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

In an association of 250 people, the Britishers and Spaniards are in the ratio of 3 : 2. After adding some more Spaniards in the association, the number of Britishers became equal to the number of Spaniards. The mean of pension that they received of all the group is \$500 and the mean of Spaniards' pension is \$50 more than that of the Britishers. Which of the following statements is/are correct? (A) Mean of Britishers' pension is \$475. (B) Mean of Britishers' pension is \$470. (C) Mean of Spaniards' pension is \$525. (D) Mean of Spaniards' pension is \$520. (E) Mean of Spaniards' pension is $500.

  1. (B) and (D)

  2. (A) and (D)

  3. (A) and (C)

  4. only (E)

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

Initial: 250 people, 3:2 ratio means 150 Britishers, 100 Spaniards. After adding Spaniards, B=S=150. Total = 300. Mean pension = 500. Let B pension = x, S pension = x + 50. Total pension = 150x + 150(x+50) = 300 * 500. 300x + 7500 = 150000. 300x = 142500. x = 475. B = 475, S = 525.

Multiple choice

The students in Juan's math class have the exact same mean height as the students in Juan's English class. However, while the standard deviation of the student heights in his math class is 3.2 inches, the standard deviation of the student heights in his English class is 6.1 inches. Which of the following statements must be true?

  1. The mean height of the students in Juan's English class is 2.9 inches greater than the mean height of the students in Juan's Math class.

  2. The median height of the students in Juan's English class is 2.9 inches greater than the mean height of the students in Juan's Math class.

  3. The heights of the students in Juan's math class are more variable than the heights of the students in Juan's English class.

  4. The heights of the students in Juan's math class are less variable than the heights of the students in Juan's English class.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Standard deviation measures the dispersion or variability of a data set. A higher standard deviation (6.1 vs 3.2) indicates that the data points are more spread out from the mean, meaning the heights in the English class are more variable than those in the math class.

Multiple choice

A test consisting of five questions, each worth 20 marks, was conducted by a school. Lee and Janny were two students who took the test, and their marks were recorded and tabulated. Question number 1 2 3 4 5 Marks scored by Lee 18 14 19 17 20 Marks scored by Janny 19 12 17 20 19 Which of the following statements accurately represents the information given about Lee's and Janny's test results?

  1. The mean marks of Lee are greater than the mean marks of Janny by 0.2.

  2. The mean marks of Lee are less than the mean marks of Janny by 0.2.

  3. The mean marks of Lee and the mean marks of Janny are equal to 17.4.

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

Lee's marks: (18+14+19+17+20)/5 = 88/5 = 17.6. Janny's marks: (19+12+17+20+19)/5 = 87/5 = 17.4. Difference = 17.6 - 17.4 = 0.2. Lee's mean is greater than Janny's mean by 0.2.

Multiple choice

Directions : Select the correct alternative from the given choices. There are n terms in an arithmetic progression. The n terms of the arithmetic progression are now distributed into eight sub-series S1, S2 ……and S8 as follows. The 1st, 9th, 17th terms and so on go into S1; the 2nd, 10th, 18th terms and so on go into S2; the 3rd, 11th, 19th terms and so on go into S3, and so on for S4 till S8. If for exactly three of the eight sub-series, the average of the sub-series is a term of the same sub-series, how many of the following values can n assume? (i)43 (ii)53 (iii)51 (iv)69 (v)77

  1. 1

  2. 2

  3. 3

  4. 5
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The condition that the average of a sub-series is a term of the sub-series implies the number of terms in that sub-series must be odd. With 8 sub-series, we analyze the distribution of n terms. This is a complex problem requiring modular arithmetic.

Multiple choice

A simple random sample of 1,000 students at a large high school was selected and asked how often they read books outside of school and whether they preferred fiction or nonfiction. The results are shown in the table. Reading Frequency Fiction Nonfiction Total Daily 180 120 300 Weekly 200 250 450 Rarely 100 150 250 Total 480 520 1,000 Based on the survey, 45% of students read weekly. If the margin of error is ±3%, which of the following is the most accurate conclusion?

  1. The percentage of all students who read weekly is exactly 45%.

  2. The percentage of all students who read weekly is between 42% and 48%.

  3. It is impossible for the percentage of all students who read weekly to be less than 40%.

  4. About 3% of students surveyed were incorrectly classified as weekly readers.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

A margin of error of 3% means the true population proportion is likely within 45% ± 3%, which is 42% to 48%.