上海大学悉尼工商学院

The Median
•Not Affected by Extreme Values
(continued)
0 1 2 3 4 5 6 7 8 9 10
0 1 2 3 4 5 6 7 8 9 10 12 14
Median = 5
Median = 5
•For skewed data, represents the “typical case” better than the average does
上海大学悉尼工商学院 SILC Chap. 3 - 22
Exercise
5 10 3 7 5 12 23 5 4 7 24 6 11 15 4 6 13 20 6 9 11 10 5 15 4 4 5 6
15 10
上海大学悉尼工商学院 SILC
Median = 50th percentile Quartiles
LQ = Lower Quartile = 25th percentile
1 n 1 int 2 2
Discard decimal, if any. int(10.5)=10 int(35)=35
Rank =
Central Tendency
Mean
Variation Range
Mode
Median Midrange
Interquartile Range
Standard Deviation Coefficient of Variation
Chap. 3 - 3
Midhinge
上海大学悉尼工商学院 SILC
上海大学悉尼工商学院 SILC
Chap. 3 - 16
Exploratory Data Analysis
Box Plot Graphical display of data using 5-number summary
X smallest
Median(Q2) Q1 Q3
SILC
上海大学悉尼工商学院 SILC
Five-Number Summary (continued)
Provides information about • Central summary • Range of the data • “Middle half” of the data • Skewness
上海大学悉尼工商学院 SILC
Chap. 3 - 20
Solution
The ordered array for these data is:
0 0 1 2 2 3 3 3 3 3 4 6 7 26
The most typical value ,or mode, is 3. Thus, the systems manager can say that the most common occurrence is to have three server failures in a day. Note that for this data set the median is equal to 3 and the arithmetic mean is equal to 4.5. The value 26 is an outlier;thus the median and the mode is a better description of central tendency than the mean.
0 1 2 3 4 5 6 7 8 9 10 12 14
Mean = 5
Mean = 6
上海大学悉尼工商学院 SILC
Chap. 3 - 6
The Median
•Important Measure of Central Tendency
•In an ordered array, the median is the
25% 25%
Q1 Q2
25%
Q3
25%
•Split ordered data into 4 quarters
上海大学悉尼工商学院 SILC
Chap. 3 - 14
Five-Number Summary
Selected landmarks to represent entire data set

上海大学悉尼工商学院 SILC Chap. 3 - 21
Exercise
决策者一旦信奉某种无效的行动方针，常会使自己所犯错误 逐步升级。组织行为学家和社会心理学家们对这一逐步升级 过程产生强烈兴趣。诸如“沉没成本”效应，“陷进泥沼” 效应，以及“投入过多，难以自拔”效应，均属这种现象。 不过大多数人则把此种现象看作是“落入陷阱”。今有52名 初学心理学的大学生参加一项实验室实验，旨在探究将先出 现的结果视作自我同一性（主观与客观的一致性）体现的个 人倾向，是否会加强上述落入陷阱效应（Administrative Science Quarterly, May. 1986）。整个实验由30项试验组成 ，试验中根据学生判断不同形状几何图形的准确性打分，每 项试验的总得分见表。计算这个数据集的平均值、中位数和 众数（类）这几个集中趋势量度是否出现在数据分布的中心 ？
上海大学悉尼工商学院 SILC Chap. 3 - 8
The Mode
•A Measure of Central Tendency •Value that Occurs Most Often •Not Affected by Extreme Values
0 1 2 3 4 5 6 7 8 9 10 11 12 13
Midrange = 5
Midrange = 3
上海大学悉尼工商学院 SILC
Chap. 3 - 12
Which summary to use?
Average
Best for normal data Preserves totals
Median
Good for skewed data or data with outliers, provided you do not need to preserve or estimate total amounts
Rank of median
UQ = Upper Quartile = 75th percentile Rank is n+1–[rank of lower quartile]

Extremes
Smallest = 0th percentile Largest = 100th percentile
Chap. 3 - 15
Practical Business Statistics
Chapter 4
Landmark Summaries:Interpreting Typical Values and Percentiles
上海大学悉尼工商学院 SILC Chap. 3 - 1
Chapter Topics
• Measures of Central Tendency
Mode = 8
上海大学悉尼工商学院 SILC Chap. 3 - 9
The Mode
•There May Not be a Mode •There May be Several Modes
(continued)
•Used for Either Numerical or Categorical Data
Variance
Measures of Central Tendency
Central Tendency
Mean Sample Mean
Median
Mode Midrange
Population Mean
上海大学悉尼工商学院 SILC
Midhinge
Chap. 3 - 4
The Mean (Arithmetic Average)
•The Arithmetic Average of data values:
X1 X 2 X n X Xi / n n Sample Size Sample Mean i 1
n
X1 X 2 X N Xi / N N Population Mean i 1
4 = int(4.5)
LQ is (0.6+0.9)/2 = 0.75 UQ is (2.8+3.8)/2 = 3.3
上海大学悉尼工商学院 SILC Chap. 3 - 18
Example: Spending (continued)
Five-number summary
0.3, Box plot 0.75, 1.25, 3.3, 5.5
Midrange
X largest X smallest 2
上海大学悉尼工商学院 SILC
Chap. 3 - 11
Midrange
•Affected by Extreme Value
(continued)
0 1 2 3 4 5 6 7 8 9 10
0 1 2 3 4 5 6 7 8 9 10
N
Population Size
上海大学悉尼工商学院 SILC
Chap. 3 - 5
The Mean
(continued)
•The Most Common Measure of Central Tendency •Affected by Extreme Values (Outliers)
0 1 2 3 4 5 6 7 8 9 10
“middle” number.
•If n is odd, the median is the middle number. •If n is even, the median is the average of the 2 middle numbers.