GC1055 Business Statistics - Chapter 3 _3 per page_ - Describing Data Numerical Measures Mean Median Mode Chapter 3 Our goals are to 1 Understand the

# GC1055 Business Statistics - Chapter 3 _3 per page_ -...

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1 Describing Data: Numerical Measures Mean, Median, Mode Chapter 3 Our goals are to… 1. Understand the arithmetic mean, weighted mean , median, and mode 2. Understand the characteristics, uses, advantages & disadvantages of each these measure of location . 3. Identify the position of the mean, median, and mode for both symmetric and skewed distributions . 4. Compute and Interpret the range, mean deviation, variance, and standard deviation A set of numbers has a: Mean or Arithmetic average of a set of numbers Average Weighted average Median Midpoint Value of a set of numbers Mode Values of a set of numbers occurring Most often
2 Characteristics of the Average / Mean circle6 The arithmetic mean/average is the most widely used measure of location . circle6 It is calculated adding all the values and dividing the result by the number of values. circle6 Major characteristics: All values are used. It is unique. The sum of the deviations from the mean is 0. Population Mean Sum of all the population values divided by the total number of population values EXAMPLE – Population Mean
3 Parameter Versus Statistics PARAMETER A measurable characteristic of a population . STATISTIC A measurable characteristic of a sample . Properties of the Mean 1. Every set of data has a mean. 2. All the values are included in computing the mean. 3. The mean is unique. . 4. The sum of the deviations of each value from the mean is ZERO Mean of a Sample circle6 Sum of all the sample values divided by the number of sample values:
4 EXAMPLE – Sample MeanWeighted Mean circle6The weighted mean of a set of numbers X12, ..., Xn, with corresponding “weights” w1, 2, ...,wn, is computed from the following formula:Example – Weighted MeanCarter Construction Company pays its 26hourly employees14@ \$16.50/hr 10@ \$19.00/hr2@ \$25.00/hrWhat is the mean hourly rate paid? , X w
5 The Geometric Mean circle6 Useful in finding the average change of percentages, ratios, indexes, or growth rates over time.
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