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by: Kristin Koelewyn

184

14

4

Kristin Koelewyn
UA
GPA 3.4

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These notes cover all of Chapter 3, or the first full week of notes for the course.
COURSE
PROF.
Dr. S. Umashankar
TYPE
Class Notes
PAGES
4
WORDS
CONCEPTS
Statistics
KARMA
Free

## 14

This 4 page Class Notes was uploaded by Kristin Koelewyn on Wednesday January 20, 2016. The Class Notes belongs to BNAD277 at University of Arizona taught by Dr. S. Umashankar in Spring 2016. Since its upload, it has received 184 views. For similar materials see Business Statistics in Business at University of Arizona.

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Date Created: 01/20/16
Bnad277: Chapter 3a Notes Numerical Measures- Location - Two types of measures: o Measures of Location o Measures of Variability - Measures of location: o Mean, median, mode, weighted mean, geometric mean, percentiles, quartiles ▯ If the measures are computed for data from a sample, they are called sample statistics. ▯ If the measures are computed for data from a population, they are called population parameters. ▯ A sample statistic is referred to as a point estimator of the corresponding population parameter. - Mean: o Most important measure of location. o Provides a measure of central location. o The mean of a data set is the average of all the values. o The same mean x̅ is the point estimator of the population mean µ. ▯ Formula for Sample Mean: ▯ Formula for Population Mean: - Median: o The median of a data set is the value in the middle when the data items are arranged in ascending order. o The Median is the preferred measure of central location when the data set has extreme values. o The median is used most often for annual income and property value data. o Just a few extremely large incomes can inflate the mean. ▯ For an ODD number of observations, the median is the MIDDLE value. ▯ For an EVEN number of observations, the median is the AVERAGE of the two middle values. - Mode: o The mode of a data set is the value that occurs with greatest frequency. o The greatest frequency can occur at two or more different values. o If the data has exactly two modes, the data is considered bimodal. o If the data has more than two modes, it’s considered multimodal. - Weighted Mean: o Sometimes, the mean is computed by giving each observation a weight that reflects its relative importance. o The choice of weights depends on the application. o For example, a 4 unit course weighs more than a 1 unit course towards GPA. o Other examples are quantities such as pounds, dollars, or volume. ▯ Formula for Weighted Mean: ▯ Xi= value of the observation i ▯ Wi= weight got observation i - Geometric Mean: o The geometric mean is calculated by finding the nth root of the product of n values. o Often used in analyzing growth rates in financial data. o Should be used when you want to determine the mean rate of change over several periods (years, quarters, weeks, days, etc). o Other examples include changes in populations of species, crop yields, population levels, and birth/death rates. ▯ Formula for Geometric Mean: - Percentiles: o A percentile provides information about how the data are spread over the interval from the smallest value to the largest value. o For example, admission test scores for colleges are usually reported in terms of percentiles. o The pth percentile of a data set is a value such that at least p percent of the items take on this value or less and at least (100-p) percent of the items take on this value or more. ▯ First, arrange data in ascending order ▯ Then, compute L =(p/100)(n+1) - Quartiles: o Quartiles are specific percentiles. o First Quartile= 25 Percentile o Second Quartile= 50 Percentile= Median o Third Quartile= 75 Percentile - Excel Functions: o Mean Function: =AVERAGE (data cell range) o Median Function: =MEDIAN (data cell range) o Mode Function: =MODE.SNGL (data cell range) o Geometric Mean Function: =GEOMEAN (data cell range) o Percentile Function: =PERCENTILE.EXC (data range, p/100) o Quartile Function: =QUARTILE.EXC (data range, quartile number) o Sample Variance Function: =VAR.S (data cell range) o Sample Standard Deviation Function: =STDEV.S (data cell range) - Measures of Variability: o Measures of variability =dispersion. o For example, in choosing what vendor to buy from, it is good to consider the variability in delivery time as well ad the average delivery time. o Measures of Variability include: range, interquartile range, variance, standard deviation, and coefficient of variation. - Range: o The range of a data set is the difference between the largest and smallest data values. ▯ Range= Largest Value- Smallest Value o Simplest measure of variability. o Very sensitive to the smallest and largest data values. ▯ Example: 3,6,7,9,12,20,19 (ascending order) ▯ 19-3=16=Range - Interquartile Range o The interquartile range of a data set is the difference between the third quartile and the first quartile. o It’s the range for the middle 50% of all the data. o Overcomes the sensitivity to the extreme data values. ▯ Q3-Q1=IQR - Variance o The variance us a measure of variability that utilizes all the data. o Based on the difference between the value of each observation (x) i and the mean (x̅ for a sample, µ for a population). o The variance is useful in comparing the variability of the two variables. o The variance is the average of the squared differences between each data value and the mean ▯ Sample Variance: ▯ Population Variance - Standard Deviation o The standard deviation for a data set is the positive square root of the variance. o It is measured in the same units as the data, making it more easily interpreted than the variance. ▯ Sample Standard Deviation: 2 s=√s ▯ Population Standard Deviation: σ=√σ 2 - Coefoicient of Variation: The coefficient of variation indicates how large the standard deviation is in relation to the mean. ▯ The Coefficient of Variation for a Sample and Population: - Example of Sample Variance, Staandard Deviation, and Coefficient of Variation: o Variance: = 2,996.16 o Standard 2eviation: s=√s = √2,996.16 = 54.74 o Coefficient of Variation: = [(57.74/590.80) x 100]% = 9.27% ▯ Standard deviation is about 9% of the mean.

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