Chapter3 - Data Summary Using Descriptive Measures Sections...

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1 Data Summary Using Descriptive Measures Sections 3.1 – 3.6, 3.8 Based on Introduction to Business Statistics Kvanli / Pavur / Keeling
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2 |»| Summary of Descriptive Measures DESCRIPTIVE MEASURES A single number computed from the sample data that provides information about the data. An example of such measures is the mean, which the average of all the observations in a sample or a population. Measures of Central Tendency Determine the center of the data values or possibly the most typical value. Measures of Variation Determine the spread of the data. Measures of Position Indicate how a particular data point fits in with all the other data points. Measures of Shape Indicate how the data points are distributed. Mean The average of the data values. Median The value in the center of the ordered data values Mode The value that occurs more than once and the most often Midrange The average of the highest and the lowest values Range Range = H - L Variance The average of the sum squared differences of the mean from individual values. Standard Deviation The positive squared root of the variance Coefficient of Variation The standard deviation in terms of the mean. Percentile P% below P-th Percentile & (1-P)% above it Quartiles The 25 th , 50 th and 75 th percentiles Z-Score Expresses the number Expresses the number of standard deviations of standard deviations the value x is from the the value x is from the mean mean. Skewness The tendency of a The tendency of a distribution to stretch distribution to stretch out in a particular out in a particular direction direction Kurtosis A measure of the A measure of the peakedness of a peakedness of a distribution distribution
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3 |»| The Mean The mean represents the average of the data and is computed by dividing the sum of the data points by the number of the data points. It is the most popular measure of central tendency. We can easily compute and explain the mean. We have two types of mean depending on whether the data set includes all items of a population or a subset of items of a population – Sample Mean and Population Mean.
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4 |»| Sample Mean It is the sum of the data values in a sample divided by the number of data values in that sample. We use (X-bar) to denote the sample mean, and n to denote the number of data values in a sample. Therefore, we obtain, X n x n x n x x x x X n i i n = = = + + + + = 1 3 2 1 ..... Example 3.1 (Accident Data): The following sample represents the number of accidents (monthly) over 11 months: 18, 10, 15, 13, 17, 15, 12, 15, 18, 16, 11. Compute the mean number of monthly accidents, i.e., compute the sample mean. 55 . 14 11 160 11 11 16 18 15 12 15 17 13 15 10 18 = = + + + + + + + + + + = = n x X
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5 |»| Sample Mean (cont.) Example 3.2: The mean of a sample with 5 observations is 20. If the sum of four of the observations is 75, what is the value of the fifth observation? 75
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This note was uploaded on 04/15/2011 for the course DSCI 2710 taught by Professor Hossain during the Spring '08 term at North Texas.

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Chapter3 - Data Summary Using Descriptive Measures Sections...

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