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Statistics versus Parameters

Types of Numerical Data.

Types of Scores

Techniques for Summarizing Quantitative Data

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- 1. Descriptive Statistics Presented by Hiba Armouche
- 2. Outline • • • • Statistics versus Parameters Types of Numerical Data. Types of Scores Techniques for Summarizing Quantitative Data
- 3. Statistics Versus Parameters • A parameter is a characteristic of a population. It is a numerical or graphic way to summarize data obtained from the population • A statistic is a characteristic of a sample. It is a numerical or graphic way to summarize data obtained from a sample
- 4. Types of Numerical Data • There are two types of data : 1- Quantitative data are obtained by determining placement on a scale that indicates amount or degree Ex:The temperatures recorded each day during the months of September through December in Lebanon in a given year (the variable is temperature ) 2- Categorical data are obtained by determining the frequency of occurrences in each of several categories Ex: The number of male and female students in a chemistry class (the variable is gender )
- 5. Types of Scores Raw Score is the initial score obtained Ex: The number of items an individual gets correct on a test. Derived Score is obtained by taking the raw score and converting it into a more useful score
- 6. Types of Scores
- 7. Types of Scores Age and Grade level Equivalent tell us of what age or grade an individual score is typical.
- 8. Types of Scores A percentile rank refers to the percentage of individuals scoring at or below a given raw score. PR = Number of Students Below Score + All Students All Scores Total Number in the Group X 100
- 9. Types of Scores Standard scores indicate how far a given raw score is from a reference point. The z scores and the t scores
- 10. Techniques for Summarizing Quantitative Data • A frequency distribution is two-column listing, from high to low, of all the scores along with their frequencies
- 11. Techniques for Summarizing Quantitative Data • A frequency polygon is a graphic display of frequency distribution. It is a graphic way to summarize quantitative data for one variable – A graphic distribution of scores in which only a few individuals receive high scores is called a positively skewed polygon – One in which only a few individuals receive low scores is called a negatively skewed polygon
- 12. Techniques for Summarizing Quantitative Data • A histogram is a bar graph used to display quantitative data at the interval or ratio level of measurement
- 13. Techniques for Summarizing Quantitative Data • The stem-leaf plot is a display that organizes a set of data to show both its shape and distribution. Each data value is split into a stem and a leaf. The leaf is the last digit of a number. The other digits to the left of the leaf form the stem Example Stem 15 9 Leaf
- 14. Techniques for Summarizing Quantitative Data • The normal distribution is a theoretical distribution that is symmetrical and in which a large proportion is concentrated in the middle • The distribution curve of a normal distribution is called a normal curve. It is a bell-shaped, and its mean, mode, and median are identical
- 15. How do you analyze the data? Conduct descriptive analysis Descriptive Statistics Central Tendency Mean Median Mode Variability Relative Standing Variance Standard Deviation Range Z-Score Percentile Ranks
- 16. Averages/Measures of central tendency • Mode: – The most frequently occurring score – Appropriate for nominal data
- 17. Averages/Measures of central tendency • Median – The score above and below which 50% of all scores lie (i.e., the midpoint) – Characteristics • Appropriate for ordinal scales • Doesn’t take into account the value of each and every score in the data
- 18. Averages/Measures of central tendency • Mean – The arithmetic average of all scores – Characteristics • Advantageous statistical properties • Affected by outlying scores • Most frequently used measure of central tendency – Formula
- 19. Skewed Distributions • Positive – many low scores and few high scores • Negative – few low scores and many high scores • Relationships between the mean, median, and mode – Positively skewed – mode is lowest, median is in the middle, and mean is highest – Negatively skewed – mean is lowest, median is in the middle, and mode is highest
- 20. Variability or Spreads • Purpose – to measure the extent to which scores are spread apart Distribution A: 19, 20, 25, 32, 39 Distribution B: 2, 3, 25, 30, 75
- 21. Variability or Spreads – Range – Quartile deviation – Boxplots – Variance & Standard deviation
- 22. Variability or Spreads • Range – The difference between the highest and lowest score in a data set – Characteristics • Unstable measure of variability • Rough, quick estimate
- 23. Variability or Spreads Quartiles and the Five-Number Summary A percentile in a set of numbers is a value below which a certain percentage of numbers fall and above which the rest of the numbers fall. Example: You received in SAT score “Raw score 630, percentile 84” This means that your score is 630 and 84% of those who took the exam scored lower than you.
- 24. Variability or Spreads Quartiles and the Five-Number Summary NB: • The median is the 50th percentile • The first quartile is the 25th percentile Q1 • The third quartile is the 75th percentile Q3.
- 25. Variability or Spreads Five-Number Summary • • • • • The lowest score Q1 The highest score The median Q3 Interquartile range IQR = Q3 - Q1
- 26. Variability or Spreads • Boxplots
- 27. Variability or Spreads • Standard Deviation SD It is a single number that represents the spread of a distribution. Every score in the distribution is used to calculate it.
- 28. Variability or Spreads • How to calculate the Standard Deviation 1- Calculate the mean 2- Subtract the mean from each score 3-Square each of these scores 4- Add all the squares of these scores 5- Divide the total by the total numbers of scores The result is called Variance. 6- Take the square root of the variance. This is the standard deviation
- 29. Variability or Spreads SD =
- 30. Variability or Spreads NB: The more spread out scores are the greater the deviation scores will be and hence the larger the standard deviation
- 31. Relative Standing • Types – Percentile ranks – the percentage of scores that fall at or above a given score – Standard scores – a derived score based on how far a raw score is from a reference point in terms of standard deviation units • z score • T score
- 32. Thank You hiba.armouche@yahoo.com www.facebook.com/TrainerHibaArmouche

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