations lie within 2 standard deviations in a normal distribution.