The Average Of All Numbers 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.

2. Describe the pattern of growth in the “Number of people told” column for both Scenario A and Scenario B.

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:

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.

Research results tell us information about data that has been collected. Within the data results, the author states the results are statistically significant, meaning that there is a relationship within either a positive and negative correlation. The M (Mean) of the data tells the average value of the results. The (SD) Standard Deviation is the variability of a set of data around the mean value in a distribution (Rosnow & Rosenthal, 2013).

Standard Deviation for the mean column is 0.476Standard Deviation for the median column is 0.754Standard deviation for the mean column has least variability

5. When is it more appropriate to use the median as a measure of center rather than the mean? Why?

8. Analyze: How does the standard deviation relate to the consistency and range of a data set?

Based on the given sample of student test scores of 50, 60, 74, 83, 83, 90, 90, 92, and 95 after rearranging them from least to greatest. As the mean is based on the average of sum, the average of this sample is 79.67 or 80. The mode refers to numbers that appear the most in a sequence and in this case 83 and 90 both appear twice. Range calculates the difference between the largest and smallest number, which are 95 and 50 which have a difference of 45. The variance is the difference between the sum of squares divided by the sample size, which is the number in the sample minus one (Hansen & Myers, 2012), meaning it takes each number of the set and subtracts

Indicating the individual number 65 gives a 5 point range to the mean. It seems the median is the most accurate way to discribe the data set, as it uneffected by the outlier value.

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.

These represent the range of the sale price. Lastly, I used the formula to get the standard deviation 48,945.28, which measures the variability.

Since the histograms for both samples are symmetrical, it is more effective to utilize the mean of the data set rather than the median which would best be used for skewed distributions. The summary statistics shows that the mean for males is 52.04 and for females 49.52. Similarily as the interquartile range, IQR, measures the variation of a set of data in regards to the median, the standard deviation measures the variability of a data set with correlation to the mean.

5. The arithmetic mean is only measure of central tendency where the sum of the deviations of each value from the mean will always be zero