C280 Probability and Statistics I
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Free C280 Probability and Statistics I Questions
1. Simplify the expression: 6(x – 2) + 4x.
- 2x – 12
- 10x – 12
- 10x – 2
- 6x – 12
Explanation
Distribute 6 across the parentheses: 6(x – 2) = 6x – 12. Then add 4x: 6x – 12 + 4x = 10x – 12. Using distributive and combining-like-term rules ensures accurate simplification of algebraic expressions.
2. If a frequency table shows that most students score near the mean with few high and low values, which shape does the distribution likely have?
- Uniform
- Skewed left
- Skewed right
- Approximately normal
Explanation
When most data cluster around the mean with symmetrical tapering toward the extremes, the distribution is approximately normal. This bell-shaped curve is common in real-world data like test scores and biological measurements.
3. Which type of graph is most appropriate for displaying how a numerical variable changes over time?
- Histogram
- Line graph
- Pie chart
- Boxplot
Explanation
A line graph effectively displays trends over time, showing how data values increase or decrease across intervals. Each point is connected by a line to emphasize progression, making it ideal for visualizing time series data such as temperature or stock prices.
4. Which of the following is the correct definition of variance in a data set?
- The average of all data points
- The square of the standard deviation
- The average of the squared differences from the mean
- The difference between the largest and smallest values
Explanation
Variance measures how far data points spread out from the mean by averaging the squared deviations of each value from the mean. This squaring prevents negative differences from canceling out. It’s a fundamental concept for standard deviation and inferential statistics.
5. In a data set of ages: 18, 20, 22, 24, 26, what is the mean age?
- 20
- 21
- 22
- 23
Explanation
Add all values and divide by the number of data points: (18 + 20 + 22 + 24 + 26) ÷ 5 = 110 ÷ 5 = 22. The mean summarizes the average age in the data set, a basic descriptive statistic.
6. Which graphical display is most appropriate for showing the distribution of a single categorical variable?
- Histogram
- Pie chart
- Scatterplot
- Boxplot
Explanation
A pie chart effectively represents categorical data by dividing a circle into sectors that correspond to the proportion of each category. It provides an intuitive visual comparison of parts to a whole. In contrast, histograms and boxplots are used for quantitative data, while scatterplots show relationships between two variables.
7. 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.
8. If the sum of all probabilities in an experiment is not equal to 1, what does this indicate?
- There is an error in assigning probabilities
- The experiment has too many outcomes
- The events are dependent
- The probabilities are conditional
Explanation
The sum of probabilities of all possible outcomes in an experiment must equal 1. If it does not, it means probabilities were incorrectly assigned or an event was omitted. This rule ensures the model accounts for every possible outcome in the probability space.
9. Which of the following statements is true about correlation and causation?
- Correlation always implies causation
- Causation can exist without correlation
- Correlation does not imply causation
- If correlation is strong, causation must exist
Explanation
Correlation does not imply causation. Two variables may move together due to coincidence or a lurking variable. Establishing causation requires controlled experiments or evidence showing one variable directly influences another.
10. A data set contains values: 5, 7, 7, 8, 9, 10, and 15. Which measure of central tendency best represents the data?
- Mean
- Median
- Mode
- Range
Explanation
The median is the middle value when the data are ordered, and it’s less affected by outliers such as 15. Here, the median (8) provides a more accurate representation of central tendency than the mean, which would be skewed higher due to the large outlier.
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