Download presentation

Presentation is loading. Please wait.

1
http://www.youtube.com/watch?v=xDIyAOBa_yU The Standard Normal Distribution

2
Notice that the x axis is standard scores, also called z scores. This means that the distribution has a population mean of zero, and a population standard deviation of 1.

3
The most significant thing about the normal distribution is that predictable proportions of cases occur in specific regions of the curve. 50%

4
Notice that: (1) 34.13% of the scores lie between the mean and 1 sd above the mean, (2) 13.6% of the scores lie between 1 sd above the mean and 2 sds above the mean, (3) 2.14% of the scores lie between 2 sds above the mean and 3 sds above the mean, and (4) 0.1% of the scores in the entire region above 3 sds. The curve is symmetrical, so the area betw 0 and -1 = 34.13%, -1 to -2 = 13.6%, etc. Also, 50% of the cases are above 0, 50% below.

5
IQ Percentile Problem 1: IQ: =100, =15. Convert an IQ score of 115 into a percentile, using the standard normal distribution. Step 1: Convert IQ=115 into a z score: z = x i - / 5; z = +1.0 (1 sd above the mean) IQ=115, z = 1.0

6
Step 2: Calculate the area under the curve for all scores below z=1 (percentile=% of scores falling below a score). Area under the curve below z=1.0: 34.13+50.00= 84.13. We get this by adding 34.13 (the area between the mean and z=1) to 50.00 (50% is the area under the curve for values less than zero; i.e., the entire left side of the bell curve). So, an IQ score of 115 (z=1.0) has a percentile score of 84.13. IQ=115, z = +1.0 The part with the slanty lines repre- sents the portion of the distribution we’re looking for.

7
IQ Percentile Problem 2: IQ: =100, =15. Convert an IQ score of 85 into a percentile, using the standard normal distribution. Step 1: Convert IQ=85 into a z score: z = x i - / 5; z = -1.0 (1 sd below the mean) IQ=85, z = -1.0

8
Step 2: Calculate the area under the curve for all scores below z=-1. Area under the curve values below z=-1.0: 50.00- 34.13=15.87. We get this by subtracting 34.13 (the area between the mean and z=-1) from 50.00 (50% is the total area under the curve for values less than zero; i.e., the entire left side of the bell curve). So, an IQ score of 85 (z=-1.0) has a percentile score of 15.87. IQ=85, z = -1.0

9
z = x i - / 5 z = -1.0 Area under the curve for z=-1.0: 50.00-34.13=15.87. We get this by subtracting 34.13 from 50.00 (50.00 is the total area under the curve for values less than zero; i.e., the entire left side of the bell curve.) We therefore want the 50% minus the area between zero and -1.0). So, an IQ score of 85 has a percentile score of 15.87. IQ=85, z=-1.0

Similar presentations

OK

The Normal Distribution: The Normal curve is a mathematical abstraction which conveniently describes ("models") many frequency distributions of scores.

The Normal Distribution: The Normal curve is a mathematical abstraction which conveniently describes ("models") many frequency distributions of scores.

© 2018 SlidePlayer.com Inc.

All rights reserved.

To ensure the functioning of the site, we use **cookies**. We share information about your activities on the site with our partners and Google partners: social networks and companies engaged in advertising and web analytics. For more information, see the Privacy Policy and Google Privacy & Terms.
Your consent to our cookies if you continue to use this website.

Ads by Google

Download ppt on civil disobedience movement in united Ppt on economic development and growth Ppt on aircraft landing gear system diagrams Ppt on sources of water pollution Ppt on australian continent nations Pdf to ppt online free converter Free ppt on reflection of light Ppt on commercial use of microorganisms in the field Ppt on disaster recovery plan Ppt on natural resources in india