Statistics Definition & Scope
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Statistics Definition & Scope

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Questions and Answers

What is the computed value of the summation ∑ 𝑥?

  • 329
  • 468
  • 406 (correct)
  • 450

    • What is the correct formula for calculating ∑ 𝑥 2?

  • (75)2 + (80)2 + (97)2 + (91)2 + (63)2 (correct)
  • ∑ 𝑥 + ∑ 𝑥
  • ∑ 𝑥 * ∑ 𝑥
  • ∑ (𝑥 2)

    • What is the outcome of (∑ 𝑥)2?

  • 164836 (correct)
  • 168906
  • 162576
  • 165408

    • Which of the following correctly describes how to sum non-contiguous cells in Excel?

    <p>=SUM(A3 + A5 + A8)</p> Signup and view all the answers

    When using AutoSum in Excel, what is the first step?

    <p>Select the cell below the column of numbers</p> Signup and view all the answers

    What is the result of the summation $ extstyle rac{1}{10} extstyle ackslash sum_{i=6}^{10} x_i$ if $ extstyle rac{1}{10} extstyle ackslash sum_{i=1}^{5} x_i$ equals 50?

    <p>21</p> Signup and view all the answers

    If each of the first five terms of $x_i$ is multiplied by 8, what does $ extstyle ackslash sum_{i=1}^{5} 8x_i$ equal?

    <p>400</p> Signup and view all the answers

    What is an alternative way to express $ extstyle ackslash sum_{i=1}^{5} 8x_i$?

    <p>$ extstyle 8ackslash sum_{i=1}^{5} x_i$</p> Signup and view all the answers

    How is the value of $50$ reached in the equation $ extstyle 8 ackslash sum_{i=1}^{5} x_i = 400$?

    <p>It represents the total of the first five $x_i$ terms.</p> Signup and view all the answers

    What happens to the total when each of the first five terms of $x_i$ is multiplied by 8 before summation?

    <p>It increases the total sum eightfold.</p> Signup and view all the answers

    What is the primary focus of applied statistics?

    <p>Analyzing and interpreting data to solve real-world problems</p> Signup and view all the answers

    Which of the following best defines a quantitative variable?

    <p>Numerical values representing an amount or count</p> Signup and view all the answers

    Which type of variable can assume any value between two specific numbers?

    <p>Continuous variables</p> Signup and view all the answers

    What is Descriptive Statistics primarily used for?

    <p>Summarizing and describing important characteristics of a data set</p> Signup and view all the answers

    What distinguishes discrete variables from continuous variables?

    <p>Discrete variables can only take on integer values.</p> Signup and view all the answers

    What does the term 'random variable' refer to?

    <p>Variables determined by chance</p> Signup and view all the answers

    In what form does the term 'statistics' refer to a collection of numerical data?

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

    Which of the following is NOT considered an aspect of statistics?

    <p>Historical analysis of mathematical theories</p> Signup and view all the answers

    What is a key characteristic of ratio level measurement?

    <p>It allows for meaningful ratios and differences.</p> Signup and view all the answers

    Which sampling method involves selecting subjects at regular intervals after a random start?

    <p>Systematic Sampling</p> Signup and view all the answers

    What is the purpose of stratified sampling?

    <p>To divide a population into homogeneous groups for sampling.</p> Signup and view all the answers

    In cluster sampling, which of the following best describes the process?

    <p>Selecting entire groups or clusters for study.</p> Signup and view all the answers

    What is a disadvantage of using cluster sampling?

    <p>It might not accurately represent the whole population.</p> Signup and view all the answers

    What is the first step in systematic sampling?

    <p>Dividing the population size by the sample size.</p> Signup and view all the answers

    Which of the following is NOT a method of data collection?

    <p>Random sampling</p> Signup and view all the answers

    What does a true zero in ratio-level measurement indicate?

    <p>The absence of the quantity being measured.</p> Signup and view all the answers

    What does the formula $\sum_{i=1}^{n} c = n c$ imply?

    <p>The sum of a constant c over n terms is equal to n times c.</p> Signup and view all the answers

    If $\sum_{i=1}^{8} 10$ is evaluated, what is the result?

    <p>80</p> Signup and view all the answers

    Which of the following formulas represents the property of summation for multiple variables?

    <p>$\sum_{i=1}^{n} (x_i + y_i + z_i) = \sum_{i=1}^{n} x_i + \sum_{i=1}^{n} y_i + \sum_{i=1}^{n} z_i$</p> Signup and view all the answers

    How can you express $\sum_{i=1}^{n} (x_i \pm c)$ using summation notation?

    <p>$\sum_{i=1}^{n} x_i \pm n c$</p> Signup and view all the answers

    Given that $\sum_{i=1}^{10} x_i = 55$ and $\sum_{i=1}^{10} y_i = 65$, what is $\sum_{i=1}^{10} (x_i + y_i)$?

    <p>110</p> Signup and view all the answers

    What does the notation $\sum_{i=1}^{n} c x_i$ equal?

    <p>$c \sum_{i=1}^{n} x_i$</p> Signup and view all the answers

    In the expression $\sum_{i=1}^{n} (x_i + c)$, what happens to the summation if c is a constant?

    <p>It adds nc to the total sum of $x_i$.</p> Signup and view all the answers

    What is the simplified result of $\sum_{i=1}^{10} (3x_i + 4y_i - 7)$?

    <p>$3 \sum_{i=1}^{10} x_i + 4 \sum_{i=1}^{10} y_i - 70$</p> Signup and view all the answers

    Study Notes

    Statistics Definition & Scope

    • Statistics is a collection of methods for planning experiments, obtaining data, and analyzing, interpreting, and drawing conclusions based on the data.
    • Statistics has two aspects: theoretical and applied.
    • Data are the values that variables can assume.
    • Variables whose values are determined by chance are called random variables.

    Types of Variables

    • Qualitative variables are words or codes that represent a class or category.
    • Quantitative variables are numbers that represent an amount or a count.
    • Discrete variables can be assigned values such as 0, 1, 2, 3, … and are said to be countable.
    • Continuous variables can assume all values between any two specific values like 0.5, 1.2, etc.

    Levels of Measurement

    • Nominal Level - classifies data into mutually exclusive categories in which no order or ranking can be imposed.
    • Ordinal Level - classifies data into categories that can be ranked or ordered.
    • Interval Level - classifies data into categories that can be ranked or ordered. Differences are meaningful.
    • Ratio Level - an Interval Level modified to include the inherent zero starting point. Differences and ratios of data are meaningful.

    Data Collection Techniques

    • Survey: Telephone, mailed questionnaire, or personal interview
    • Surveying Records: Collecting data from existing records.
    • Direct Observation: Observing a situation or phenomenon to collect data.

    Sampling Techniques

    • Random Sampling/Simple Random Sampling: Using chance methods or random numbers to select subjects for a sample.
    • Systematic Sampling/Systematic Random Sampling: Numbering each subject in the population and selecting every kth subject.
    • Stratified Sampling: Dividing the population into distinct groups (strata) and drawing SRSs from each group.
    • Cluster Sampling: Selecting intact groups called clusters, such as hospitals.

    Summation Notation

    • ∑ represents the sum of a series.
    • 𝑖 is the index of summation, which starts at a lower limit and ends at an upper limit.
    • 𝑥𝑖 represents the 𝑖th term in the series.
    • 𝑛 is the upper limit of summation, indicating the last term in the series.
    • 𝑐 is a constant value.

    Formulas of Summation

    • Formula 1: For any constant c, ∑𝑐𝑥𝑖 = 𝑐 ∑ 𝑥𝑖
    • Formula 2: For any constant c, ∑ 𝑐 = 𝑛𝑐
    • Formula 3: ∑(𝑥𝑖 + 𝑦𝑖 + 𝑧𝑖 ) = ∑ 𝑥𝑖 + ∑ 𝑦𝑖 + ∑ 𝑧𝑖
    • Formula 4: ∑(𝑥𝑖 ± 𝑐) = (∑ 𝑥𝑖 ) ± 𝑛𝑐

    Technology Application: Summation Notation in Excel

    • SUM function: Sum a range of cells, an entire column, or non-contiguous cells.
    • AutoSum: Quickly sum a column or row of numbers.
    • Press ALT + = for AutoSum.

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    Stat-213 Chapter 1 PDF

    Description

    Explore the fundamental concepts of statistics, including its methods for planning experiments, analyzing data, and understanding variables. This quiz covers types of variables, their measurements, and the theoretical and applied aspects of statistics.

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