C280 Probability and Statistics I
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Free C280 Probability and Statistics I Questions
1. 32. Which of the following best explains why standard deviation is a more useful measure of spread than range?
- A) It uses only the smallest and largest values
- B) It measures how far each value deviates from the mean
- C) It identifies the median of the data set
- D) It shows the most frequent value in the data set
Explanation
Standard deviation measures how much individual data points differ from the mean, providing insight into variability across all observations. Unlike the range, which depends only on two extreme values, standard deviation reflects the spread of all data, making it a more accurate measure of dispersion.
2. 85. Which of the following represents a situation involving sampling bias?
- A) Randomly selecting students from a school list
- B) Surveying only morning shoppers to represent all customers
- C) Assigning numbers and using random generators for selection
- D) Using every fifth person in a line to create a sample
Explanation
Sampling bias occurs when certain members of a population are more likely to be included than others. Surveying only morning shoppers misses other customer groups, leading to inaccurate generalizations about the entire population.
3. 7. Which graphical display is most appropriate for showing the distribution of a single categorical variable?
- A) Histogram
- B) Pie chart
- C) Scatterplot
- D) 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.
4. 3. Which of the following best describes the interquartile range (IQR) in a data set?
- A) The difference between the highest and lowest data values
- B) The range of values that contains the middle 50% of the data
- C) The average of the upper and lower quartiles
- D) 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.
5. 24. If a number is multiplied by 0, the result is always:
- A) 1
- B) 0
- C) Undefined
- D) The number itself
Explanation
Any number multiplied by zero equals zero. This fundamental property of multiplication reflects that zero represents the absence of quantity, so combining any number with nothing yields nothing. This property is often used in simplifying algebraic expressions.
6. 40. A teacher records the number of books read by students each month. Which measure of spread would best show variation in the data?
- A) Range
- B) Mode
- C) Mean
- D) Median
Explanation
The range, calculated as the difference between the highest and lowest values, reveals the degree of variation within a data set. In this case, it shows how reading activity differs across students, providing a simple but clear measure of dispersion.
7. 48. If 15% of a store’s 400 customers buy gift cards, how many customers purchase them?
- A) 45
- B) 50
- C) 60
- D) 75
Explanation
To find 15% of 400: 0.15 × 400 = 60. Percentage calculations are used frequently in descriptive statistics, finance, and business decision-making to represent proportions.
8. 15. The range of a data set is determined by:
- A) Subtracting the smallest value from the largest value
- B) Adding all values and dividing by the number of values
- C) Finding the middle value when data are ordered
- D) 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.
9. 31. If 40% of a class are left-handed and 60% are right-handed, what is the probability that a randomly selected student is right-handed?
- A) 0.2
- B) 0.4
- C) 0.6
- D) 0.8
Explanation
Probabilities express the likelihood of events and always range between 0 and 1. Given that 60% of the students are right-handed, the probability of randomly selecting one who is right-handed equals 0.6, which represents 60 out of every 100 students.
10. 13. Which of the following statements best describes the purpose of descriptive statistics?
- A) To make predictions about a population based on a sample
- B) To organize and summarize data in a meaningful way
- C) To identify causal relationships between variables
- D) To determine the probability of rare events
Explanation
Descriptive statistics are used to organize, summarize, and present data in a clear and informative manner. They involve measures such as mean, median, mode, range, and standard deviation, as well as graphical representations like histograms and pie charts. The goal is to describe the main features of a dataset without making inferences beyond the data itself.
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