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1、Description of Measurement Data,Chapter 2,Content,Frequency distribution Descriptions of central tendency Measures of dispersion Normal distribution Range of reference value,Section 1 Frequency Distribution,1、Frequency table ： Example 2-1 To acquire the values of total cholesterol in serum of 101 he
2、althy female adults as below,and to work out the frequency table.,Approach： (1). Range : The difference between the maximum and the minimum, R.,。,(2)Class Interval (i) : Usually divided into 10-15 groups (3)Group： Lower limit（L）：the beginning of every group Upper limit（U）：the end of every group,Grou
3、p 2.30 2.60 2.90 3.20 5.605.90,2.30,2.60,(4)Grouping and Counting Frequencies,2.30,2.60,2、Graph of frequency distribution,3、 Use of frequency table and graph of frequency distribution,1Describing the type of frequencies distribution （1）Symmetric distribution ：,（2） Skewed to the right distribution/ P
4、ositively skewed distribution (3) Skewed to the left distribution/ negatively skewed distribution,2Describing the characteristic of frequencies distribution 3. Finding shadiness value 4. Convenient for next statistical analysis and management,Section 2 Descriptions of Central Tendency,Average in com
5、mon use: Mean Geometric mean Median,1、Mean,A descriptive statistic used as a measure of central tendency. All scores in a set of scores are added together and divided by the number of subjects.,(1)、Calculate Method,Direct Account: Formula ：,Example 2-2 To calculate mean of the values of total choles
6、terol in serum of 100 healthy female adults in direct method.,Weighting Method： Formula ：,Example 2-3 Calculate the mean of values in table 2-1 by weighting method,(2)、Application,Adapt to describe Symmetric distribution ，specially of normal distribution data.,2、 Geometric mean,The geometric mean is
7、 simply the average of symmetric values after logarithm transition. (1)、Calculate Method Direct method Formula： or,Example 2-4 To acquire reciprocal titer of sera as below,calculate the geometric mean . 10，20，40，40,160,Weighting method,Formula：,(2)、Application： Adapt to data of geometric progression
8、 growth，especially of logarithm normal distribution.,3、 Median and Percentile,(1) Median The median is the score/value that is exactly in the middle of a distribution.,Formula: n-odd number n-even number,Example 2-5 Calculate the medium of latent period of 7 patients as below. 2,3,4,5,6,9,16,Example
9、 2-6 Calculate the medium of latent period of 8 patients as below. 1,2,2,3,5,8,15,24,Application,1、All kinds of data 2、Data of skewed distribution and those of no exact value in one end or two,（2）Percentile,Percentile is a kind of position index.,Direct method,-decimal fraction： -integer：,Example 2-
10、7 Calculate no.5 and no. 99 percentile as below.,Patients： Days in hospital： n=120，120X5%=6：,Weighting method,Formula：,Section 3 Measures of Dispersion,Range Quartile Variance and Standard Deviation Coefficient of Variation,1、 Range The difference between the maximum and the minimum, R.,2、Quartile,Q
11、R= Lower Quartile Upper Quartile,3、Variance and Standard Deviation,Variance: A measure of dispersion or variability (spread), calculated by squaring the value of the standard deviation. Sample variance:,Population standard deviation Sample standard deviation,Sample standard deviation can also be cal
12、culated as below：,Example2-8 Calculate the standard deviation of values in table 2-1,4、 Coefficient of Variation,Unit 4 Normal Distribution,Fig.2-3.Frequencies Distribution Approaches ti Normal Distribution,1、Concept,Mathematic function expression:,2、Characteristic,Bell Curve The normal curve was de
13、veloped mathematically in 1733. Gauss used the normal curve to analyze astronomical data in 1809. The normal curve is often called the Gaussian distribution. The term bell-shaped curve is often used in everyday usage.,Two Parameters The normal distribution is characterized by two parameters: the mea
14、n and the standard deviation sigma. The mean is a measure of location or center and the standard deviation is a measure of scale or spread.,The mean can be any value between infinity and the standard deviation must be positive. Each possible value of and sigma define a specific normal distribution a
15、nd collectively all possible normal distributions define the normal family.,Fig2-4 Position Transform of Normal Distribution,Fig2-5 Illustration for the changing of normal distribution,Distribution characteristics of Proportion,Fig.2-6 .Proportion Rule of Normal Distribution,3、Standard Normal Distri
16、bution,The standard (or canonical) normal distribution is a special member of the normal family that has a mean of 0 and a standard deviation of 1.,The standard normal distribution is important since the probabilities and percentiles of any normal distribution can be computed from the standard norma
17、l distributionif and sigma are known.,Unit 5 Medical Reference Range,1、Concept The reference range is derived mathematically by taking the average value for the mass normal population and allowing for natural variation around that value.,One-sided/Two-sided Medical reference range include 、 、 And is
18、 in common use,2、Calculate Medical Reference Range,1、Normal Distribution Method 2、Percentile Method,Formula,Normal Distribution Method Two-sided reference range: One-sided reference range: or,Example2-9 Evaluate the 95% reference range of values in example 2-1. Lower limit Upper limit,Percentile Method,Two-sided reference range: One-sided reference range:,THANK YOU !,Tel:4805466(office),