2.3 Measures of the center of the data  (Page 3/11)

References

Data from The World Bank, available online at http://www.worldbank.org (accessed April 3, 2013).

“Demographics: Obesity – adult prevalence rate.” Indexmundi. Available online at http://www.indexmundi.com/g/r.aspx?t=50&v=2228&l=en (accessed April 3, 2013).

Chapter review

The mean and the median can be calculated to help you find the "center" of a data set. The mean is the best estimate for the actual data set, but the median is the best measurement when a data set contains several outliers or extreme values. The mode will tell you the most frequently occuring datum (or data) in your data set. The mean, median, and mode are extremely helpful when you need to analyze your data, but if your data set consists of ranges which lack specific values, the mean may seem impossible to calculate. However, the mean can be approximated if you add the lower boundary with the upper boundary and divide by two to find the midpoint of each interval. Multiply each midpoint by the number of values found in the corresponding range. Divide the sum of these values by the total number of data values in the set.

Formula review

$\mu =\frac{{\displaystyle \sum fm}}{{\displaystyle \sum f}}$ Where f = interval frequencies and m = interval midpoints.

The arithmetic mean for a sample (denoted by $\overline{x}$ ) is $\bar{x}=\frac{\text{Sum of all values in the sample}}{\text{Number of values in the sample}}$

The arithmetic mean for a population (denoted by μ ) is $\mu =\frac{\text{Sum of all values in the population}}{\text{Number of values in the population}}$

The geometric mean is $\tilde{x}={\left(\prod _{i=1}^n{\pi }_i\right)}^{\frac{1}{n}}=\sqrt{x_1*x_2\mathrm{\bullet \bullet \bullet }{x}_{n}n}={(x_1*x_2\mathrm{\bullet \bullet \bullet }{x}_n)}^{\frac{1}{n}}$

Use the following information to answer the next three exercises: The following data show the lengths of boats moored in a marina. The data are ordered from smallest to largest:

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Use the following information to answer the next three exercises: Sixty-five randomly selected car salespersons were asked the number of cars they generally sell in one week. Fourteen people answered that they generally sell three cars; nineteen generally sell four cars; twelve generally sell five cars; nine generally sell six cars; eleven generally sell seven cars. Calculate the following:

Bringing it together

Use the following information to answer the next three exercises : We are interested in the number of years students in a particular elementary statistics class have lived in California. The information in the following table is from the entire section.