Statistics Unit 1 Notes
Statistics Unit 1 Notes Math 141-08
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This 2 page Class Notes was uploaded by Kasandra Angermeier on Sunday September 4, 2016. The Class Notes belongs to Math 141-08 at Lincoln Land Community College taught by Dr. Richard Monke in Fall 2016. Since its upload, it has received 10 views. For similar materials see Statistics in Mathmatics at Lincoln Land Community College.
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Date Created: 09/04/16
Introductory Statistics Unit One: Descriptive Statistics Descriptive Statistics – tabulate, organize or summarize information about an entire population. Example – A reputable breeder says the average weight of a litter of puppies is 4 pounds. Since the breeder is summarizing information about an entire population, it is a descriptive statistic. Inferential Statistics – draw and measure the reliability of conclusions about a population based on a representative sample of the population. Example – The breeder states the average size of an adult female is between 26 and 32 pounds. Obviously the breeder did not take measurements of the entire population. Instead, an inference about the entire population is made based on a representative sample; this is an inferential statistic. Sampling – If data about every subject in a study has been collected, then a census has been conducted of the population. If data is only collected from a portion of the society, then a sampling of the population occurred. Simple Random Sampling – Use a random device to select a sample. Systematic Random Sampling – Divide the population by the sample size. Round the result down to the nearest whole number, say ‘m.’ Use a random device to select a first observation, number ‘k,’ between 1 and ‘m.’ Select subsequent observations ‘m’ increments from ‘k.’ Cluster Random Sampling – Divide the population into groups. Obtain a simple random sample of the clusters. All of the members of the selected clusters serve as the sample. Stratified Random Sampling – Divide the population into strata. For each stratum, obtain a simple random sample of the size proportional to the size of the strata. Use the selections from each strata as the sample. Qualitative data is nonnumerical. Quantitative data is numerical. The place of the finisher is a quantitative, discrete variable. The sex of the runner is a qualitative variable. The finishing time of the runners is a quantitative, continuous variable. Grouped Data Table – where data is organized into classes. Frequency – the number of observations in a class. Relative Frequency – the number of observations in a class divided by the total number of observations. Example The following groupeddata table shows the frequency and relative frequency of asthma related deaths in the U.S. in 1999. Class Frequency Relative Frequency [5,15) 126 0.027 [15,25) 182 0.039 [25,35) 262 0.057 [35,45) 447 0.097 [45,55) 606 0.131 [55,65) 583 0.126 [65,75) 773 0.167 [75,85) 925 0.200 Over 85 720 0.156 A Histogram is a useful visual representation of counts of a continuous variable. When creating a histogram, you must decide how the data will be grouped. First, it is helpful to order the data. Generally, you need at least 5 bins between the lowest and highest numbers, but can have more bins if needed. Stemandleaf Diagrams is on Learning Outcome 6 Learning Outcome 7 is about the distribution patterns of a data set. Mean – the average of a data set. Sum of the observations and divide by the number of observations. Median – the observation in the middle of the data set. Mode – The most frequent occurrence in the data set. If the greatest frequency is one, then there is no mode. Standard Deviation – convey the spread of a data set. The variance of a data set is the average of the squared deviations. Taking the square root of the variance yields the standard deviation. See Equations Below ==== Outliers – data points that lie outside of the overall pattern of behavior. Outliers are sometimes omitted. FiveNumber Summary: First, find the median of the entire data set; this serves as the second quartile. Next, find the median of the lowerhalf and upperhalf of the data set; these serve as the first and third quartiles respectively. Then, sandwich the quartiles with the minimum and maximum numbers. Interquartile Range IQR = Q 3 Q 1 ZScores – The standardized version of a variable ‘x.’ See formula below ==
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