统计学课件

4-11
Chapter 4
LO4-3
4.2 Measures of Center
Geometric Mean
Growth Rates A variation on the geometric mean used to find the average
growth rate for a time series.
LO4-1: Explain the concepts of center, variability, and shape.
Three key characteristics of numerical data:
4-5
Chapter 4
LO4-2
4.1 Numerical Description
LO4-2: Use Excel to obtain descriptive statistics and visual displays.
LO4-7: Calculate quartiles and other percentiles. LO4-8: Make and interpret box plots. LO4-9: Calculate and interpret a correlation coefficient and
covariance.
Transform a data set into standardized values.
Apply the Empirical Rule and recognize outliers.
4-3
Chapter 4
Descriptive Statistics
Chapter Learning Objectives
114.70
113 111 113.35
=AVERAGE(Data)
=MEDIAN(Data) =MODE.SNGL(Data) =GEOMEAN(Data)
Midrange:
5% Trim Mean: •
126.5
113.94
(MIN(Data)+MAX(Data))/2
=TRIMMEAN(Data, 0.1)
•
•
4-15
Chapter 4
LO4-3
4.2 Measures of Center
Here is a summary of all the measures of central tendency for the J.D. Power data.
Trimmed Mean •
Mean:
Median: Mode: Geometric Mean:
A PowerPoint Presentation Package to Accompany
Applied Statistics in Business & Economics, 4th edition
David P. Doane and Lori E. Seward
Prepared by Lloyd R. Jaisingh
4-2
Chapter 4
Descriptive Statistics
Chapter Learning Objectives
LO4-1: LO4-2: LO4-3: LO4-4: LO4-5: LO4-6:
Explain the concepts of center, variability, and shape. Use Excel to obtain descriptive statistics and visual displays. Calculate and interpret common measures of center. Calculate and interpret common measures of variability.
Chapter 4
fn
LO4-3 Median
4.2 Measures of Center
4-9
Chapter 4
LO4-3 Mode
• • •
4.2 Measures of Center
The most frequently occurring data value. May have multiple modes or no mode. The mode is most useful for discrete or categorical data with only a few distinct data values. For continuous data or data with a wide range, the mode is rarely useful.
Statistic Range Sample Variance (s2) Formula xmax – xmin Excel =MAX(Data) MIN(Data) Pro Con Sensitive to Easy to calculate extreme data values. Nonintuitive meaning.
4.1 Numerical Description 4.2 Measures of Center 4.3 Measures of Variability 4.4 Standardized Data 4.5 Percentiles, Quartiles, and Box Plots 4.6 Correlation and Covariance 4.7 Grouped Data 4.8 Skewness and Kurtosis
2009
2010
The average growth rate:
3,292
3,779
or 12.5 % per year.
4-13
Chapter 4
LO4-3
4.2 Measures of Center
The midrange is the point halfway between the lowest and highest values of X.
4-17
Plays a key role =VAR.S(Data) in mathematical statistics.
Chapter 4
LO4-4
4.3 Measures of Variability
Measures of Variation
Statistic
Sample standard deviation (s)
Sample coefficient. of variation (CV)
None
Requires nonnegative data.
4-18
Chapter 4
LO4-4
4.3 Measures of Variability
Measures of Variability
Statistic
Mean absolute deviation (MAD)
LO4-10: Calculate the mean and standard deviation from
grouped data.
LO4-11: Assess skewness and kurtosis in a sample.
4-4
Chapter 4
LO4-1
4.1 Numerical Description
•
•
For example, for the n = 33 P/E ratios, we want a 5 percent trimmed mean (i.e., k = .05). To determine how many observations to trim, multiply k by n, which is 0.05 x 33 = 1.65 or 2 observations. So, we would remove the two smallest and two largest observations before averaging the remaining values.
Midrange
•
•
Easy to use but sensitive to extreme data values.
•
For the J.D. Power quality data:
•
Here, the midrange (126.5) is higher than the mean (114.70) or median (113).
The trimmed mean mitigates the effects of very high values, but still exceeds the median.
4-16
Chapter 4
LO4-4
4.3 Measures of Variability
LO4-4: Calculate and interpret common measures of variability.
Population Mean
Sample Mean
4-7
Chapter 4
LO4-3
4.2 Measures of Center
•
The mean balances the positive and negative deviations ( from the mean, in that .
)
4-8
• Variation is the “spread” of data points about the center of the distribution in a sample. Consider the following measures of variability:
Measures of Variability
4-12
Chapter 4
LO4-3
4.2 Measures of Center
Year 2006 2007 2008 Revenue (mil) 2,361 2,843 3,392
Growth Rates
• For example, from 2006 to 2010, JetBlue Airlines revenues are:
4-10
Chapter 4
LO4-1
4.2 Measures of Center
LO4-1: Explain the concepts of center, variability, and shape. Shape
• Compare mean and median or look at the histogram to determine degree of skewness. • Figure 4.10 shows prototype population shapes showing varying degrees of skewness.
Revised by Sung K. Ahn
McGraw-Hill/Irwin
Copyright © 2013 by The McGraw-Hill Companies, Inc. All rights reserved.
Chapter 4
Descriptive Statistics
Chapter Contents
EXCEL Histogram Display for Tables 4.3
4-6
Chapter 4
LO4-3
4.2 Measures of Center
LO4-3: Calculate and interpret common measures of center. Mean
• A familiar measure of center
4-14
Chapter 4
LO4-3
4.2 Measures of Center
To calculate the trimmed mean, first remove the highest and lowest k percent of the observations.
Trimmed Mean
Formula
Eห้องสมุดไป่ตู้cel
Pro
Con
Nonintuitive meaning.
Most common measure. Uses =STDEV.S(Data) same units as the raw data ($ , £, ¥, grams etc.). Measures relative variation in percent so can compare data sets.