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PSY 1110 Notes for September 23rd and 26th.

by: Kelsey Jackson

PSY 1110 Notes for September 23rd and 26th. PSY 1110

Marketplace > Ohio University > Psychology > PSY 1110 > PSY 1110 Notes for September 23rd and 26th
Kelsey Jackson
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About this Document

These notes cover the lecture information from Friday, September 23rd and Monday, September 26th.
Elementary Statistical Reasoning
Susan Tice-Alicke
Class Notes
Statistics, variance, deviation




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This 6 page Class Notes was uploaded by Kelsey Jackson on Monday September 26, 2016. The Class Notes belongs to PSY 1110 at Ohio University taught by Susan Tice-Alicke in Fall 2016. Since its upload, it has received 36 views. For similar materials see Elementary Statistical Reasoning in Psychology at Ohio University.


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Date Created: 09/26/16
PSY 1110 rd th Notes for Friday, September 23  and Monday, September 26 . By Kelsey A. Jackson 1. Comparison of Three Measures of Central Tendency a. Normal Distribution i. Huffingtonp ii. A graph that is shaped like a bell curve has the same mean, median, and  mode.  iii. In this case, the best measurement of central tendency would be the mean,  or average, because it is the easiest to understand.  b. Bimodal Symmetrical Distribution i. statisticsh ii. with a bimodal graph, the mean and median are in the middle, but most of  the data is at the modes, so the modes are the best way to represent the  data in this graph.  c. Skewed Distribution i. ii. For both a positive and negatively skewed distribution, the best  measurement of central tendency is the median, since it accurately  displays the data that is in the center.  2. Measures of Variability a. For this example, we are going to the following simple data set.  A B C 0 4 6 2 5 6 6 6 6 10 7 6 12 8 6 Mean: 6 Mean: 6 Mean: 6 b. A measure of variability is a number that reflects how spread out the scores  are in a distribution i. Also known as the distance. c. Range i. The range is a measurement of the width of the entire distribution ii. Range = highest score – lowest score iii. For example: 1. The range for set A is 12 2. The range for set B is 4 3. The range for set C is 0 iv. A downside of using a range is that it can be sensitive to outliers. (Outliers are a score of scores that stand apart from the rest of the distribution.) d. Interquartile Range (IQR) i. The IQR is a range of the middle 50% of the distribution. th th ii. IQR = score at the 75  percentile – score at the 25  percentile iii. How to find the IQR: 1. Arrange the scores according to magnitude. Sample data set:  9 9 8 7 6 5 5 4 3 3 2 2. Find the median of the set. (5 in this case) 3. Find the median of the upper and lower halves of the data set.  (9 9 8 7 6) 5 (5 4 3 3 2) In this case, the medians are 8 and 3 4. Subtract these two means for the IQR (8­3 = 5, so 5 is the IQR in  this example.) 5. For this next example, we will have a data set with an even amount of numbers. For this, you want to take the middle two numbers and average them together to find the median.  12 10 10 9 8 8 7 6 6 4 2 2  (12 10 10 9 8 8) 7.5(median) (7 6 6 4 2 2) the two medians of these data sets are 9.5 and 5 9.5­5 = 4.5 IQR = 4.5 e. Variants i. The variant is the average of the squared deviations of the scores around  the mean. ii. iii. Example computation: X Mean of X (X­Mean of X) (X­Mean of X) ^2 9 5 4 16 8 5 3 9 6 5 1 1 4 5 ­1 1 2 5 ­3 9 1 5 ­4 16 For this data set, the EX = 30, and the EX^2 = 202 so: S^2 = (202­(900/6)/5 S^2 = (202­150)/5 S^2 = 52/5 S^2 = 10.4. (The standard variance is equal to 10.4) To find the standard deviation, take the square root of the standard variance (3.22 in this case) How to find the Population Variance (^2) The formula for population variance is: Example Computation: X X^2 14 196 10 100 10 100 9 81 8 64 8 64 7 49 6 36 6 36 4 16 2 4 2 4 The EX^2 is 750, and the EX is 86, so: (750­(86) ^2/12)/12 (750­(7396/12)/12 (750­616.33)/12 (133.67)/12 ^2 = 11.14 To find the population deviation, just take the square root of the population variance (3.34 in this case)


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