1Describing Data: Numerical MeasuresMean, Median, Mode Chapter 3Our goals are to…1.Understand the arithmetic mean, weighted mean, median, and mode2.Understand the characteristics, uses, advantages & disadvantages of each these measure of location.3.Identify the position of the mean, median, and modefor both symmetricand skewed distributions.4. Compute and Interpret therange, mean deviation, variance, and standard deviationA set of numbers has a:Mean orArithmetic average of a set of numbersAverageWeightedaverageMedianMidpointValue of a set of numbersModeValues of a set of numbers occurring Most often
2Characteristics of the Average / Meancircle6The arithmetic mean/average is the most widely used measure of location. circle6It is calculated adding all the values and dividing the result by the number of values.circle6Major characteristics:–All values are used.–It is unique.–The sum of the deviations from the mean is 0.Population MeanSumof all the population values dividedby the total number of population valuesEXAMPLE – Population Mean
3Parameter Versus StatisticsPARAMETER A measurable characteristic of a population.STATISTICA measurable characteristic of a sample.Properties of the Mean1.Every set of data has a mean.2.All the values are included in computing the mean.3.The mean is unique.. 4. The sumof the deviationsof each value from the mean is ZEROMean of a Samplecircle6Sum of all the sample values divided by the number of sample values:
4EXAMPLE – 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?, Xw
5The Geometric Meancircle6Useful in finding the average change of percentages, ratios, indexes, or growth rates over time.