《Chapter 3 Descriptive Statistics Numerical Measures Part A商务统计 教学课件》由会员分享，可在线阅读，更多相关《Chapter 3 Descriptive Statistics Numerical Measures Part A商务统计 教学课件（35页珍藏版）》请在金锄头文库上搜索。
1、Chapter 3 Descriptive Statistics: Numerical Measures Part A,Measures of Location Measures of Variability,Measures of Location,If the measures are computedfor data from a sample, they are called sample statistics.,If the measures are computedfor data from a population, they are called population para
2、meters.,A sample statistic is referred to as the point estimator of the corresponding population parameter.,Mean,Median,Mode,Percentiles,Quartiles,Mean,The mean of a data set is the average of all the data values. The sample mean is the point estimator of the population mean m.,Sample Mean,Number of
3、 observations in the sample,Sum of the values of the n observations,Population Mean m,Number of observations in the population,Sum of the values of the N observations,Seventy efficiency apartmentswere randomly sampled ina small college town. Themonthly rent prices forthese apartments are listedin as
4、cending order on the next slide.,Sample Mean,Example: Apartment Rents,Sample Mean,Sample Mean,Median,Whenever a data set has extreme values, the medianis the preferred measure of central location.,A few extremely large incomes or property valuescan inflate the mean.,The median is the measure of loca
5、tion most oftenreported for annual income and property value data.,The median of a data set is the value in the middlewhen the data items are arranged in ascending order.,Median,12,14,19,26,27,18,27,For an odd number of observations:,in ascending order,26,18,27,12,14,27,19,7 observations,the median
6、is the middle value.,Median = 19,12,14,19,26,27,18,27,Median,For an even number of observations:,in ascending order,26,18,27,12,14,27,30,8 observations,the median is the average of the middle two values.,Median = (19 + 26)/2 = 22.5,19,30,Median,Averaging the 35th and 36th data values:,Median = (475
7、+ 475)/2 = 475,Mode,The mode of a data set is the value that occurs withgreatest frequency.,The greatest frequency can occur at two or moredifferent values.,If the data have exactly two modes, the data arebimodal.,If the data have more than two modes, the data aremultimodal.,Mode,450 occurred most f
8、requently (7 times),Mode = 450,Percentiles,A percentile provides information about how thedata are spread over the interval from the smallestvalue to the largest value.,Admission test scores for colleges and universitiesare frequently reported in terms of percentiles.,The pth percentile of a data se
9、t 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.,Percentiles,Percentiles,Arrange the data in ascending order.,Compute index i, the position of the pth percentile.,i = (p/100)n,If i is not an inte
10、ger, round up. The p th percentileis the value in the i th position.,If i is an integer, the p th percentile is the averageof the values in positions i and i +1.,90th Percentile,i = (p/100)n = (90/100)70 = 63,Averaging the 63rd and 64th data values:,90th Percentile = (580 + 590)/2 = 585,90th Percent
11、ile,“At least 90%of the itemstake on a valueof 585 or less.”,“At least 10%of the itemstake on a valueof 585 or more.”,63/70 = .9 or 90%,7/70 = .1 or 10%,Quartiles,Quartiles are specific percentiles.,First Quartile = 25th Percentile,Second Quartile = 50th Percentile = Median,Third Quartile = 75th Per
12、centile,Third Quartile,Third quartile = 75th percentile,i = (p/100)n = (75/100)70 = 52.5 = 53,Third quartile = 525,Measures of Variability,It is often desirable to consider measures of variability(dispersion), as well as measures of location.,For example, in choosing supplier A or supplier B wemight
13、 consider not only the average delivery time foreach, but also the variability in delivery time for each.,Measures of Variability,Range,Interquartile Range,Variance,Standard Deviation,Coefficient of Variation,Range,The range of a data set is the difference between thelargest and smallest data values
14、.,It is the simplest measure of variability.,It is very sensitive to the smallest and largest datavalues.,Range,Range = largest value - smallest value,Range = 615 - 425 = 190,Interquartile Range,The interquartile range of a data set is the differencebetween the third quartile and the first quartile.
15、,It is the range for the middle 50% of the data.,It overcomes the sensitivity to extreme data values.,Interquartile Range,3rd Quartile (Q3) = 525,1st Quartile (Q1) = 445,Interquartile Range = Q3 - Q1 = 525 - 445 = 80,The variance is a measure of variability that utilizesall the data.,Variance,It is
16、based on the difference between the value ofeach observation (xi) and the mean ( for a sample,m for a population).,Variance,The variance is computed as follows:,The variance is the average of the squareddifferences between each data value and the mean.,for a sample,for a population,Standard Deviation,The standard deviation of a data set is the positivesquare root of the variance.,
