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# NORMAL DISTRIBUTION

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STATISTICAL TREATMENT in Research

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### NORMAL DISTRIBUTION

1. 1. STATISTICA L TREATMENT Using the appropriate statistical tool to arrive at accurate and definite interpretation of results.
2. 2. STATISTICS It is a science of collecting, presenting, analyzing and interpreting data to arrive at an effective decision.
3. 3. TYPES OF DATA 1. QUALITATIVE DATA ---- Non-numeric data 2. QUANTITATIVE DATA ---- Numeric data
4. 4. CLASSIFICATION OF STATISTICS 1. DESCRIPTIVE STATISTICS ---is a manner of organizing, presenting or summarizing a set of data or observations in an informative way. 2. INFERENTIAL STATISTICS ---proceeds from conducting a study of a subset taken from a population.
5. 5. NORMAL DISTRIBUTION
6. 6. PROPERTIES OF NORMAL DISTRIBUTION  Bell-shaped  The mean, median, and mode are all equal and are located at the center of the distribution.  The distribution is symmetric.  The total area under a normal curve is 1 or 100%  The distribution is asymptotic.  The location of the distribution is determined by the mean and the standard deviation determines dispersion of the distribution.
7. 7. STANDARDIZED SCORE (Z-value) Formula: Z = 𝑥 − µ 𝛿 z = Normal Value X = value of any particular observation µ = mean of the distribution 𝛿 = standard deviation
8. 8. The scores of 120 students in a stat preliminary examination show a bell-shaped distribution. The mean score is 29 and the standard deviation is 3.02. if a student is selected at random, find the probability of selecting a student whose score is a. Between 24 and 35? b. Between 33 and 37? c. Greater than 34? d. Less than 37?
9. 9. SOLUTIONS: STEP 1: Standardize the given observation using the formula. Z = 𝑥 − µ 𝛿 STEP 2: Find the area of the standardized score using the areas under the normal curve.
10. 10. STEP 3: Draw the curve and write the z-value along the horizontal line to where it should belong. Positive written to the right side of 0 and negative value is written to left side of 0. shade the corresponding area. STEP 4: Calculate the area. The shaded region serves as our guide on what we are going to do with the areas corresponding to their respective z-value.
11. 11. Z-values Rules 1. The z-values are POSITIVE and NEGATIVE ADD the areas of the corresponding z values 2. Both z-values are POSITIVE or Both z-values are NEGATIVE In either case, SUBTRACT the smaller area from the bigger area. 3. To the right of a POSITIVE z- value or to the left of a NEGATIVE z-value SUBTRACT the area from 0.5 4. To the right of a NEGATIVE z value or to the left of a POSITIVE z-value ADD area to 0.5
12. 12. THANK YOU! REFERENCE: Pagala, R. 2008; Statistics. Mindshapers Co., Inc.