STAT 110: Notes for Week of 9/20/16
STAT 110: Notes for Week of 9/20/16 STAT 110
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This 4 page Class Notes was uploaded by runnergal on Sunday September 25, 2016. The Class Notes belongs to STAT 110 at University of South Carolina taught by Dr. Wilma J. Sims in Fall 2016. Since its upload, it has received 6 views. For similar materials see Introduction to Statistical Reasoning in Statistics at University of South Carolina.
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Date Created: 09/25/16
STAT 110 – Notes for Week of 9/20/16 Chapter 11 Continued o Stemplot: essentially a histogram turned on its side. It shows the exact values of a distribution. It is used for smaller distributions, since all of the values need to be listed. Also known as a stem-and-leaf plot. o Each observation is separated into a stem (all of the digits of a value except the last digit) and a leaf (the last digit of a value). o There is a line between each stem and the leaf; write each leaf to the right of each stem. For example, if you had the values 40, 42, 43, and 45, the stemplot would say: 4 | 0 2 3 5 . o You also use a stemplot to determine whether a distribution is skewed or symmetrical. Chapter 12 o Median (M): the middle point of a distribution when the values are in increasing order. To find the position of the median, use the formula (n+1)/2, where n = number of observations. For example, the median of the distribution 40, 42, and 44 is (3+1)/2 = 4/2 = 2. The number in the second position is 42, so the median is 42. If (n+1)/2 = x.5, then take the average of the numbers surrounding that position. For example, if the distribution is 50, 51, 52, and 53, then the median is (4+1)/2 = 5/2 = 2.5. The numbers in the second and third positions are 51 and 52, so the average of those two numbers is 51.5. o Quartiles (Q , Q1): 3ivides the distribution into equal quarters when the values are in increasing order. Q 1 median (M) of smaller half of values. Q 3 median (M) of larger half of values. To find the position of the quartiles, use the same formula (n+1)/2, except n = number of observations on one side of the median. If M is a number in a position (not an average of two numbers), then do not use the median when finding the position of the quartiles If M is an average of two numbers, use the numbers that you used to take the average when finding the position of the quartiles. o Five-Number Summary: a list of numbers. This list is comprised of the smallest value, Q 1 M, Q ,3and the largest value. There are no commas between these observations. For example, the five-number summary of the distribution 1, 2, 3, 4, 5, 6, 7, 8, and 9 would be 1 3 5 7 9. o Boxplot: a graph of the five-number summary. The ends of the line are the highest and lowest numbers, the middle of the two boxes is the median, and the ends of the two boxes are Q and Q . 1 3 For example: 25 35 45 55 65 75 85 95 105 115 125 25 is the smallest number, 45 is 1 , 65 is M, 85 is3Q , and 125 is the largest number. If M is pulled towards the left, then there is a right-skewed distribution. If M is pulled towards the right, then there is a left-skewed distribution. o Mean: the average of a distribution. To find the mean, use the formula (sum of observations)/n, where n is the number of observations. o Standard Deviation (s): the average distance of a value from the mean. s (standard deviation) = 0 when there is no spread. Only occurs if all of the values are the same, ex. 42 42 42 42. s can never be negative. Range Rule of Thumb: s is usually near range/4. For example, if the distribution is 5 7 9 15 26 35, then s is about (35- 5)/4 = 30/4 = 7.25. o The mean is influenced by outliers; the median is not. o Use the mean and standard deviation to describe relatively symmetrical distributions; otherwise, use a five-number summary. Chapter 13 o Density Curve: shows the proportion of values in any region under the curve, since the area under the curve equals 1. Is drawn between the bars of a histogram to outline the general shape of the graph. o Median of a density curve: the point on a curve where half of all observations are on each side. o Mean of a density curve: the point on a curve where the graph would balance if it was made out of solid material.
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