1 / 11

Topic-2

Topic-2. Summarizing Data: Frequency Distributions and Graphic Presentation. Summarizing Data: Frequency Distribution. Frequency Distribution : Grouping data into categories showing the number of observations in each group. (Examples)

oona
Download Presentation

Topic-2

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Topic-2 Summarizing Data: Frequency Distributions and Graphic Presentation

  2. Summarizing Data: Frequency Distribution • Frequency Distribution: Grouping data into categories showing the • number of observations in each group. (Examples) • Middle Point (Group Mark): the Average between the Lower • and Upper limits of each group. • Group (Class) Interval: the (equal or unequal) sizes of groups • within the distribution. • Suggestions for Constructing a Frequency Distribution: • Use equal-size class intervals (whenever possible). • Find the suggested class interval [Equations (2-1)/(2-2)]. • Choose an appropriate number of classes: • Not "too many" or "too few". • No Overlapping and Avoiding "open-end" classes. • Relative Frequency Distribution: Grouping data into categories with • the ratio (in terms of percentage) of the number of observations • in each group over the total number of observations. (Examples)

  3. Data Graphic Presentation • Three commonly used graphic presentation forms: • Histogram (Bar Chart): Most widely used and easy to understand. • Disadvantage: loss of some information. • Stem-and-Leaf Display Technique: • [Stem - Leading Digit /Leaf - Trailing Digit] • (Examples) • Frequency Polygon (Midpoint Curve): Similar to Histogram, but with line segments connecting the points formed by the • intersection of the group midpoint and the frequency. • (Examples) • Cumulative Frequency Polygon (Cumulative Frequency • Distribution Curve, called "Ogive Curve"): Used to show – How many observations are below (or above) a certain value. • Less-than Cumulative Frequency Polygon: • How many observations are below .....? • More-than Cumulative Frequency Polygon: • How many observations are above .....? • (Examples)

  4. Summarizing Data: Line, Bar and Pie Chart • Three widely used types of Charts are Line Chart, Bar Chart, and Pie Chart. • Line Chart: Used for Demonstration or Comparison of one or two sets of data over a period of time. • (Examples) • Bar Chart: Can be used to depict any level of measurement (nominal, ordinal, interval, ratio) for demonstration or comparison purposes. • Horizontal Bar Chart vs. Vertical Bar Chart • One-Dimensional Bar Chart vs. Two-Dimensional Bar Chart • One-Directional Bar Chart vs. Two-Directional Bar Chart • (Examples) • Pie Chart: Designed to show a relative frequency distribution with percentage (%) comparisons. • (Examples) • Understanding Statistics Correctly: Be careful in reading different statistics. There are many misuse (or abuse) of statistics to mislead readers or misrepresent original data (intentionally or unintentionally). • (Examples)

  5. Example 1 • Mr. Bagdonos is the city manager for the town of Geneva. He has been asked by the city council to study the water usage in the community. He selects a random sample of 30 families and determines the number of gallons of water used by each family last year. The data is reported in thousands of gallons: • 15.0, 23.7, 19.7, 15.4, 18.3, 23.0, 14.2, 20.8, 13.5, 20.7, 17.4, 18.6, 12.9, 20.3, 13.7, 21.4, 18.3, 29.8, 17.1, 18.9, 10.3, 26.1, 15.7, 14.0, 17.8, 33.8, 23.2, 12.9, 27.1, 16.6. • Organize the data into a frequency distribution. • Consider the classes 8 – 12 and 13 – 17. The class marks will be 10 and 15. The class interval will be (13 – 8) = 5.

  6. Suggestions on Constructing aFrequency Distribution • Arrange the data in order from the lowest value to the highest value. • Decide on the appropriate number of classes. You should choose between 5 and 15 classes. • Determine a suggested class interval. You can use this formula: • Suggested class interval = Highest value – Lowest value Number of classes • Use the computed suggested class interval to construct the frequency distribution. Note: You may have to adjust the computed class intervals. For example, if the computed class interval is 96, it may be better to use 100. Use your own judgment. • Count the number of values in each class. • Note: You should try to avoid open-ended classes.

  7. Relative Frequency Distribution (1) • The relative frequency of a class is obtained by dividing the class frequency by the total frequency.

  8. Relative Frequency Distribution(2)

  9. Stem-and-Leaf Displays • When summarizing the data by a group frequency distribution, some information is lost since we would only have the classes and the frequency counts for the classes. We will not know what are the actual values in the classes. • A stem-and-leaf display offsets this loss of information. • The stem is the leading digit. • The leaf is the trailing digit. • The stem is placed to the left of a vertical line and the leaf to the right. • The Dean of the College of Business reports the following number of students in the 15 sections of basic statistics offered this semester (quarter). Construct a stem-and-leaf chart for the data. • 27, 36, 29, 21, 24, 26, 32, 30, 36, 30, 28, 23, 17, 41, 19.

More Related