Presentation1.ppt.education and learning

education and learning

1. Is this normal?

2. Is this normal? Why do you think its not normal?

3. Is this normal? Why should we normalize this kind of practice?

4. Is this normal? Why should we NOT normalize this kind of behavior? NILAIT VS NANLAIT

5. Example 1. Height Distribution of Grade 3 students in Wangyu Elementary School.

6. Example 2. Employees daily wages in peso in Gaisano mall, Cagayan de Oro. 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 1-100 101-200 201-300 301-400 401-500 501-600 601-700 701-800 801-900-1000 1001-1100

7. N R O M A L C U R V E

8. N R O M A L C U R V E

9. Normal Distribution is also called as Gaussian Distribution. It is the probability of continuous random variable and consider as the most important curve in statistics.

10. z The equation of the theoretical normal distribution is given by the formula.

11. Properties of Normal Curve.   The distribution curve is bell shaped. The curve is symmetrical to its center, the mean. The mean, median and mode coincide at the center.

12. Properties of Normal Curve.   3. The width of the curve is determined by the standard deviation of the distribution. 4. The curve is asymptotic to the horizontal axis. 5. The area under the curve is 1, thus it represents the probability or proportion, or percentage associated with specific sets of measurements values.

13. Normal distribution is determined by two parameters: the mean and the standard deviation.   1. Mean Value 2. Standard Deviation Value

14. z Empirical Rule referred to as the 68-95-99.7% Rule. It tells that for a normally distributed variable the following are true. Distribution Area Under The Normal Curve

15.   Approximately 68% of the data lie within 1 standard deviation of the mean. Pr (μ- <X> μ- ), this is the formula for getting range and interval of the normal distribution.  

16.  Approximately 95% of the data lie within 2 standard deviations of mean. Pr (μ- <X> μ- ), this is the formula for getting range and interval of the normal distribution.  

17.   Approximately 99.7% of the lie within 3 standard deviations of the mean. Pr (μ- <X> μ- ), this is the formula for getting range and interval of the normal distribution.  

18. z Example 1. What is the frequency and relative frequency of babies’ weight that are within; a. What is the frequency or percentage of one standard deviation from mean. b. What is the frequency or percentage of two standard deviation from mean. 4.94 4.69 5.26 7.29 7.19 9.47 6.61 5.84 6.83 3.45 2.93 6.38 4.38 6.76 9.02 8.47 6.80 6.40 8.60 3.99 7.68 2.24 5.32 6.24 6.29 5.63 5.37 5.26 7.35 6.11 7.34 5.87 6.56 6.18 7.35 4.21

19. 2.24 4.21 5.16 5.63 6.18 6.40 6.80 7.34 8.47 2.93 4.38 5.26 5.84 6.19 6.56 6.83 7.35 8.60 3.45 4.69 5.32 5.87 6.24 6.61 7.19 7.35 9.01 3.99 4.94 5.37 6.11 6.38 6.76 7.29 7.68 9.47

20. z   a. What is the frequency or percentage of one standard deviation from mean. Solution: Step 1. Draw a normal Curve. Step 2 . In the middle of the curve, plot the value of the mean which is 6.11.     6.11 6.11

21. z Step 3. The value of our standard deviation will become our interval in the normal distribution.     1.22 2.85 4.48 6.11 7.74 9.37 11 When you are going to the right starting in the middle, mean plus the standard deviation meanwhile when you are going to the left of the curve standard deviation is subtracted from the mean.  

22.   Step 4. Since the question is frequency of one standard deviation from the mean, we are in the empirical rule 68% which ranges to 4.48 to 7.74, now we are going to count.

23. 2.24 4.21 5.16 5.63 6.18 6.40 6.80 7.34 8.47 2.93 4.38 5.26 5.84 6.19 6.56 6.83 7.35 8.60 3.45 4.69 5.32 5.87 6.24 6.61 7.19 7.35 9.01 3.99 4.94 5.37 6.11 6.38 6.76 7.29 7.68 9.47   ÷÷

24. z b. What is the frequency or percentage of two standard deviation from mean.     6.11 Step 1. Draw a normal Curve. Step 2. In the middle of the curve, plot the value of the mean which is 6.11.

25. z Step 3. The value of our standard deviation will become our interval in the normal distribution.   1.22 2.85 4.48 6.11 7.74 9.37 11 Step 4. Since the question is frequency of two standard deviation from the mean, we are in the empirical rule 95% which ranges to 2.85 to 9.37, now what is the next thing to do?

26. 2.24 4.21 5.16 5.63 6.18 6.40 6.80 7.34 8.47 2.93 4.38 5.26 5.84 6.19 6.56 6.83 7.35 8.60 3.45 4.69 5.32 5.87 6.24 6.61 7.19 7.35 9.01 3.99 4.94 5.37 6.11 6.38 6.76 7.29 7.68 9.47   ÷÷

27. How about if we compare two data sets with normal curve?

28. =50 =10   =50 =5  

29. z     The Standard Normal Distribution Standard Normal Curve is a normal probability distribution that has a μ= 0 and =1.     -3 -2 -1 0 1 2 3 z-score

30. The letter Z is used to denote the standard normal random variable. The specific value of the random variable z is called the z-score. The Table of Area Under the Normal Standard Curve is also known as the Z-table. It is where you are going to look for the value of random variable z or the z-core.

31. Areas Under Normal Curve using z-table.   z=1.09

32. z=0.62 z=-1.65 z=3

33. z Example. Find the area between z=0 and z=1.54. 0.4382

34. z Areas Under Standard Normal Curve   Find the area between z=1.52 and z=2.5  

35. Find the area between z= -1.5 and z=-2.5

36. Let’s try this !   1. Anna is planning to enroll in MSU taking up Bachelor of Science in Civil Engineering. The average academic performance of all the students 80 and a standard deviation of 5, it follows a normal distribution.   a. Sketch a Normal Curve using Empirical Rule and describe the curves. 2. Find the area between z=1.7 and z=2

37. Let's have a short quiz.   Instruction : Answer the following questions and make sure your writings clear and readable.   I. Find the area under the normal curve in each of the following cases.   1. Find the Area between z= -1.36 and z=2.25. 2. To the right of z=1.85 3. To the left z=-0.45  

38. II. Sketch a normal curve .   1. Mean of 15 and a standard deviation of 4. On same axis, sketch another curve that has a mean of 25 and a standard deviation of 4. Describe the two random curves.   III. Essay 1. State a real-life situation that a normal curve distribution can be used.