Summation Notations and Data Presentation

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Questions and Answers

What is the primary purpose of using a nominal scale of measurement?

  • To identify and distinguish objects (correct)
  • To specify the absolute amount of measurement
  • To measure the amount of difference between objects
  • To rank objects according to their characteristics

Which of the following best describes the interval scale?

  • Measures the exact difference between values (correct)
  • Categorizes data without any order
  • Allows for ranking but not the specification of differences
  • Includes an absolute zero point

Which scenario represents data measured on a ratio scale?

  • Assigning zip codes to areas
  • Measuring the height of students in centimeters (correct)
  • Ranking contestants in a contest
  • Categorizing types of vehicles

In what way does the ordinal scale differ from the nominal scale?

<p>Ordinal scale provides ranking, while nominal does not. (D)</p>
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Which of the following is an example of the nominal scale?

<p>Blood types of individuals (C)</p>
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What characteristic is unique to the ratio scale compared to other scales?

<p>It possesses a true zero point and allows for comparison of ratios. (D)</p>
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When measuring data in an ordinal scale, which statement is true?

<p>The exact difference between ranks cannot be quantified. (C)</p>
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Which of the following is a property of the interval scale?

<p>It allows for the calculation of differences between values. (A)</p>
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What is the main advantage of non-probability sampling techniques?

<p>They are inexpensive and easy to conduct (B)</p>
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Which sampling method is characterized by selecting members based on the researchers' judgment?

<p>Non-probability sampling (A)</p>
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In which sampling method are individuals drawn from different strata after creating clusters?

<p>Cluster sampling (D)</p>
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How does quota sampling differ from stratified random sampling?

<p>Quota sampling does not consider subgroup proportions (B)</p>
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What is a significant drawback of convenience sampling?

<p>It ignores the opinions of those less accessible (A)</p>
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Which sampling method is best suited for predicting specific outcomes based on objective criteria?

<p>Purposive sampling (B)</p>
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What is a potential issue with results obtained from non-probability sampling methods?

<p>They are typically biased and less reliable (D)</p>
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Which of the following best describes purposive sampling?

<p>Sampling according to the characteristics relevant to the study (B)</p>
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Which of the following describes grouped data?

<p>Data organized and arranged into different classes or categories. (A)</p>
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What is a disadvantage of presenting data in textual form?

<p>It can be difficult to catch the reader's immediate interest. (B)</p>
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Which method is NOT listed as a way to present data?

<p>Numerical (A)</p>
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What provides a comprehensive picture of the data in textual presentation?

<p>Enumerating important characteristics. (B)</p>
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Which part is NOT a component of a table used in data presentation?

<p>Data points (C)</p>
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In presenting data, what is the primary advantage of using tabular format?

<p>It allows for easy comparison between different data points. (A)</p>
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What is true about ungrouped data?

<p>It can only be arranged from highest to lowest or vice versa. (B)</p>
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Which of the following is an example of data presented in textual format?

<p>A narrative about currency exchange rates. (C)</p>
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What is the expanded form of the summation notation $\sum_{i=2}^{5}(A + B)_i$?

<p>(A_2 + B_2) + (A_3 + B_3) + (A_4 + B_4) + (A_5 + B_5) (D)</p>
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What will be the result of evaluating $\sum_{i=1}^{3} X_i$ given that $X_1=2$, $X_2=4$, and $X_3=5$?

<p>11 (A)</p>
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In the expression $\sum_{i=1}^{3}(X_i + Y_i)$, what is the result if $Y_1=1$, $Y_2=3$, and $Y_3=7$?

<p>20 (A)</p>
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Evaluate $\sum_{i=1}^{2} (X_i - i)$. What is the outcome if $X_1=2$ and $X_2=4$?

<p>3 (D)</p>
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What does the notation $\sum_{i=2}^{3}(X_i - i)^2$ evaluate to given the values $X_2=4$ and $X_3=5$?

<p>5 (B)</p>
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Identify the expanded form of $\sum_{i=1}^{3} (2X_i + 3Y_i)$?

<p>2X_1 + 3Y_1 + 2X_2 + 3Y_2 + 2X_3 + 3Y_3 (B)</p>
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If $X_1=2$, $X_2=4$, and $X_3=5$, what is $\sum_{i=1}^{3} 2X_i$?

<p>10 (A)</p>
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The expression $\sum_{i=1}^{3} Y_i^2$ evaluates to which of the following if $Y_1=1$, $Y_2=3$, and $Y_3=7$?

<p>60 (D)</p>
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What is the primary purpose of calculating class boundaries?

<p>To facilitate the creation of graphs such as histograms (A), To identify the unit of accuracy for interval data (B)</p>
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In a stem and leaf plot, what does the 'stem' represent?

<p>The leading digits of the data values (D)</p>
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How is a frequency polygon constructed?

<p>By connecting the class midpoints with straight lines (B)</p>
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Which graph closely resembles a bar chart but uses class boundaries in its construction?

<p>Histogram (C)</p>
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What should be added to complete a frequency polygon?

<p>An additional class mark at both ends of the distribution (C)</p>
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What is the correct formula for the lower class boundary?

<p>Lower class limit - 0.5 (A)</p>
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What is the relationship between the class marks and the class midpoints?

<p>Class marks are always the average of two class limits (A)</p>
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Which of the following best describes a frequency ogive?

<p>A cumulative frequency distribution represented graphically (B)</p>
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Flashcards

Nominal Scale Purpose

Identifies and categorizes objects or data without any numerical significance or order.

Interval Scale

Measures the precise difference between values, but has no true zero point.

Ratio Scale Example

A scale that has a true zero point and allows for comparison of ratios.

Ordinal vs Nominal

The ordinal scale provides ranking, while nominal scale does not.

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Nominal Scale Example Answer

Categorizes data by name or type.

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Ratio Scale Uniqueness

Unique because it possesses a true zero point, allowing ratio comparisons.

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Ordinal Scale Measurement

The exact difference between ranks cannot be quantified.

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Interval Scale Property

It enables the calculation of differences between values.

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Non-Probability Advantage

They are cheaper and easier to conduct compared to probability sampling.

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Non-Probability Sampling

Selecting members based on the researchers' subjective choice.

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Cluster Sampling

Individuals are drawn from different subgroups after clusters are created.

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Quota vs. Stratified Sampling

Quota sampling does not consider the exact subgroup proportions.

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Convenience Sampling Issue

It might not accurately represent the entire population.

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Purposive Sampling Usage

Purposive sampling is used to predict specific outcomes based on objective criteria.

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Non-Probability Results Issue

Results can be skewed and less trustworthy due to selection bias.

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What is Purposive Sampling?

Sampling according to characteristics relevant to the study.

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Grouped Data

Data arranged into classes or categories.

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Textual Data Disadvantage

Reader's immediate interest isn't easily grabbed.

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Not a Presentation Method

Numerical presentation method.

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Comprehensive Picture

Enumerating important characteristics provides a complete portrayal.

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Not a Table Component

Data points

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Tabular Advantage

Allows for easy comparison between different data points.

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Ungrouped Truth

Can only be arranged from highest to lowest or vice versa.

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Textual Data Example

A narrative about currency exchange rates.

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Summation Expansion

(A_2 + B_2) + (A_3 + B_3) + (A_4 + B_4) + (A_5 + B_5)

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Summation Result

11

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Evaluate Summation

20

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Find Summation value

3

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Find Summation Result

5

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Expanded Form of Expression

2X_1 + 3Y_1 + 2X_2 + 3Y_2 + 2X_3 + 3Y_3

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Study Notes

Summation Notations

  • Summation notation is a shorthand method for writing sums of numbers.
  • The symbol used to represent summation is the Greek capital letter sigma (Σ)
  • The summation notation is used to express the sum of all the values of a variable x, where i=1 to n.

Evaluating Summation Notations

  • In evaluating summation notations, substitute each value of the variable into the expression and then add the results.

Presenting Data

  • There are three methods for presenting data:
    • Textual
    • Tabular
    • Graphical

Textual Presentation

  • Textual presentation involves describing data using words in paragraphs.

Tabular Presentation

  • A table is a structured and organized arrangement of data in rows and columns.
  • It helps present data in a concise and easily understandable format.
  • A table will show complete information regarding the data.
  • Parts of a table include:
    • Heading: includes the table number, title, and headings for rows and columns
    • Body: contains the actual data being presented
    • Footnotes: provides additional information about the table

Graphical Presentation

  • Graphical presentation of data can be achieved using:
    • Bar charts and histograms: Used for nominal data with bars representing different categories or for numerical data with bars representing frequency of each class.
    • Frequency polygons: connect the midpoints of the tops of each bar in a histogram, creating a line graph.
    • Frequency ogives: plot the cumulative frequencies against the upper class boundaries.

Scales of Measurement

  • Nominal Scale: used for categorizing data into distinct groups.
  • Ordinal Scale: used for ranking data in a specific order, but doesn't indicate differences in magnitude.
  • Interval Scale: used to measure data with intervals that are equal, but no true zero point.
  • Ratio Scale: used to measure data with intervals, equal units, and a true zero point.

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