Summary Of Naked Statistics: Stripping The Dread From The Delta
Naked Statistics: Stripping the Dread from the Delta by Charles Wheelan breaks down the Lebron James of statistics. The Central Critical Theorem is able to draw somewhat precise conclusions from small amounts of data. The Central Critical Theorem is the power source for many of the statistical activities that involve using a sample to make inferences about a large population. Wheelan dissects the theorem by using multiple examples to support the claim that the theorem only works if large samples of data are collected. Wheelan starts off breaking down the theorem with a city hosting a marathon for runners, and one bus did not make it. While you are driving home you run into this bus. When you step on the bus you apply an assumption that this
bus cannot be a bus heading to the marathon because of the weight of the individuals on the bus. From the quick assumption Wheelan states, “The core principle underlying the theorem is that large, properly drawn sample will resemble the population from which it is drawn”. Wheelan feels if the mean and standard deviation is giving to you in the data about a sample an accurate inference about a population can be drawn from the same sample. He uses an example of a bureaucrat who administers a test to 100 students in a school. From the data collected you can determine the performance of the students in this particular school from the results. The theorem tells us that a large sample of any population will not deviate to far from the underlying population. If a sample usually looks like the population from which it is drawn, it must also be true that a population will usually look like a sample drawn from that population. Wheelan uses an example portraying two buses colliding and each heading to different locations. One bus is headed to the marathon, and the other to the Sausage festival. The theorem allows us to see which bus is headed to which festival. The sample means for any population will be distributed roughly as a normal distribution around the population mean. The example from the bus makes this statement valid. If a bus is discovered with marathon runners their weights will be within 9 pounds of all the marathon runners 99 out of a 100 percent of time. The theorem allows us to go beyond just an assumption. Wheelen to further support his claim he uses an example about the distribution of income in households in America. No matter the outcome of either the lower or higher income households a properly drawn sample will look like America. The income will also will also be distributed around the population mean. The last example of the Central Critical Theorem is standard error. Standard error measures the dispersion of the sample means. A large standard error means that the sample means will be spread widely around population, and the opposite for the small standard error. Wheelen used three examples involving the Changing Lives population. The example returned us back to the lost bus. The bus has crashed this time as you find it, and we know the standard deviation and the mean weight for the entire Changing Lives population. Wheelen uses a 62 person sample, and after the calculation the conclusion is that there is no way this bus can full of Changing Lives population. We know this because the weight is 32 pounds away from the mean population weight, so this large sample spread wide of the sample population.
In conclusion if we draw a large random sample from any population the means of those samples will be distributed normally around the population mean. The theorem tells us the probability of a sample mean. The theorem makes most statistical inference possible.
bus cannot be a bus heading to the marathon because of the weight of the individuals on the bus. From the quick assumption Wheelan states, “The core principle underlying the theorem is that large, properly drawn sample will resemble the population from which it is drawn”. Wheelan feels if the mean and standard deviation is giving to you in the data about a sample an accurate inference about a population can be drawn from the same sample. He uses an example of a bureaucrat who administers a test to 100 students in a school. From the data collected you can determine the performance of the students in this particular school from the results. The theorem tells us that a large sample of any population will not deviate to far from the underlying population. If a sample usually looks like the population from which it is drawn, it must also be true that a population will usually look like a sample drawn from that population. Wheelan uses an example portraying two buses colliding and each heading to different locations. One bus is headed to the marathon, and the other to the Sausage festival. The theorem allows us to see which bus is headed to which festival. The sample means for any population will be distributed roughly as a normal distribution around the population mean. The example from the bus makes this statement valid. If a bus is discovered with marathon runners their weights will be within 9 pounds of all the marathon runners 99 out of a 100 percent of time. The theorem allows us to go beyond just an assumption. Wheelen to further support his claim he uses an example about the distribution of income in households in America. No matter the outcome of either the lower or higher income households a properly drawn sample will look like America. The income will also will also be distributed around the population mean. The last example of the Central Critical Theorem is standard error. Standard error measures the dispersion of the sample means. A large standard error means that the sample means will be spread widely around population, and the opposite for the small standard error. Wheelen used three examples involving the Changing Lives population. The example returned us back to the lost bus. The bus has crashed this time as you find it, and we know the standard deviation and the mean weight for the entire Changing Lives population. Wheelen uses a 62 person sample, and after the calculation the conclusion is that there is no way this bus can full of Changing Lives population. We know this because the weight is 32 pounds away from the mean population weight, so this large sample spread wide of the sample population.
In conclusion if we draw a large random sample from any population the means of those samples will be distributed normally around the population mean. The theorem tells us the probability of a sample mean. The theorem makes most statistical inference possible.