C280 Probability and Statistics I
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Free C280 Probability and Statistics I Questions
Which type of graph is most appropriate for displaying how a numerical variable changes over time?
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Histogram
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Line graph
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Pie chart
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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.
A scatterplot shows a cloud of points with no clear upward or downward trend. Which of the following best describes the relationship between the variables?
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Strong positive correlation
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Strong negative correlation
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No correlation
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Curvilinear relationship
Explanation
When the points on a scatterplot appear randomly distributed without any discernible trend, there is no correlation between the variables. This indicates that changes in one variable do not predict or influence changes in the other variable.
Simplify the expression: 6(x – 2) + 4x.
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2x – 12
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10x – 12
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10x – 2
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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.
When two variables show a consistent increase or decrease together, what type of correlation exists?
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Positive correlation
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Negative correlation
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No correlation
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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.
Which of the following correctly describes a symmetric distribution?
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The mean and median are far apart
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Data are clustered to one side
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Both sides of the distribution mirror each other
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The distribution has two peaks
Explanation
In a symmetric distribution, data values are evenly spread around the mean, and both sides of the graph mirror one another. The mean and median are equal, indicating balance in the dataset with no skewness present.
Which of the following best describes the interquartile range (IQR) in a data set?
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The difference between the highest and lowest data values
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The range of values that contains the middle 50% of the data
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The average of the upper and lower quartiles
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The distance between the mean and median
Explanation
The interquartile range (IQR) measures variability by describing the range of the middle 50% of data points. It is calculated as Q3 – Q1, where Q3 is the third quartile and Q1 is the first quartile. This measure helps reduce the impact of outliers and provides a more reliable view of data spread compared to the overall range.
What is the decimal equivalent of 3/8?
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0.25
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0.4
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0.375
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0.5
Explanation
To convert a fraction to a decimal, divide the numerator by the denominator: 3 ÷ 8 = 0.375. This process allows fractional measurements to be used more easily in digital or financial contexts where decimals are preferred.
Which of the following represents the sample space for flipping two coins?
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{H, T}
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{HH, HT, TH, TT}
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{HH, TT}
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{HT, TT}
Explanation
The sample space lists all possible outcomes. For two coins: First coin – H or T; second coin – H or T; Total outcomes = {HH, HT, TH, TT}. This forms the basis for calculating probabilities of specific combinations.
A data set contains values: 5, 7, 7, 8, 9, 10, and 15. Which measure of central tendency best represents the data?
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Mean
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Median
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Mode
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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.
In a survey, 60% of respondents are female, and 40% are male. Which type of variable does gender represent?
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Quantitative
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Continuous
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Categorical
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Numerical
Explanation
Gender is a categorical variable because it classifies individuals into distinct groups without numerical value. Categorical data are analyzed using frequencies or proportions rather than numerical calculations.
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