Normal Distribution

This is a histogram were the tail goes to the right, it means the average is larger than the median.

Since in a normal distribution, the curve is symmetrical, skewness can affect the accuracy to which normal distribution can be applied to a data set. To determine how close the distribution of the weight of the AFL population is to being normal, the degree of skewness was found as a large degree of skewness would reduce the practicality of applying normal distribution to the data set.

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.

(b) The value of Z with an area of 5% in the right tail, but not the sample mean.

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.

and SD are _______________________ statistics. The mean is the measure of Central tendency of a distribution while SD is a measure of dispersion of its scores. Both X and SD is descriptive statistics.

10. Identify whether these distributions are negatively skewed, positively skewed, or not skewed at all, and why.

Slide 17: This curve demonstrates a one-tail hypothesis with the critical region representing 5% showing a negative relationship.

Mean is the better estimate for the parameter of interest. The mean is more centered with least variability.

It is one of the most popular and well known measures of central tendency. It can be used with both discrete and continuous data, although its use is most often with continuous data

In this dotplot I compared Golden State Warriors and the Cleveland Cavaliers. I took the points each team scored in their past twenty-one games and graphed them. In the dotplot the shape of the Warriors’ distribution is roughly symmetric and is unimodal with a peak at 108 points. The Cavaliers’ distribution is also roughly symmetric. The center of the Warriors’ at 108 points which is slightly higher than the Cavaliers’ center of 106 points. The spread of the Warriors’ distribution is about 43 points while the Cavaliers’ distribution has a spread of 46 points. Neither the Warriors or the Cavaliers have outliers.

negative skew: The left tail is longer; the mass of the distribution is concentrated on the right of the figure.

Definition - Large number of low scores and very few high scores (McMillian, 2012, Pg. 123)

Whereas, poverty shows a positive skewness value of .670 since its variables have numerous high values, which justifies the right skewness of the histogram.

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