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Quizzes > High School Quizzes > Mathematics

Unit 8: Probability & Statistics Practice Quiz

Sharpen skills with practice and answer key

Difficulty: Moderate
Grade: Grade 8
Study OutcomesCheat Sheet
Colorful paper art promoting Ace Unit 8 Stats practice quiz for high school statistics students.

Easy
What does probability measure?
The difference between the highest and lowest outcomes
The chance or likelihood that an event will occur
The total number of outcomes of an event
How frequently an event happens over a long period
Probability measures the chance or likelihood that an event will occur. It is usually expressed as a fraction, decimal, or percentage.
Which of the following represents a fair coin toss outcome?
Head: 80%, Tail: 20%
Head: 50%, Tail: 50%
Head: 60%, Tail: 40%
Head: 70%, Tail: 30%
A fair coin toss implies equal likelihood for heads and tails, each with a probability of 50%. This is the definition of fairness in probabilities.
What does the term 'sample space' in probability refer to?
A specific outcome in an experiment
The event that never occurs
The most likely result in a set of outcomes
The set of all possible outcomes of an experiment
The sample space is the set of all possible outcomes in a probability experiment. It provides the foundation for calculating probabilities.
When rolling a standard six-sided die, what is the probability of getting a 3?
1/6
1/3
1/2
1/4
A standard die has six equally likely outcomes, so the probability of rolling any specific number, including 3, is 1/6. This is a basic probability scenario.
Which of the following is a measure of central tendency?
Interquartile Range
Mean
Range
Standard Deviation
Mean is a measure of central tendency, representing the average of a set of numbers. It provides a central point for the data distribution.
Medium
If a bag contains 4 red, 5 blue, and 3 green marbles, what is the probability of drawing a blue marble?
5/12
1/3
4/12
3/12
There are 5 blue marbles out of a total of 12. Thus, the probability is 5/12 by dividing the number of blue marbles by the total number of marbles.
A spinner is divided into 8 equal sections numbered 1 to 8. What is the probability that the spinner lands on a number greater than 6?
1/4
1/2
2/3
1/8
Only two numbers (7 and 8) are greater than 6 out of 8 total numbers. The probability is calculated by dividing 2 by 8, which simplifies to 1/4.
What is the complement of the event 'rolling an even number' on a standard die?
Rolling a prime number
Rolling a number greater than 3
Rolling an odd number
Rolling a number less than 4
The complement of an event consists of all outcomes that are not part of the event. Since the event describes rolling an even number, its complement is rolling an odd number.
In a data set, which measure tells you the middle value when the numbers are arranged in order?
Mean
Range
Median
Mode
The median represents the middle value in an ordered data set. It divides the dataset into two equal halves.
Which of the following best describes a bar graph?
A graphical display of data using bars to represent values
A pie chart divided into different sectors
A plot showing the frequency of data along a continuous number line
A diagram that shows relationships among parts of a whole
A bar graph uses rectangular bars to represent data values. It is useful for comparing quantities across different categories.
If the mean of a set of numbers is 20 and you add a new data point of 30, what can be said about the mean?
It will increase from 20
It will decrease
It cannot be determined from the given information
It will remain 20
Adding a data point that is higher than the existing mean will raise the overall average. Therefore, the mean will increase when a value larger than 20 is added.
Which measure of variability is calculated by taking the square root of the variance?
Median absolute deviation
Range
Standard deviation
Interquartile range
The standard deviation is obtained by taking the square root of the variance. It provides a measure of dispersion in the same units as the original data.
What does a large standard deviation indicate about a data set?
The data points are spread out over a wide range
The data set has a high median but low mean
The data points are close to the mean
The data set has only one unique value
A large standard deviation means that the data values are more dispersed around the mean. It indicates significant variability in the data set.
In statistics, what is an outlier?
The middle value in an ordered dataset
The most frequently occurring value
A data point that is significantly different from the others
The average of all data points
An outlier is a data point that deviates markedly from the other values in a data set. It can indicate variability or possible errors in data collection.
If two events, A and B, are mutually exclusive, what does this mean?
They always occur together
One event causes the other to occur
Their probabilities add up to one
They cannot occur at the same time
Mutually exclusive events are those that cannot happen simultaneously. If one event occurs, the other cannot, which is the definition of mutual exclusivity.
Hard
A classroom survey recorded the number of hours students studied per week. The data is: 5, 7, 7, 8, 9, 10, 10, 10, 11, 12. What is the mode of the dataset?
11
9
7
10
The mode is the value that appears most frequently in a dataset. In this case, the number 10 appears three times, more than any other number.
A die is rolled twice. What is the probability of getting a sum of 7 on the two rolls?
1/6
1/12
1/3
1/8
There are 36 possible outcomes when rolling two dice, and there are six combinations that give a sum of 7. Thus, the probability is 6/36, which simplifies to 1/6.
A data set has a mean of 50 and a standard deviation of 5. If the data is normally distributed, approximately what percentage of values fall between 45 and 55?
95%
68%
50%
99%
In a normal distribution, about 68% of the values lie within one standard deviation of the mean. Since 45 and 55 are one standard deviation away from 50, approximately 68% of the values fall in this range.
If a probability experiment is repeated independently many times, which law states that the experimental probability will converge to the theoretical probability as the number of trials increases?
Regression to the Mean
Central Limit Theorem
Law of Averages
Law of Large Numbers
The Law of Large Numbers explains that as an experiment is repeated, the experimental probability tends to approach the theoretical probability. This principle is fundamental in probability and statistics.
In a survey, 60% of respondents like chocolate ice cream and 40% like vanilla. If a respondent is chosen at random from those who like either chocolate or vanilla, what is the probability that they like chocolate?
70%
60%
40%
50%
Since the respondents only like chocolate or vanilla, and 60% prefer chocolate, the probability that a randomly selected respondent likes chocolate is 60%. This is a simple application of conditional probability.
0
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Study Outcomes

  1. Understand core probability concepts including independent and dependent events.
  2. Calculate and interpret measures of central tendency and variability.
  3. Apply probability rules to solve real-world problems.
  4. Analyze data using appropriate graphical representations.
  5. Evaluate statistical conclusions based on sample data.

Unit 8 Probability & Stats Answer Key Cheat Sheet

  1. Understand the 68 - 95 - 99.7 Rule - Roughly 68% of data falls within one standard deviation of the mean, 95% within two, and 99.7% within three. This rule is perfect for predicting spread and finding outliers. OpenStax: Normal Distributions
  2. Learn to construct and interpret scatter plots - Scatter plots map one variable against another, letting you spot trends, clusters, or rogue outliers instantly. They're a visual powerhouse for understanding relationships! The Core Standards: Scatter Plots
  3. Master calculating and interpreting confidence intervals - Confidence intervals craft a range where the true population value likely sits, pairing your point estimate with a margin of error. They highlight how precise your stats really are. Quizlet: Confidence Intervals
  4. Grasp the concept of standard error - Standard error gauges how much your sample statistic might wiggle around the true population parameter. Smaller standard errors mean more reliable, rock-solid estimates! Quizlet: Standard Error
  5. Understand the importance of random sampling - Random sampling gives every individual an equal shot at selection, cutting bias and boosting result reliability. It's the unsung hero behind trustworthy studies. CliffsNotes: Random Sampling
  6. Learn about the Central Limit Theorem - The Central Limit Theorem promises that bigger sample sizes make the distribution of sample means look normal, even from weird populations. It's the backbone of inferential stats! OpenStax: Central Limit Theorem
  7. Familiarize yourself with hypothesis testing - Hypothesis testing is your statistical courtroom: you assume a parameter value, gather sample evidence, then decide if there's enough proof to reject the status quo. Quizlet: Hypothesis Testing
  8. Understand the difference between correlation and causation - Correlation shows variables moving together but doesn't prove one causes the other - no sneaky cause-and-effect conclusions! Always dig deeper before claiming a true causal link. The Core Standards: Correlation vs. Causation
  9. Learn to calculate and interpret p-values - A p-value measures how likely your data could occur under the null hypothesis. Tiny p-values shout "reject the null!" and give your results some serious cred. Quizlet: P-Values
  10. Understand the concept of statistical power - Statistical power is the chance you'll catch a real effect, influenced by sample size, effect magnitude, and the alpha level. Higher power means fewer false negatives. Quizlet: Statistical Power
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