统计学 入门基础概念篇 - Descriptive Statistics: Quantitative Measures(个人笔记)

Qualitative variable: qualitative variable take on values that are names or labels. The color of a ball or the breed of a dog.

Quantitative variable: are numeric. it represent a measurable quantity. 

Discrete variable and continuous variable: 离散数据和连续数据.  离散数据大多数 count 点数。 连续数据是一个值得范围.

univariate data:   when we conduct a study that looks at only one variable, we say that we are woking with univariate data.

bivariate data: when we conduct a study that examine the relationship between two variables, we working with bivariate data.

population and samples:  population include each element from data set. sample include one or more observations. population就是数据的总体 sample就是从总体中抽取部分的数据。

                         sampling with and without replacement: with mean that the population element can be selected more than one time, the other is not.

median: 中位数，奇数个的数据中位数是中间那个数据，偶数个的数据中位数是中间两个数据的平均值。

range 最大和最小值得差

interquartile range:(IQR) is a measure of variability,based on dividing a data set into quartiles.  

                              for example. the set of numbers. 1, 3, 4, 5, 5, 6, 7, 11  the median is 5. the Q2 is median 5. the Q1 is median of first half of data set,the Q3 is the second half of data set.

                                  Q1 is 3.5 Q3 is 6.5                          the IQR = 6.5 - 3.5 = 3

the variance: it is theaveragesquared deviation from the populationmean. 

the standard deviation: it is the square root of variance. 

Percentiles: 

Example: You are the fourth tallest person in a group of 20

80% of people are shorter than you:

That means you are at the 80th percentile.

If your height is 1.85m then "1.85m" is the 80th percentile height in that group. 

if your height is 1.85cm then the value of 80th percentiles is 1.85.

Quartiles:

it divided a rank-ordered data set into four equal parts. The values that divide each part are called the first, second and third quartiles; and they are denoted by Q1, Q2, Q3, respectively. 

Standard Scores(z-score)

it indicates how many standard deviations an element is from the mean. A standard score can be calculated from the following formulas. 

z = (X - μ) / σ