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Elementary Stats 8/29/16

by: Amanda Selly

Elementary Stats 8/29/16 STATS 154

Amanda Selly
Minnesota State University, Mankato

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Here are my class notes from this morning 8/29!
Elementary Statistics
Kyle Zachrich
Class Notes
Stats, distribution
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This 3 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 4 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 8/29/2016  Mean: average  To find the mean you add up all the values and then divide by the number of values you have o Population mean: µ= x1+x2+x3+…+xN/N µ= Σx/N o Sample mean: ~x= x1+x2+x3+…+xn/n µ= Σx/n Please note that sample mean is indicated by an x with a bar on top but since I can't make the computer do that we're just using a swivel thing in front of it.  Median: the middle number To find the median do the following: o Put all your data in ascending order o Cross off PAIRS of numbers (one is the highest and one the lowest) until there are 1-2 values left (there will be 1 value when it’s an odd amount of numbers and 2 if it's even) When there are a lot of numbers and the above method would take a great deal of time use this formula: Median= n+1 /2  Mode: the most frequently entered number:  {1,1,2,3,4} mode= 1  {1,1,2,2,3} mode= 1 and 2, yes there can be more than one mode  {1,1,1,1,1} there is no mode, the mode is NOT 1. Don't say the mode is 1 that's wrong o Midrange: its like taking the average of the range  Maximum- minimum/ 2  Range: maximum- minimum Section 2.6: Measures of Variation: Both the red and the blue lines are normally distributed curves the only difference being they have different amount of variation. o Blue line: the blue line has less variance than the red line. Meaning it doesn't go as far away from the median as the red one does. o Red line: so the red line has high variance in comparative to the blue line. However it's all relative. The red line has high variance in comparison to the blue line but if we had a purple line that deviated further than the red line than the red line would have low variance and the purple line would have high variance. Variance: how much a data set deviates from the median o Population variance: o` = Σ(x-µ) 2  Note: the computer does not have a sigma sign so I used an o with an accent after it to indicate sigma 2 2 o Sample Variance: s = Σ(x-~x) / n-1  Example: We have this data set that we need to find the variance of {19,18,17.5,16.5,17,16,14.5,14,14,13.5}  So we need to plug into the formula for sample variance because we are only testing a sample of the entire population: 2 2 s = Σ(x-~x) / n-1  First I'm going to rewrite our formula with all the data 2= 2 2 2 2 s (19-16) +(18-16) + (17.5-16) +(16.5-16) + (17- 16) +(16-16) +(14.5-16) +(14-16) +(14-16) +(13.5-16) / 2 10-1  Next its important to make sure you compute what's in the parenthesis before applying the square. s = 3 + 2 + 1.5 + .5 + 1 + 0 + -1.5 + -2 + -2 + -2.5 /9 2  After that we apply the square and its just simple algebra s = 9+4+2.25+.25+1+0+2.25+4+4+6.25 /9 = 33/9= 11/9= 3.66 Standard Deviation: the most typical amount that a data set deviates from the mean. In other wards the standard deviation is how far away a number is from the mean. o Population Standard Deviation: o`= the square root of o` 2  2 Remember from variance o` is the population variance so this means that in order to fine population standard deviation you have to take the square root of population variance  Again note I don't have access to a sigma button or a square root button so we're being creative 2 o Sample Standard Deviation: s= the square root of s 7 9 11 13 15 17 19 age -3 -2 -1 0 1 2 3 z score Z-score: is the number of standard deviations away from the mean a long with positive or negative direction Z= distance from the mean/ distance of one standard deviation Z= x-M/ o`


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