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Stats 214

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by: Rio Notetaker
Rio Notetaker
University of Louisiana at Lafayette

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Chapter 3 section 3
Introductory Psychology
Nolan Williams
Class Notes
25 ?




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"Can you just teach this course please? lol :)"

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This 5 page Class Notes was uploaded by Rio Notetaker on Friday February 5, 2016. The Class Notes belongs to PSYC 110 at University of Louisiana at Lafayette taught by Nolan Williams in Winter 2016. Since its upload, it has received 23 views. For similar materials see Introductory Psychology in Psychlogy at University of Louisiana at Lafayette.


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Can you just teach this course please? lol :)



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Date Created: 02/05/16
3.1 Measures of Position DEF: Let x be a value from a population with mean _____ and standard deviation _______. The z­score for x is  Z= Example Compute and Interpret: A national center for Health Statistics study states that the mean height for an adult male in thμ=¿S is  69.4 inches with a standard deviation ofσ=¿ 3.1 inches. The mean height of an adult female iμ=¿ 63.8  inches with a standard deviation ofσ=¿ 2.8 inches. Who is taller relative to their gender, a 73 inches tall  male or a 68 inches tall female? Solution: Z­score and the Empirical Rule: When a population has a histogram that is approximately bell­shaped, then ­Approximately 68% of the data will have z­scores between _______ and _______. ­Approximately 95% of the data will have z­scores between _______ and _______. ­All, or almost all, of the data will have z­scores between ________ and ________. DEF: For a number p between 1 and 99, the pth percentile separates the lowest _______ of the data from the  highest (100­p)%. Procedure for Computing the Data Value Corresponding to a Given Percentile Step 1: Arrange the data in ______________ order. Step 2: Let n be the number of values in the data set. For the pth percentile, compute the value: L = Step 3: If L is a whole number, then the pth percentile is the average of the number in position L and and the  number in position L+1. If L is not a whole number, round up to the next higher whole number. The pth percentile is the number in the  position corresponding to the rounded up value. Example: Compute the percentiles below given the following data set. 1.2 1.3 1.3 1.4 1.4 1.4 1.5 1.9 1.9 2.3 2.6 3.7 6.8 9 12.1 14.3 15.6 16.7 16.9 20.3 a. 15% percentile b. 64% Percentile Procedure for Computing the Percentile Corresponding to a Given Data Value: Step 1: Arrange the data in increasing order Step 2: Let x be the data value whose percentile is to be computed. Use the following formula to compute the  percentile: Percentile: Round the result to the nearest whole number. Example Continued:   Based on the above table from previous example, the number 6.8, what is the percentile corresponding to this  data value? Solution: DEF: Every data set has three quartiles: ­The first quartile, denoted _________, is the _______ percentile. ______ separates the lowest ____________  of the data from the highest ________. ­The second quartile, denoted ________, is the ________ percentile. ______ separates the lower ______ of the  data from the upper ______. _______ is the same as the _________ The third quartile, denoted _____, is the _______ percentile. ______ separates the lowest _______ of the data  from the highest _________. Example: Based on the above definitions, determine the first, second, and third quartiles for the following data: 3.8 3.9 4.2 4.6 4.8 4.9 5.1 5.7 5.8 6.7 6.9 DEF: The five­number summary of a data set consists of the following quantities:  DEF: An outlier is a value that is considerably _______ or considerably ______ than most of the values in the  data set. Q: How do we determine outliers? A:  DEF: The interquartile range (IQR) is found by subtracting the first quartile from the third quartile. IQR = The IQR Method for Finding Outliers Step 1: Find the first quartile and the third quartile of the data set. Step 2: Compute the _________________________ Step 3: Compute the outlier boundaries. These boundaries are the cutoff points for determining outliers.  Lower Outlier Boundary =  Upper Outlier Boundary =  Step 4: Any data values that is less than the lower outlier boundary or greater than the upper outlier boundary is  considered to be an outlier. **Example: Find the five number summary and if there are any outliers of the data for the following data set: .001 1.5 1.7 1.9 2.4 2.6 6 18.5 Solution: DEF: A boxplot is a graph that presents the __________________ along with some additional information  about the data. Procedure for Constructing A Boxplot Step 1: Compute the first quartile, the median, and the third quartile. Step 2 Draw vertical lines at the first quartile, the median, and the third quartile. Draw horizontal lines between  the first and the third quartiles to complete the box. Step 3: Compute the lower and upper outlier boundaries. Step 4: Find the largest data value that is less than the upper outlier boundary. Draw a horizontal line from the  third quartile to this value. This horizontal line is called a whisker. Step 5: Find the smallest data that is greater than the lower outlier boundary. Draw a horizontal line (whisker)  from the first quartile to this value. Step 6: Determine which values if any, are outliers. Plot each outlier separately.  Example: Construct a boxplot based on the previous example (**).


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