Central tendency is the extent to which data values conjoin around a specific value or central value (Levine, Stephan, Krehbiel, & Berenson, 2008). The mean is a balance point in a set of data (Levine, et al., 2008). In order to calculate the mean, you must add together all the values and then divide that sum by the amount of values present in the data set (Levine, et al., 2008). One extreme value can alter the mean greatly, when this happens the mean my not be the best measure of central tendency (Levine, et al., 2008).
The median is another measure of central tendency that measures the half waypoint in a data set (Levine, et al., 2008). If the data set has an odd number, the median will be the middle ranked value (n+1 / 2) (Levine, et al., 2008). If the data set has an even number of values the median with be measured using the average of the two middle-ranked values (Levine, et al., 2008).
The mode is the value in a set of data that appears more frequently than any other value (Levine, et al., 2008). There are times there are no modes and there are times that there is more than one mode (Levine, et al., 2008).
The geometric mean is used to measure the rate of change of a variable over time (Levine, et al., 2008). The geometric mean is equivalent to the nth root of the product of n values (Levine, et al., 2008). The geometric mean rate of return measures the average percentage return on an investment over a period (Levine, et al., 2008).
Data can also be characterized by its variation and shape (Levine, et al., 2008). Variation measures the spread, or dispersion, of the values in the data set (Levine, et al., 2008). The range is one measure of variation that determines the difference between the largest and smallest values ...
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... a right-skewed data set, this cluster occurs to the left of the mean, and left-skewed to the right of the mean (Levine, et al., 2008). Using the empirical rule will help to measure how the values distribute above and below the mean and can help identify outliers (Levine, et al., 2008). The Chebyshev rule states that for any data set, the percentage of values that are found within distances of K standard deviations from the mean must be at least (1- 1 / k2) X 100% (Levine, et al., 2008).
The covariance measures the strength of the linear relationship between two numerical variables (Levine, et al., 2008). The coefficient of correlation measures the relative strength of a linear relationship between two numerical variables (Levine, et al., 2008). The coefficient of correlation indicates the linear relationship between two numerical variables (Levine, et al., 2008).
iv)Taking the middle value for each birth weight category calculate the mean birth weight and standard deviation, across all singleton live babies. For the category of "999g and under" use 750g as the "middle value" for this category. For the category "5000 or over" use 5250 as the middle value. Calculate the mean birth weight and standard deviation for multiple live babies. Explain the method you used giving formulae. (5 marks)
Then, a scatterplot was formed with the data (Figure 3). It was a crucial graph as it helped determine the outliers in the information (see Appendix D for the outlier chart). Some of these outliers were located in towns with really low population numbers (the average population for an American city or town is around 20000)
...will fall within the first standard deviation, 95% within the first two standard deviations, and 99.7% will fall within the first three standard deviations of the mean. The Empirical Rule is used in statistics for showing final outcomes. After a standard deviation is found, and before exact data can be collected, this rule can be used as an estimate to the outcome of the new data. This probability can be used for gathering data that may be time consuming, or even impossible to found. When the mean equals the median and the values cluster around the mean and median, producing a bell-shaped distribution, then we can use the empirical rule to examine the variability. In this bell-shaped data set, we can calculate the mean and the standard deviation. The mean means the average value of the set of data. The standard deviation means the average scatter around the mean.
There are some basic characteristics that result from this definition and they are the following:
closer the line of best fit is to 1; the more evidence there is to
Dollar cost average is an effective investment strategy that is used to build wealth over time. Invest for the long term should be the goal of all investors. If this is the goal, stock market fluctuations can be a good thing. You benefit when the market is down because you are purchasing stocks at a low price when over time you are attaining more bang for your dollar.
Trend lines; are the rates in a data table either showing a negative slope or a positive one. In this instance, the trend lines of crimes like homicides, rapes, and shooting in the US are on a downwards slope (para. 6). However, trend lines on the subject are rarely researched because they are no competition for headlines. Headlines are what grasp the worlds attention, even if it’s not true. Headlines create audience awareness which promotes the reader to engage in the story. As a reader, the first thing my eyes are drawn to in an article is the headlines. Pinker and Mack use resources from the Bureau of Justice Statistics and the FBI Uniform Crime Reports in order to get accurate data without using media and headlines. Bold, exciting, and even simple words convey the reader into buying the article just out of curiosity, that is how the media makes its profit, through casual wording and interesting
The Damon Investment Company manages a mutual fund composed mostly of speculative stocks. You recently saw an ad claiming that investments in the funds have been earning a rate of return of 21%. This rate seemed quite high so you called a friend who works for one of Damon’s competitors. The friend told you that the 21% return figure was determined by dividing the two-year appreciation on investments in the fund by the average investment. In other words, $100 invested in the fund two years ago would have grown to $121 ($21 ÷ $100 = 21%).
...ferred because it produces meaningful information about each data point and where it falls within its normal distribution, plus provides a crude indicator of outliers. (Ben Etzkorn 2011).
How could it be interpreted as a value? How could it be interpreted as a norm?
I would eliminate the outlier if I need to get a better line of best
The extent to which a distribution of values deviates from symmetry around the mean is the skewness. A value of zero means the distribution is symmetric, while a positive skewness indicates a greater number of smaller values, and a negative value indicates a greater number of larger values (Grad pad, 2013). Values for acceptability for psychometric purposes (+/-1 to +/-2) are the same as with kurtosis.
Ø The “central tendency effect” is when supervisors rate their employees as meeting standards on each task they are being evaluated on. They don’t want to provide documentation when the employee is not performing to expectations. They don’t want to be the “bad guy” and choose to not “upset” the employee with negative feedback. (Neely, G.)
In evaluating statistical data one thing to consider is the measure that is used. By understanding the different statistical measurement tools and how they differ from one another, it is possible to judge whether a statistical graph can be accepted at face value. A good example is using the mean to depict averages. This was demonstrated by using the mean as a measure of determining the distribution of incomes. The mean income depicted was, $70,000 per year. At face value, it looks as though the sample population enjoys a rather high income. However, upon seeing individual salaries, it becomes obvious that only a few salaries are responsible for the high average income as depicted by the mean. The majority of the salaries were well under the $70,000 average. Therefore, the mean distributed income of $70,000 was at best misleading. By also looking at the median and mode measures of the income distributions, one has a clearer picture of the actual income distributions. Because this data contained extreme values, a standard deviation curve would have given better representation of salary distribution and would have highlighted the salaries at the high level and how they skewed the mean value.
Data is collected and the patterns are recognized, in order to understand the physical properties, and further to visualize the data as