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# Descriptive statistics

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Decriptive Statistics
Statistics versus Parameters
Types of Numerical Data.
Types of Scores
Techniques for Summarizing Quantitative Data

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### Descriptive statistics

1. 1. Descriptive Statistics Presented by Hiba Armouche
2. 2. Outline • • • • Statistics versus Parameters Types of Numerical Data. Types of Scores Techniques for Summarizing Quantitative Data
3. 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. 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. 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. 6. Types of Scores
7. 7. Types of Scores Age and Grade level Equivalent tell us of what age or grade an individual score is typical.
8. 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. 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. 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. 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. 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. 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. 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. 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. 16. Averages/Measures of central tendency • Mode: – The most frequently occurring score – Appropriate for nominal data
17. 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. 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. 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. 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. 21. Variability or Spreads – Range – Quartile deviation – Boxplots – Variance & Standard deviation
22. 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. 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. 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. 25. Variability or Spreads Five-Number Summary • • • • • The lowest score Q1 The highest score The median Q3 Interquartile range IQR = Q3 - Q1
26. 26. Variability or Spreads • Boxplots
27. 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. 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. 29. Variability or Spreads SD =
30. 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. 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. 32. Thank You hiba.armouche@yahoo.com www.facebook.com/TrainerHibaArmouche