Mean and standard deviation

Week 5 Post (300+ words): Collect some quantitative data (if your data from week 1 is quantitative you can use it). Find the sample mean and standard deviation. Plot it in a histogram. Does the data seem to follow the bell curve of the normal distribution? What features of the data do or do not fit in with the shape of the normal curve. How much deviation from the curve is to be expected? Now perform a normality test on your data (Shapiro-Wilk test: http://sdittami.altervista.org/shapirotest/ShapiroTest.html or http://www.brianreedpowers.com/MAT240/stats/descriptiveStats.html)– the test will give you a p-value. The higher the p-value the more closely your data follows the normal distribution. Based on the test do you think your data could have been drawn from a normal distribution? Week 6 Responses (100+ words x2): Choose two of your classmates’ data sets. Take 30 random samples of 5 data points each (one way: Past the data here http://www.randomizelist.com/ randomize the list and take the first 5 numbers or use the sampling feature at http://www.brianreedpowers.com/MAT240/stats/descriptiveStats.html) and calculate the average for each of these samples. You will now have 30 sample means. Create and post a histogram for your sample means. What is the mean of these means? What is the standard deviation? Does this make sense based on the Central Limit Theorem? Do the sample means follow a normal distribution? What p-value does the normality test give? How and why does this differ from the original data? REPLY MY CLASSMATE: Jasmine Alicea The quantitative data I chose to use was the number hours I slept on an average week as discussed from my previous post. Finding the mean (or average) of my numbers simply list all variables in ascending order à 6.57777.589. Add all the variable to equal one sum (=52). Then divide by the number of numbers presented. 52/7= 7.428. We want to present the sum to the nearest hundredth; to do so we need to round up (7.43). To find the median we need find the middle number between all variables. Fortunately I have 7 variables and can find the median between the first three numbers and last three numbers (7). Standard Deviation Equation for standard Deviation for sample is as follows: Sample Deviationà Sample(x)=n−1∑∣x−xˉ∣2 = Square root of unbiased sample variance Population Deviation equationà σ=N∑(xi−μ)2 ∑= “sum of” X= is a value in the data set μ=is the mean of the data set N= is the number of data points in the population (not used for this week’s discussion N-1= is used for dealing with a sample variable. (we are using in this week’s discussion) To find the sample subtract the variable by the mean times square- Add them together and then divide by mean. S-(squared) (6.5-7) sq+(7-7)sq+(7-7)sq+(7-7)sq+(7.5-7)sq+(8-7)sq+(9-7)sq 7-1 n-1 (mean) 0.25+0+0+0.25+1+4= 5.5/6= à 0.93 Unbiased sample variance S= sq root of unbiased sample variance à 0.93 squared = 0.86 Sample standard deviation Frequency Histogram 4 3 2 1 >=0 2 4 6 8 10 I’m not sure if the histogram follows the bell curve of a normal distribution as I am still trying to see how all the different representations equal the original data; hours I sleep per week. If I am analyzing it visually I can see how the average time in hours I sleep will be 7 as the spike in the bell curve is narrow and in between 6-9. It does represent a normative distribution. The deviation from the curve is skewed to the right. If my calculations are correct I sleep on average 7 hours and 45mins but on a good night’s rest 8 ½ hours and a not-so-great night 6 hours. The Shapiro-Wilk test is usually recommended for data with <10 variables. It provides a Null Hypothesis (sample size of n comes from a normal distribution). Results: Shapiro-Wilk Normality Test n = 7 Mean = 7.428571428571428 SD = 0.8380817098475258 W = 0.885157374718934 Threshold (p=0.01) = 0.7300000190734863 –> HO accepted Threshold (p=0.05) = 0.8029999732971191 –> HO accepted Threshold (p=0.10) = 0.8379999995231628 –> HO accepted –> “

Your data seems normal” REPLY TO MY CLASSMATE: Tabitha Thuguri The central limit theorem states that the sampling distribution of any statistic will be normal or nearly normal if the sample size is large enough. Requirements for accuracy. The more closely the sampling distribution needs to resemble a normal distribution the more sample points will be required. Requirements for accuracy. The more closely the sampling distribution needs to resemble a normal distribution the more sample points will be required.

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