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

For the data set ${10, 12, 40, 35, 14, 24, 13, 21, 42, 30}$, find the mean absolute deviation to the nearest hundredth.
  1. $9.12$
  2. $11.12$
  3. $12.12$
  4. $10.12$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

First, find the mean: (10+12+40+35+14+24+13+21+42+30) / 10 = 241 / 10 = 24.1. Then, calculate the absolute deviations from 24.1: |10-24.1|=14.1, |12-24.1|=12.1, |40-24.1|=15.9, |35-24.1|=10.9, |14-24.1|=10.1, |24-24.1|=0.1, |13-24.1|=11.1, |21-24.1|=3.1, |42-24.1|=17.9, |30-24.1|=5.9. Sum of deviations = 101.2. Mean absolute deviation = 101.2 / 10 = 10.12.

Multiple choice

Grades for the test on proofs did not go as well as the teacher had hoped. The mean grade was 68, the median grade was 64, and the standard deviation was 12. The teacher curves the score by raising each score by a total of 7 points. Which of the following statements is true? I. The new mean is 75. II. The new median is 71. III. The new standard deviation is 7.

  1. I only

  2. III only

  3. I and II only

  4. I, II, and III

  5. None of the statements are true
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Adding a constant to every data point increases the mean and median by that constant, but does not change the standard deviation. New mean = 68 + 7 = 75. New median = 64 + 7 = 71. Standard deviation remains 12.

Multiple choice

Calculate Mean deviation about median for the given data Marks $100-110$ $110-120$ $120-130$ $130-140$ $140-150$ Frequency $4$ $6$ $5$ $3$ $2$
  1. $10.5$
  2. $31.5$
  3. $12.5$
  4. $66.16$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

First, find the median class by cumulative frequency. Total frequency is 20, so median is at 10th value, which falls in 110-120. Median = 110 + ((10-4)/6)10 = 120. Mean deviation about median = sum(f|x-median|) / sum(f). Midpoints are 105, 115, 125, 135, 145. Deviations are 15, 5, 5, 15, 25. MD = (4*15 + 6*5 + 5*5 + 3*15 + 2*25) / 20 = (60 + 30 + 25 + 45 + 50) / 20 = 210 / 20 = 10.5.

Multiple choice

A school finds that scores of a recent 20-question exam are distributed as shown in the histogram as shown above. The school observes that $25$ % of the results are to be omitted from the list. Of the omitted ones, $80$% are greater than what the school thought the mean was; the rest are less. Assuming all new data points fit in the current histogram range, which of the following is most likely to occur upon adding the new scores to the data?

  1. The data will be skewed to the right

  2. The data will be skewed to the left

  3. The median will decrease

  4. The range will decrease
Reveal answer Fill a bubble to check yourself
B Correct answer