C280 Probability and Statistics I
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Free C280 Probability and Statistics I Questions
1. Which of the following values represents a parameter rather than a statistic?
- The mean height of 50 randomly selected students
- The average weight of all students in a school
- The median income of a sample of 200 households
- The proportion of left-handed students in a class sample
Explanation
A parameter describes an entire population, whereas a statistic describes a sample. “The average weight of all students in a school” is a parameter because it represents the complete population being studied rather than a subset or sample.
2. If the mean of five numbers is 12, what is the total sum of the numbers?
- 24
- 48
- 60
- 72
Explanation
The mean equals the total sum divided by the number of data points. Mean = Sum ÷ Number of values → 12 = Sum ÷ 5 → Sum = 12 × 5 = 60. Thus, the total of all five numbers must be 60.
3. A researcher finds that as study hours increase, test anxiety decreases. This is an example of:
- Positive correlation
- Negative correlation
- No correlation
- Spurious correlation
Explanation
A negative correlation means that as one variable increases, the other decreases. In this case, more study hours correspond to lower anxiety levels. The correlation coefficient (r) would have a negative value, indicating an inverse relationship between the two variables.
4. Simplify the algebraic expression: 4x – 3(2x – 5).
- 10x – 15
- –2x + 15
- 2x + 15
- –2x – 15
Explanation
Distribute –3 across the parentheses: 4x – 3(2x – 5) = 4x – 6x + 15 = –2x + 15. Applying the distributive property accurately prevents sign errors during algebraic manipulation.
5. The range of a data set is determined by:
- Subtracting the smallest value from the largest value
- Adding all values and dividing by the number of values
- Finding the middle value when data are ordered
- Finding the most frequently occurring value
Explanation
The range is a measure of dispersion calculated by subtracting the minimum value from the maximum value. It provides a simple way to understand the spread of data but does not reflect how values are distributed between the extremes, unlike standard deviation or IQR.
6. Which of the following situations would best be represented by a Venn diagram?
- Comparing monthly sales totals for different years
- Showing student overlap between sports and music clubs
- Displaying temperature changes over time
- Illustrating average exam scores
Explanation
A Venn diagram visually represents relationships and overlaps between groups. In this case, it effectively shows students who participate in both sports and music, only one, or neither activity—highlighting intersections among sets.
7. Which of the following would cause the range of a data set to increase?
- Adding a value near the mean
- Removing an outlier
- Adding a new extreme value
- Reducing the largest number
Explanation
The range depends on the difference between the largest and smallest values. Adding a new extreme (either very high or low) value increases that difference, thereby increasing the range and overall variability in the data.
8. When two variables show a consistent increase or decrease together, what type of correlation exists?
- Positive correlation
- Negative correlation
- No correlation
- Curvilinear correlation
Explanation
A positive correlation occurs when one variable increases as the other increases. This indicates a direct relationship between the two variables. For example, height and weight often show a positive correlation. The relationship is measured using the correlation coefficient (r), where values closer to +1 signify a strong positive relationship.
9. When converting a fraction to a decimal, what operation should be performed?
- Multiply the numerator and denominator
- Add the numerator and denominator
- Divide the numerator by the denominator
- Subtract the denominator from the numerator
Explanation
To convert a fraction to a decimal, divide the numerator (top number) by the denominator (bottom number). For example, 3/4 = 3 ÷ 4 = 0.75. This conversion allows fractional values to be expressed in decimal form, making comparison and computation easier.
10. When data points fall closely along a straight line in a scatterplot, the correlation between the variables is:
- Weak
- Strong
- Nonexistent
- Negative
Explanation
A strong correlation exists when data points cluster tightly around a straight line, indicating a consistent linear relationship between variables. The closer the correlation coefficient (r) is to ±1, the stronger the relationship.
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