Statistics Basics Quiz
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Questions and Answers

What is the first step in calculating the standard deviation from a set of values?

  • Average the square differences
  • Subtract the mean from each value and square the difference
  • Calculate the mean (correct)
  • Determine the range

    • A frequency polygon is a type of graph used to represent frequency distribution by connecting midpoints of intervals.

    True

    What are the three measures of central tendency?

    Mean, Median, Mode

    The _____ shows how spread out the values in a data set are.

    <p>range</p> Signup and view all the answers

    Match the following statistical terms with their definitions:

    <p>Mean = The average of a set of values Median = The middle value when data is ordered Mode = The most frequently occurring value Range = The difference between the maximum and minimum values</p> Signup and view all the answers

    Which of the following represents a valid way to summarize data?

    <p>Frequency distribution table</p> Signup and view all the answers

    The mode is always a unique value in a data set.

    <p>False</p> Signup and view all the answers

    What is one practical application of using a stem-and-leaf plot?

    <p>To display data while retaining the original values and showing distribution.</p> Signup and view all the answers

    Which level of measurement would the survey responses of yes, no, and undecided represent?

    <p>Nominal</p> Signup and view all the answers

    Quantitative data can be categorized based on qualities, such as color or type.

    <p>False</p> Signup and view all the answers

    What is one advantage of using stratified sampling?

    <p>It ensures representation from different subgroups within the population.</p> Signup and view all the answers

    For a survey with 10 questions, where 2 questions are identical and 3 others are also the same, how many different arrangements are possible?

    <p>39</p> Signup and view all the answers

    In convenience sampling, researchers select a sample based on their ______ to access it.

    <p>ease</p> Signup and view all the answers

    A continuous random variable can take on an infinite number of values.

    <p>True</p> Signup and view all the answers

    Match the following sampling techniques with their descriptions:

    <p>Systematic Sampling = Selection of every nth individual from a list Cluster Sampling = Dividing the population into groups and sampling entire groups Convenience Sampling = Choosing individuals who are easiest to reach Stratified Sampling = Dividing the population into subgroups and sampling from each</p> Signup and view all the answers

    What are the three requirements of a probability distribution?

    <ol> <li>The sum of probabilities must equal 1. 2. All probabilities must be between 0 and 1. 3. Each outcome must be independent.</li> </ol> Signup and view all the answers

    Which of the following is an example of cluster sampling?

    <p>Sampling all students from three different classrooms</p> Signup and view all the answers

    In a binomial distribution, the variable 𝑛 represents the number of ______ selected.

    <p>trials</p> Signup and view all the answers

    Match the following parameters of a probability distribution with their definitions:

    <p>Mean = Average of all possible values Variance = Measure of dispersion Standard Deviation = Square root of variance Range = Difference between maximum and minimum values</p> Signup and view all the answers

    A Pareto chart is used to display quantitative data over time.

    <p>False</p> Signup and view all the answers

    What is the probability of winning the jackpot in the Pennsylvania Match 6 Lotto with one ticket purchased?

    <p>1 in $13,983,816$</p> Signup and view all the answers

    What does a bar graph represent?

    <p>A bar graph visually represents categorical data with rectangular bars.</p> Signup and view all the answers

    In a binomial distribution, the outcomes must be dependent on each other.

    <p>False</p> Signup and view all the answers

    If the probability of an event is 0.85, what is the probability that the event does not occur?

    <p>0.15</p> Signup and view all the answers

    What is the probability that a subject has a positive test result given that they use drugs?

    <p>0.044</p> Signup and view all the answers

    The factorial of a number 'n' is the product of all positive integers from 1 to 'n'.

    <p>True</p> Signup and view all the answers

    What represents the most basic unit of information in computing?

    <p>bit</p> Signup and view all the answers

    The number of ways to select 'r' items from a set of 'n' distinct items is given by the formula for __________.

    <p>combinations</p> Signup and view all the answers

    In a race with 20 horses, what is the probability of winning an exacta bet by selecting Super Saver to win and Ice Box to finish second?

    <p>1/380</p> Signup and view all the answers

    If a student makes a random guess while arranging names, what method is being displayed?

    <p>permutations</p> Signup and view all the answers

    How many different characters can be represented by a byte?

    <p>256</p> Signup and view all the answers

    Match the following terms with their appropriate definitions:

    <p>Permutations = Different arrangements of a set where order matters Combinations = Selections from a set where order does not matter Factorial = The product of all positive integers up to a given number Bit = The smallest unit of data in computing</p> Signup and view all the answers

    What is the mean number of participants recognizing the McDonald's brand in a group of 12 adults, given a recognition rate of 95%?

    <p>11.4</p> Signup and view all the answers

    The variance of a binomial distribution increases as the probability of success increases.

    <p>False</p> Signup and view all the answers

    What does a standard deviation of 0.15 meters indicate about the heights of students at LCC?

    <p>The heights of students vary about 0.15 meters from the mean of 1.4 meters.</p> Signup and view all the answers

    In a standard normal distribution, approximately _____% of data falls within one standard deviation of the mean.

    <p>68</p> Signup and view all the answers

    Match the following heights with their descriptions.

    <p>168 cm = Giselle's height 174 cm = Mean boy's height 6 cm = Standard deviation of boys' heights 186 cm = Height percentile threshold</p> Signup and view all the answers

    For the given height data, which would indicate a left skew?

    <p>The mean is less than the median.</p> Signup and view all the answers

    The empirical rule states that approximately 99.7% of data in a normal distribution falls within three standard deviations of the mean.

    <p>True</p> Signup and view all the answers

    What does a negatively skewed distribution look like?

    <p>It has a long left tail and the bulk of data points are on the right.</p> Signup and view all the answers

    What z-score corresponds to a value that is 1.27 standard deviations above the mean?

    <p>1.27</p> Signup and view all the answers

    The standard normal distribution has a mean of 1 and a standard deviation of 0.

    <p>False</p> Signup and view all the answers

    What is the percentile for a z-score of -2.83?

    <p>0.0023</p> Signup and view all the answers

    The z-score for the lower 93.7% of the data is __________.

    <p>1.81</p> Signup and view all the answers

    Match the following values with their corresponding z-scores:

    <p>Percentile 13.6% = z = -1.06 Percentile 40% = z = -0.25 Percentile 92.65% = z = 1.44 Percentile 50% = z = 0</p> Signup and view all the answers

    Which scenario describes an unusual value?

    <p>A result of 30 chocolate chips when the mean is 24 and the standard deviation is 2.6.</p> Signup and view all the answers

    Women have normally distributed heights with a mean of __________ inches.

    <p>63.8</p> Signup and view all the answers

    Calculate the probability that a randomly selected adult has a bone density score above -1.00.

    <p>0.8413</p> Signup and view all the answers

    Study Notes

    Mathematics of Data Management

    • Part 1 covers Descriptive Statistics, making up 30% of the course.
    • Course notes are from Lower Canada College.

    Unit 1 - Introduction to Statistics

    • A. Basics
      • A survey is a process of gathering information for informed decisions.
      • Data are observations (e.g., eye color, salary, height).
      • A population is the complete group.
      • A sample is a subset of the population.
      • Sampling Techniques
        • Voluntary Response Sample: Participants decide whether to participate. This method has limitations, as the sample may not represent the population
        • Simple Random Sample: Participants are selected randomly. This approach can ensure the sample represents the population fairly. An example is selecting 10 students from each grade randomly.
      • Sources of Bias
        • Sampling Bias: When the sample doesn't reflect the characteristics of the whole population. An example is only surveying Montreal Canadiens fans to determine favourite NHL team.
        • Non-Response Bias: When specific groups aren't represented in a survey because they opted out of participating. This often arises when surveys are optional. An example is when only 50% of students respond to a survey on athletics.

    Generating A Simple Random Sample

    • Steps to generate a simple random sample using a calculator are described, including seeding the random number generator.

    Types of Data

    • Qualitative Data: Characterized by names or labels. Examples are eye color, political party affiliations.
    • Quantitative Data: Characterized by numerical measurements.
      • Discrete Data: Finite or countable values. Examples include the number of eggs laid in a week, rolls of a die.
      • Continuous Data: Infinite possible values. An example is the amount of milk a cow yields in a year (any value between 0 to 7000 liters).

    Levels of Measurement

    • Nominal: Categories, no order (e.g., favorite food).
    • Ordinal: Categories with an order (e.g., letter grade).
    • Interval: Has meaningful differences between values but no true zero (e.g., temperature in Celsius).
    • Ratio: Has meaningful differences and a true zero (e.g., salary, age).

    C. Collecting Data

    • Sampling Techniques
      • Systematic Sampling: Select participants at regular intervals. Good for large populations, but potentially prone to bias if the intervals have a hidden pattern
      • Stratified Sampling: Divides the population into strata (groups with shared characteristics). Random sampling within each strata. Can improve representation, but also requires significant effort
      • Cluster Sampling: Divide the population into clusters, randomly select clusters. Can be more efficient with large populations, but may reduce diversity.
      • Convenience Sampling: Selecting accessible participants. This method usually isn't reliable, as the sample is unlikely to represent the population truly.

    Unit 2 - Graphing and Summarizing Data

    • A. Graphing data
      • Data visualisation facilitates easier understanding and makes predictions.
      • Creating bar charts, pie charts, and Pareto charts is discussed.
      • Graphs organise and summarise data, allowing quicker analysis.
    • Frequency Distribution Table
      • Tabulates data with frequencies, relative frequencies and cumulative frequencies
    • Histograms
      • Bars are side by side, similar to bar graphs, where each bar shows frequency of data within a class interval
    • Frequency Polygon
      • Connect the midpoints of adjacent bars
    • Ogive (Cumulative Frequency Polygon) -Shows cumulative frequencies
    • Stem and Leaf Diagrams -Visualises data by separating each data value into a stem and leaf

    Measures of Central Tendency

    • Mean: Average of the data values
    • Median: Middle value when data is ordered
    • Mode: Most frequent value

    Measures of Dispersion (Spread)

    • Range: Difference between highest and lowest data values.
    • Variance: Average of the squared differences from the mean.
    • Standard Deviation: Square root of the variance.

    Finding the mean, variance and standard deviation

    • Steps for calculating mean, variance and standard deviation are illustrated with an example of dog heights.
      • Calculate the mean (average) of the data values
      • Calculate the difference between each value and the mean, and square these differences
      • Calculate the average (mean) of the squared differences
      • Calculate the square root of the variance to get the standard deviation

    Unit 3 - Probability

    • A. Basics of Probability
      • Probability is about the likelihood of an event occurring. An example of an event is getting a boy or a girl.
      • An event is a group of outcomes from a particular procedure.
      • A simple event has no subsets. The sample space is the whole group of all the possible simple events.
      • Probability of an event is between zero and one.
    • Types of Events
    • Complementary Events: The events that do not occur. The complement of event A occurs if A doesn't occur
    • Compound Events A compound event occurs if two or more simple events occur. An example is if both A and B occur
    • Independent/Dependent Events: If the occurence of event one does not affect the probability of the other (indepedent), or if the occurrence of one event does affect the probability of the other (dependent).
    • Conditional probability The probability of an event given some additional information, that some other event has already occurred.

    Counting

    • Permutations: Order matters.
    • Combinations: Order does not matter.
    • Rules for calculating them are given, for both when all items are different, or some items are the same.
      • Factorial Rule: Calculating permutations when there are the same number of items as options
      • Fundamental Counting Rule: Calculating possible outcomes of multiple events
      • Permutation Rule: Calculating permutations when there are multiple items that are identical

    Unit 4 - The Normal Distribution

    • A. Normal Distributions and standard deviations:

    • Normal curves are symmetrical and bell shaped

    • mean, median, mode are equal and centered in the distribution

    • 68% of data values are within one standard deviation of the mean

    • 95% are within two standard deviations of the mean

    • 99.7% are within three standard deviations of the mean. -z-scores convert any normal distribution to a standard normal distribution. Standardized z-scores allow for comparisons between different distributions.

    • Range Rule of Thumb: The vast majority of values live within 2 standard deviations of the mean

    • B. Skewness:

      • Visual representation of how the distribution is lopsided or not
      • Measures of skewness quantify how symmetrical the distribution is

    • C. Standard Normal distributions and z-scores:

      • Allows for comparison between different distributions

    • E. Percentages and values (Normal Distribution):

      • Identifying specific values (e.g., heights) that fall within given percentiles of a normal distribution.

    • F. Proving Normalcy:

      • Identify if distribution satisfies characteristics of a normal distribution

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    Mathematics of Data Management Notes (Lower Canada College)

    Description

    Test your understanding of fundamental statistical concepts including standard deviation, central tendency, and data summarization methods. This quiz covers essential aspects of statistics, making it perfect for beginners and intermediate learners alike.

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