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# Statistics Notes 8/26/16 STATS 154

Minnesota State University, Mankato

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This 5 page Class Notes was uploaded by Amanda Selly on Tuesday August 30, 2016. The Class Notes belongs to STATS 154 at Minnesota State University - Mankato taught by Kyle Zachrich in Winter 2016. Since its upload, it has received 5 views. For similar materials see Elementary Statistics in Statistics at Minnesota State University - Mankato.

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Date Created: 08/30/16

Elementary Statistics Notes Amanda Selly 8/26/2016 We obtained this set of data by dropping a pen seven times to see where it lands {3,4,3,2,4,3,4,2,4,4,5,2,4,4,2,2,5,2,6,3,2,4,4,3,2,1,3} So obviously this set of numbers doesn't really mean anything to us and we can't get any information about it this way so we make a Frequency Table: Value Frequenc Relative y Frequency 0 0 0/28 1 1 1/28 2 8 8/28 3 7 7/28 4 9 9/28 5 2 2/28 6 1 1/28 7 0 0/28 Total N=28 N is representative of the total number of values f Relative frequency= n where f= frequency and n= the total n = Σ f Σ= sigma: indicates that summation must occur. So in this case to find the total we have to add up all of the frequency values. As a slight side note it is important to recognize the different between 2 2 –4 (which is equal to –16) and (-4) (which is equal to 16). Remember that when the sign is in parenthesis it must be included as apart of the exponent. We can then use this information to make a visual bar graph so we can display the information. Normal distribution curve: Normal distribution curves occur a lot in nature. They have the most points centered at the median and mean (which is the middle of the curve and the highest point) and fewer as you deviate further away. If we continued our experiment above 500 times eventually it would be shaped as a normal distribution curve and the top would be centered right on 3.5 which is the median. Whenever we are doing an experiment as n gets closer and closer to infinity the relative frequency will approach its true probability and the bar chart or histogram will approach normal distribution. When normal distribution is symmetrical the mean, median and mode are all the same number. The normal distribution curve extends to infinity in the positive and negative directions however as you get further and further away the possibility of that actually occurring is so small its not practically possible There are four other types of distributions that we look at besides the normal distribution curve: 1 Bimodal and Symmetrical: Typically this result indicates fraud or unnatural data. Usually something is just off 1 Skewed Right: Please note that the skewed right curve has the most points on the right side and this is not a mistake. This graph indicated that there were more lower values than high ones 1 Skewed Left: Indicates more high values than low ones The skewed left curve has more values on the right than on the left. 1 Uniform and Symmetrical: Difference Between Bar Graphs and Histograms: In a bar graph each bar represents its own number while in a histogram each bar represents a range of numbers. In a bar graph each individual bar does not touch the bar next to it, the bar stands alone. In a histogram each bar touches the one beside it because the beginning of the bar will follow the end of its neighbor. Finding Histogram Range: 1. Find the range (max-min) 2. Determine the number of categories you will need to have. Categories are denoted with a 'c' C= ln(n) 'ln' is the natural log and n is the total 3. Last you determine how wide each category is Width= range/ c 1. With this collected information you put together the histogram. So lets say your category value was 7 and your width was .5 you would have 7 bars each one would indicate .5 of whatever you were measuring.

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