第7章 描述性统计.ppt

第7章描述性统计
Descriptive Statistics
一、集中趋势(Central Tendency )
1、What is the most typical value?
The Average: A typical value for quantitative data
The Weighted Average: Adjusting for importance
The Median: A typical value for quantitative and ordinal data
The Mode: A typical value even for nominal data
2、What percentile is it?
Extremes, Quartiles, and Box Plots
The Cumulative distribution function displays the percentiles
平均值或均数(Average or Mean)
Add the data, divide by n or N (the number of elementary units)
Divides total equally. The only such summary
A representative, central number (if data set is approximately normal近似正态分布)
Summation notation
S is capital Greek sigma
(样本) Sample average
(总体)Population average
“X-bar”
“mu”
Example: 次品数(Number of Defects)
Defects measured for each of 10 production lots
4, 1, 3, 7, 3, 0, 7, 14, 5, 9
0
2
0
5
10
15
20
Defects per lot
Frequency (lots)
Average is
defects per lot
中位数(Median)
Also summarizes the data
The middle one:强调它是一个位置指标!
Put data in order(先排序)
Pick middle one (or average middle two if n is even(偶数))
Median (9, 4, 5) = Median(4, 5, 9) = 5
Median (9, 4, 5, 7) = Median (4, 5, 7, 9) = = 6
Rank(秩) of the median is (1+n)/2
If n=3, rank is (1+3)/2 = 2
If n=4, rank is (1+4)/2 = (so average 2nd and 3rd)
If n=262, rank is (1+262)/2 =
5+7
2
中位数(续)
A representative, central number
If data set has a center
Less sensitive to outliers than the average
For skewed data, represents the “typical case(代表性个案即大多数的)” better than the average does
., es
Average e for a country equally divides the total, which may include some very high es
Median e chooses the middle person (half earn less, half earn more), giving less influence to high es (if any)
Example: 消费(Spending)
Customers plan to spend ($thousands)
, , , , , , ,
Rank(秩) ordered from smallest to largest
, , , , , , ,
1 2 3 4 5 6 7 8
Median is (+)/2 =
Smaller than the average