1 / 87

Educational Statistics

Educational Statistics. GURU K MOORTHY. Outline. Introduction Frequency Distribution Measures of Central Tendency Measures of Dispersion. Outline-Continued. Other Measures Concept of a Population and Sample The Normal Curve Tests for Normality. Learning Objectives.

xavier-caldwell
Download Presentation

Educational Statistics

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. Educational Statistics GURU K MOORTHY

  2. Outline Introduction Frequency Distribution Measures of Central Tendency Measures of Dispersion

  3. Outline-Continued Other Measures Concept of a Population and Sample The Normal Curve Tests for Normality

  4. Learning Objectives When you have completed this chapter you should be able to: Know the difference between a variable and an attribute. Perform mathematical calculations to the correct number of significant figures. Construct histograms for simple and complex data.

  5. Learning Objectives-cont’d. When you have completed this chapter you should be able to: Calculate and effectively use the different measures of central tendency, dispersion, and interrelationship. Understand the concept of a universe and a sample. Understand the concept of a normal curve and the relationship to the mean and standard deviation.

  6. Learning Objectives-cont’d. When you have completed this chapter you should be able to: Calculate the percent of items below a value, above a value, or between two values for data that are normally distributed. Calculate the process center given the percent of items below a value Perform the different tests of normality Construct a scatter diagram and perform the necessary related calculations.

  7. Introduction Definition of Statistics: • A collection of quantitative data pertaining to a subject or group. Examples are blood pressure statistics etc. • The science that deals with the collection, tabulation, analysis, interpretation, and presentation of quantitative data

  8. Introduction Two phases of statistics: • Descriptive Statistics: • Describes the characteristics of a product or process using information collected on it. • Inferential Statistics (Inductive): • Draws conclusions on unknown process parameters based on information contained in a sample. • Uses probability

  9. Collection of Data Types of Data: Attribute: Discrete data. Data values can only be integers. Counted data or attribute data. Examples include: • How many of the products are defective? • How often are the machines repaired? • How many people are absent each day?

  10. Collection of Data – Cont’d. Types of Data: Attribute: Discrete data. Data values can only be integers. Counted data or attribute data. Examples include: • How many days did it rain last month? • What kind of performance was achieved? • Number of defects, defectives

  11. Collection of Data Types of Data: Variable: Continuous data. Data values can be any real number. Measured data. Examples include: • How long is each item? • How long did it take to complete the task? • What is the weight of the product? • Length, volume, time

  12. Collection of Data • Significant Figures • Rounding

  13. Significant Figures • Significant Figures = Measured numbers • When you measure something there is always room for a little bit of error • How tall are you 5 ft 9 inches or 5 ft 9.1 inches? • Counted numbers and defined numbers ( 12 ins. = 1 ft, there are 6 people in my family)

  14. Significant Figures • Significant figures are used to indicate the amount of variation which is allowed in a number. • It is believed to be closer to the actual value than any other digit. • Significant figures: • 3.69 – 3 significant digits. • 36.900 – 5 significant digits.

  15. Significant Figures – Cont’d. • Use Scientific Notation • 3x10^2 (1 significant digit) • 3.0x10^2 (2 significant digits)

  16. Significant Figures • Rules for Multiplying and Dividing • Number of sig. = the same as the number with the least number of significant digits. • 6.59 x 2.3 = 15 • 32.65/24 = 1.4 (where 24 is not a counting number) • 32.64/24=1.360(24 is a counting number i.e. 24.00)

  17. Significant Figures Rules for Adding and Subtracting • Result can have no more sig. fig. after the decimal point than the number with the fewest sig. fig. after the decimal point. • 38.26 – 6 = 32 (6 is not a counting number) • 38.2 -6 = 32.2 (6 is a counting number) • 38.26 – 6.1 = 32.2 (rounded from 32.16) • If the last digit >=5 then round up, else round down

  18. Precision and Accuracy Precision The precision of a measurement is determined by how reproducible that measurement value is. For example if a sample is weighed by a student to be 42.58 g, and then measured by another student five different times with the resulting data: 42.09 g, 42.15 g, 42.1 g, 42.16 g, 42.12 g Then the original measurement is not very precise since it cannot be reproduced.

  19. Precision and Accuracy Accuracy • The accuracy of a measurement is determined by how close a measured value is to its “true” value. • For example, if a sample is known to weigh 3.182 g, then weighed five different times by a student with the resulting data: 3.200 g, 3.180 g, 3.152 g, 3.168 g, 3.189 g • The most accurate measurement would be 3.180 g, because it is closest to the true “weight” of the sample.

  20. Precision and Accuracy Figure 4-1 Difference between accuracy and precision

  21. DescribingData • Frequency Distribution • Measures of Central Tendency • Measures of Dispersion

  22. Frequency Distribution • Ungrouped Data • Grouped Data

  23. Frequency Distribution 2-7 There are three types of frequency distributions • Categorical frequency distributions • Ungrouped frequency distributions • Grouped frequency distributions

  24. Categorical 2-7 Categorical frequency distributions • Can be used for data that can be placed in specific categories, such as nominal- or ordinal-level data. • Examples - political affiliation, religious affiliation, blood type etc.

  25. Categorical Example :Blood Type Frequency Distribution 2-8

  26. Ungrouped 2-9 Ungrouped frequency distributions • Ungrouped frequency distributions - can be used for data that can be enumerated and when the range of values in the data set is not large. • Examples - number of miles your instructors have to travel from home to campus, number of girls in a 4-child family etc.

  27. Ungrouped Example :Number of Miles Traveled 2-10

  28. Grouped 2-11 • Grouped frequency distributions • Can be used when the range of values in the data set is very large. The data must be grouped into classes that are more than one unit in width. • Examples - the life of boat batteries in hours.

  29. Grouped Example: Lifetimes of Boat Batteries 2-12 Class Class Frequency Cumulative limits Boundaries frequency 24 - 30 23.5 - 37.5 4 4 38 - 51 37.5 - 51.5 14 18 52 - 65 51.5 - 65.5 7 25

  30. Frequency Distributions Table 4-3 Different Frequency Distributions of Data Given in Table 4-1

  31. Frequency Histogram

  32. Relative Frequency Histogram

  33. Cumulative Frequency Histogram

  34. The Histogram The histogram is the most important graphical tool for exploring the shape of data distributions. Check: http://quarknet.fnal.gov/toolkits/ati/histograms.html for the construction ,analysis and understanding of histograms

  35. Constructing a Histogram The Fast Way Step 1: Find range of distribution, largest - smallest values Step 2: Choose number of classes, 5 to 20 Step 3: Determine width of classes, one decimal place more than the data, class width = range/number of classes Step 4: Determine class boundaries Step 5: Draw frequency histogram

  36. Constructing a Histogram Number of groups or cells • If no. of observations < 100 – 5 to 9 cells • Between 100-500 – 8 to 17 cells • Greater than 500 – 15 to 20 cells

  37. Constructing a Histogram For a more accurate way of drawing a histogram see the section on grouped data in your textbook

  38. Other Types of Frequency Distribution Graphs • Bar Graph • Polygon of Data • Cumulative Frequency Distribution or Ogive

  39. Bar Graph and Polygon of Data

  40. Cumulative Frequency

  41. Characteristics of FrequencyDistribution Graphs Figure 4-6 Characteristics of frequency distributions

  42. Analysis of Histograms Figure 4-7 Differences due to location, spread, and shape

  43. Analysis of Histograms Figure 4-8 Histogram of Wash Concentration

  44. Measures of Central Tendency The three measures in common use are the: • Average • Median • Mode

  45. Average There are three different techniques available for calculating the average three measures in common use are the: • Ungrouped data • Grouped data • Weighted average

  46. Average-Ungrouped Data

  47. Average-Grouped Data h = number of cells fi=frequency Xi=midpoint

  48. Average-Weighted Average Used when a number of averages are combined with different frequencies

  49. Median-Grouped Data Lm=lower boundary of the cell with the median N=total number of observations Cfm=cumulative frequency of all cells below m Fm=frequency of median cell i=cell interval

  50. Example Problem Table 4-7 Frequency Distribution of the Life of 320 tires in 1000 km

More Related