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Questions and Answers
What is the computed value of the summation ∑ 𝑥?
What is the computed value of the summation ∑ 𝑥?
- 329
- 468
- 406 (correct)
- 450
What is the correct formula for calculating ∑ 𝑥 2?
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?
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?
Which of the following correctly describes how to sum non-contiguous cells in Excel?
When using AutoSum in Excel, what is the first step?
When using AutoSum in Excel, what is the first step?
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?
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?
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?
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?
What is an alternative way to express $ extstyle ackslash sum_{i=1}^{5} 8x_i$?
What is an alternative way to express $ extstyle ackslash sum_{i=1}^{5} 8x_i$?
How is the value of $50$ reached in the equation $ extstyle 8 ackslash sum_{i=1}^{5} x_i = 400$?
How is the value of $50$ reached in the equation $ extstyle 8 ackslash sum_{i=1}^{5} x_i = 400$?
What happens to the total when each of the first five terms of $x_i$ is multiplied by 8 before summation?
What happens to the total when each of the first five terms of $x_i$ is multiplied by 8 before summation?
What is the primary focus of applied statistics?
What is the primary focus of applied statistics?
Which of the following best defines a quantitative variable?
Which of the following best defines a quantitative variable?
Which type of variable can assume any value between two specific numbers?
Which type of variable can assume any value between two specific numbers?
What is Descriptive Statistics primarily used for?
What is Descriptive Statistics primarily used for?
What distinguishes discrete variables from continuous variables?
What distinguishes discrete variables from continuous variables?
What does the term 'random variable' refer to?
What does the term 'random variable' refer to?
In what form does the term 'statistics' refer to a collection of numerical data?
In what form does the term 'statistics' refer to a collection of numerical data?
Which of the following is NOT considered an aspect of statistics?
Which of the following is NOT considered an aspect of statistics?
What is a key characteristic of ratio level measurement?
What is a key characteristic of ratio level measurement?
Which sampling method involves selecting subjects at regular intervals after a random start?
Which sampling method involves selecting subjects at regular intervals after a random start?
What is the purpose of stratified sampling?
What is the purpose of stratified sampling?
In cluster sampling, which of the following best describes the process?
In cluster sampling, which of the following best describes the process?
What is a disadvantage of using cluster sampling?
What is a disadvantage of using cluster sampling?
What is the first step in systematic sampling?
What is the first step in systematic sampling?
Which of the following is NOT a method of data collection?
Which of the following is NOT a method of data collection?
What does a true zero in ratio-level measurement indicate?
What does a true zero in ratio-level measurement indicate?
What does the formula $\sum_{i=1}^{n} c = n c$ imply?
What does the formula $\sum_{i=1}^{n} c = n c$ imply?
If $\sum_{i=1}^{8} 10$ is evaluated, what is the result?
If $\sum_{i=1}^{8} 10$ is evaluated, what is the result?
Which of the following formulas represents the property of summation for multiple variables?
Which of the following formulas represents the property of summation for multiple variables?
How can you express $\sum_{i=1}^{n} (x_i \pm c)$ using summation notation?
How can you express $\sum_{i=1}^{n} (x_i \pm c)$ using summation notation?
Given that $\sum_{i=1}^{10} x_i = 55$ and $\sum_{i=1}^{10} y_i = 65$, what is $\sum_{i=1}^{10} (x_i + y_i)$?
Given that $\sum_{i=1}^{10} x_i = 55$ and $\sum_{i=1}^{10} y_i = 65$, what is $\sum_{i=1}^{10} (x_i + y_i)$?
What does the notation $\sum_{i=1}^{n} c x_i$ equal?
What does the notation $\sum_{i=1}^{n} c x_i$ equal?
In the expression $\sum_{i=1}^{n} (x_i + c)$, what happens to the summation if c is a constant?
In the expression $\sum_{i=1}^{n} (x_i + c)$, what happens to the summation if c is a constant?
What is the simplified result of $\sum_{i=1}^{10} (3x_i + 4y_i - 7)$?
What is the simplified result of $\sum_{i=1}^{10} (3x_i + 4y_i - 7)$?
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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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