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Chapter 1

Chapter 1. Measure of Variability. Measure of variability. Variability provides a quantitative measure of the degree to which scores in a distribution are spread out or clustered together.

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Chapter 1

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  1. Chapter 1 Measure of Variability

  2. Measure of variability • Variability provides a quantitative measure of the degree to which scores in a distribution are spread out or clustered together.

  3. How well does the mean represent the scores in a distribution? The logic here is to determine how much spread is in the scores. • How much do the scores "deviate" from the mean? Think of the mean as the true score or as your best guess. • If every X were very close to the Mean, the mean would be a very good predictor. • If the distribution is very sharply peaked then the mean is a good measure of central tendency and if you were to use the mean to make predictions you would be right or close much of the time.

  4. The larger the standard deviation figure, the wider the range of distribution away from the measure of central tendency

  5. Measure of variability • Range =Xhighest– Xlowest • Quartile: • describing a division of observations into four defined intervals based upon the values of the data and how they compare to the entire set of observations. Each quartile contains 25% of the total observations. Generally, the data is ordered from smallest to largest with those observations falling below : • 25% of all the data analyzed allocated within the 1st quartile, • 50% and allocated in the 2nd quartile, • 75% allocated in the 3rd quartile, • and finally the remaining observations allocated in the 4th quartile. • 3. Interquartile=Q3-Q1. • 4. Semi-interquartile=(Q3-Q1)/2.

  6. Measure of variability

  7. Measure of variability • Variance • Deviation: deviation of one score from the mean • Variance: taking the distribution of all scores into account.

  8. Standard deviation

  9. Exercise 1. Calculate the mean, median, mode, range and standard deviation for the following sample:

  10. Homework • Draw a histogram to show the distribution of the scores. • Calculate the mean and standard deviation of the scores. • Suppose Lihua scored 55 in this test, what’s her position in the whole class? II. Suppose there will be 418,900 test takers for the NMET in 2006 in Guangdong, the key universities in China plan to enroll altogether 32,000 students in Guangdong. What score is the lowest threshold for a student to be enrolled by the key universities? (Remember the mean is 500, standard deviation is 100).

  11. Homework

  12. Homework

  13. Interquartil • Interquartil (IQR) dirumuskan : IQR = Q3-Q1 • Inner fences & Outer fences

  14. UKURAN BENTUK • SKEWNESS

  15. KURTOSIS

  16. Ex Susun boxplot dari data berikut dan tentukan apakah terdapat outlier atau tidak ! Jika ada, tentukan data tersebut dan tentukan apakah outlier atau ekstrem outlier ? 340, 300, 520, 340, 320, 290, 260, 330

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