Aptitude Questions on Statistics
Q. 1 The students of Bright Future Academy recently received their exam scores. The class of 50 students had an average mark of 72. However, two students, who scored 64 and 58 respectively, moved to a different section, prompting the teacher to recalculate the average marks of the remaining students. What is the new average for the 48 students?
A) 73.2
B) 72.5
C) 71.8
D) 70.9
Check Solution
Ans: B) 72.5
Original total marks = $50 \times 72 = 3600$
Marks of two excluded students = 64+58=122
New total marks = 3600−122=3478
New average = $\frac{3478}{48} = 72.458 \approx 72.5$
Q. 2 The marks scored by 11 students in Aptitude Exams are: 48, 55, 63, 45, 52, 65, 70, 40, 50, 60, 58. Teacher is more interested in understanding the median score to understand proficiency of the students as a group. What is the median score?
A) 55
B) 58
C) 60
D) 63
Check Solution
Ans: A) 55
Arranging the scores in ascending order: 40, 45, 48, 50, 52, 55, 58, 60, 63, 65, 70
Median = Middle value = 55
Q. 3 An engineering college organized quiz competition as part of the tech-fest. The scores of quiz participants were: 5, 7, 9, 11, and 13. Find the standard deviation?
A) 2.58
B) 2.82
C) 3.16
D) 3.45
Check Solution
Ans: B) 2.82
Mean $\mu = \frac{5+7+9+11+13}{5}$
Variance $\sigma^2 = \frac{(5-9)^2 + (7-9)^2 + (9-9)^2 + (11-9)^2 + (13-9)^2}{5}$
Standard deviation $\sigma = \sqrt{8} \approx 2.82$
Q. 4 In a probability distribution, the mean is 25, and the standard deviation is 5. Approximately what percentage of values lie between 20 and 30 (assuming a normal distribution)?
A) 68%
B) 50%
C) 95%
D) 99%
Check Solution
Ans: A) 15 and 25.
In a normal distribution, approximately 68% of data lies within 1 standard deviation of the mean.
Here, 25−5=20 and 25+5=30.
Q. 5 A sports coach is analyzing the performance of her players based on their practice session scores: 56, 62, 56, 64, 70, 56, and 68. She decides to use the mode to identify the most frequently occurring score. What is the mode of this dataset?
A) 56
B) 62
C) 64
D) 70
Check Solution
Ans: A) 56
The number 56 appears 3 times, more than any other score.
Q. 6 Two groups of students have averages of 75 and 85, with 30 and 20Two classes in a school participated in a math contest. The first class of 30 students had an average score of 75, while the second class of 20 students had an average score of 85. The principal wanted to calculate the overall average score of the 50 students combined. What is the combined average?
A) 79
B) 80
C) 81
D) 82
Check Solution
Ans: A) 79
Combined total marks = $75 \times 30 + 85 \times 20 = 2250 + 1700 = 3950$
Combined average = $\frac{3950}{50} = 79$
Q. 7 A meteorologist recorded the daily temperature extremes in a week. The minimum recorded temperature was 15°C, and the maximum was 95°C. She then calculated the range of temperatures for her report. What is the range of the dataset?
A) 70
B) 75
C) 80
D) 85
Check Solution
Ans: C) 80
Range = 95−15=80
Q. 8 A dataset has a mean of 50 and a standard deviation of 5. What is the coefficient of variation (CV)?
A) 5%
B) 10%
C) 20%
D) 50%
Check Solution
Ans: B) 10%
Coefficient of Variation CV=$ \frac{\sigma}{\mu} \times 100 = \frac{5}{50} \times 100 = 10\%$
Q. 9 In a dataset, the mean is greater than the median. What type of skewness does it have?
A) No skewness
B) Positive skewness
C) Negative skewness
D) Cannot be determined
Check Solution
Ans: B) Positive skewness
If the mean is greater than the median, the dataset is positively skewed
Q. 10 The marks obtained by 8 students are: 12, 18, 24, 30, 36, 42, 48, 54. What is the third quartile (Q3)?
A) 36
B) 42
C) 48
D) 54
Check Solution
Ans: C) 48
Q3=Value at (3/4)(n+1)th position=(3/4)(8+1)=6.75
Interpolating between the 6th and 7th values (42 and 48):
$Q3 = 42 + 0.75(48 – 42) = 42 + 4.5 = 46.5 \approx 48$
Refer Topic wise Aptitude Questions with Solutions
Refer Questions for next topic: https://www.learntheta.com/aptitude-questions-data-interpretation/