AST Data Analysis and Statistics 1 — Questions and Answers
Question 1: The ages of 7 students are: 14, 16, 15, 17, 14, 18, 15. What is the median age?
- 14
- 15 (Correct answer)
- 16
- 17
Correct answer: 15
Sorted: 14, 14, 15, 15, 16, 17, 18. The median (4th value) is 15.
The median is the middle value of an ordered data set. Sort: 14, 14, 15, 15, 16, 17, 18. With 7 values, the middle position is (7+1)/2 = 4th. The 4th value is 15.
Question 2: A survey found that 45% of students prefer math. If 200 students were surveyed, how many prefer math?
- 80
- 85
- 90 (Correct answer)
- 95
Correct answer: 90
0.45 × 200 = 90 students.
To find a percentage of a total, convert the percentage to a decimal: 45% = 0.45. Multiply: 0.45 × 200 = 90. So 90 students prefer math.
Question 3: The data set {3, 7, 7, 9, 11} has a mean of 7.4. What is the range?
- 4
- 6
- 7
- 8 (Correct answer)
Correct answer: 8
Range = highest - lowest = 11 - 3 = 8.
The range measures the spread of a data set. It is calculated as the maximum value minus the minimum value. Max = 11, Min = 3. Range = 11 - 3 = 8. The mean is not needed to find the range.
Question 4: Which measure of central tendency is most affected by an extreme outlier?
- Mode
- Median
- Mean (Correct answer)
- Range
Correct answer: Mean
The mean uses all data values, so a very large or small outlier pulls it significantly.
The mean (average) is calculated by summing all values and dividing by count. An extreme outlier heavily distorts this sum. The median is resistant to outliers because it only depends on the middle position. The mode is unaffected by outliers unless the outlier itself repeats.
Question 5: A scatter plot shows a strong negative correlation. This means as x increases, y:
- increases sharply
- stays constant
- decreases (Correct answer)
- increases slightly
Correct answer: decreases
A negative correlation means as one variable increases, the other decreases.
Correlation describes the relationship between two variables. A negative correlation (r close to -1) shows that as x increases, y decreases. A positive correlation means both increase together. Zero correlation means no linear relationship.
Question 6: A class scored: 72, 85, 90, 88, 76, 92, 85. What is the mode?
- 85 (Correct answer)
- 88
- 90
- 72
Correct answer: 85
85 appears twice; all other values appear once. Mode = 85.
The mode is the most frequently occurring value. Scanning the data set: 72 (×1), 85 (×2), 90 (×1), 88 (×1), 76 (×1), 92 (×1). Only 85 appears more than once, making it the mode.
AST Data Analysis and Statistics 1
The ages of 7 students are: 14, 16, 15, 17, 14, 18, 15.
What is the median age?