Population Standard Deviation Help Essay

Due to financial hardship, the Nyke shoe company feels they only need to make one size of shoes, regardless of gender or height. They have collected data on gender, shoe size, and height and have asked you to tell them if they can change their business model to include only one size of shoes – regardless of height or gender of the wearer. In no more 5-10 pages (including figures), explain your recommendations, using statistical evidence to support your findings. The data found are below:

Standard deviation is a way of visualizing how spread out points of data are in a set. Using standard deviation helps to determine how rare or common an occurrence is. For example, data points falling within the boundaries of one standard deviation typically account for about 68% of data and those between (+/-)1 standard deviation and (+/-)2 standard deviations make about 27% combined. This can be better visualized by using a bell graph. Using the mean and standard deviation, the points where standard deviations occur can be drawn on the graph to better understand which data is rare and which is common.

The United States is the third most populated country in the world. This country holds about 4.5% of the world’s population. The U.S. population is currently estimated to have 308.7 million persons. This number is more than double of the population from 1950. Besides the fact of the population has doubled its size, the population has also become qualitatively different from the one from 1950. As noted by the Population Reference Bureau, “The U.S. is getting bigger, older, and more diverse.” The growth of the population is the result of the trends over time in the relationship of increased births, decreased deaths, and increased net immigration.

Standard deviation is important in comparing two different sets of data that has the same mean score. One standard deviation may be small (1.85), where the other standard deviation score could be quite large (10)(Rumsey,

Answer: The standard deviation can be calculated by subtracting the expected return from the actual return for each year and squaring the results. The squares are summed, and divided by the number of observances minus 1. The square root of that result is the standard deviation.

Theoretically from the recorded data the calculated mean, median, and mode will be the most accurate representation of the real world value. The difference between the highest recorded value and lowest recorded value is the range in the set of data. Standard deviation (s) is a quantity calculated to indicate an extend of deviation for a group of data as a whole (Marshall). This is calculated using:

(1) A study of the number of cars sold looked at the number of cars sold at 500

Standard Deviation of Mean= 0.4762Standard Deviation of Median= 0.7539The standard deviation of the Mean is smaller, which means all of the data points will tend to be very close to the Mean. The Median with a larger Standard Deviation will tend to have data points spread out over a large range of values. Since the Mean has the smaller value of the Standard Deviations, it has the least variability.

Let’s assume you have taken 1000 samples of size 64 each from a normally distributed population. Calculate the standard deviation of the sample means if the population’s variance is 49.

It sounds like using the stratified random sampling would be a good choice for using a particular group of people.  In stratified random sampling the individuals conducting the research know some things about the community that is providing date such as age, gender, ethnicity, and medical diagnosis. This is also a good option when there is a time restraint to obtain the information that is being gathered.  The survey would also have to be ensured it is written in a way that the average person can clearly understand the question to get a proper answer.

A pharmaceutical company is testing the effectiveness of a new drug for lowering cholesterol. As part of this trial, they wish to determine whether there is a difference between the effectiveness for women and for men. Using   = .05, what is the value the test statistic?

Statistical dispersion is measured by a number system. The measure would be zero, if all the data were the same. As the data varies, the measurement number increases. There are two purposes to organizing this data. The first is to show how different units seem similar, by choosing the proper statistic, or measurement. This is called central tendency. The second is to choose another statistic that shows how they differ. This is known as statistical variability. The most commonly used statistics are the mean (average), median (middle or half), and mode (most frequent data). After the data is collected, classified, summarized, and presented, then it is possible to move on to inferential statistics if there is enough data to draw a conclusion.

c.)Find a 95% confidence interval for the difference between the above obtained mean starting salaries.

Why does the sampling distribution of the mean follow a normal distribution for a large enough sample size, even though the population may not be normally distributed?

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