Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics for Economist Chap 2. The Histogram 1.Arrange of Data 2.Examples of the Histogram 3.Drawing a Histogram 4.The Density Scale 5.Controlling for a variable

Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics STATISTICS 2/22 INDEX 1 Arrange of Data 2 Examples of the Histogram 3 Drawing a Histogram 4 The Density Scale 5 Controlling for a variable

Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics STATISTICS 3/22 1. Arrange of Data  We use plots to summarize data Data summary  time-series plot  stem-and-leaf plot  histogram  pie chart  box plot  scatter plot

Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics STATISTICS 4/ Babe Ruth ’ home runs by year 홈 런 수 Time-series plot For examining the changes over time or a trend 1. Arrange of Data

Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics STATISTICS 5/22 stemleaf stem-and-leaf plot Babe Ruth ’ home runs by year (except 1925) Stem ; 10 ’ place Leaf ; 1 ’ place Ex) 41-homeruns is twice: stem 4 has two 1 leaves 1. Arrange of Data

Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics STATISTICS 6/22 Number of leaves per stem stem Outline of the leaves Outline the leaves of the stem- and-leaf plot. 90 degree counter clockwise rotation gives a histogram. 1. Arrange of Data

Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics STATISTICS 7/22 stem leaf Double-stem-and-leaf plot Home runs of Babe Ruth and Mark McGwire To eliminate the illusion by differences of size of data, one leaf of McGwire is larger than that of Babe by 14/ Arrange of Data

Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics STATISTICS 8/22 Babe Ruth ’ home runs by year 30~ % 40~ % 50~ % 20~30 7.1% 60~70 7.1% Market shares of the mobiles SKT 40.8% KT 11.7% KTF 19.7% LGT 14.7% SK 13.1% Pie Chart sizes of pieces = component ratio of data 1. Arrange of Data

Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics STATISTICS 9/22 INDEX 1 Arrange of Data 2 Examples of the Histogram 3 Drawing a Histogram 4 The Density Scale 5 Controlling for a variable

Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics STATISTICS 10/22 2. Examples of Histogram Distribution of families by income in  To find the ratio of families with incomes $15,000 ~$21,000 In that range, the size of the block is ¼. That is, 25% of all the families have earned between $15,000 and $21,000

Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics STATISTICS 11/22 INDEX 1 Arrange of Data 2 Examples of the Histogram 3 Drawing a Histogram 4 The Density Scale 5 Controlling for a variable

Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics STATISTICS 12/22 3. Drawing a Histogram  class interval  frequency  relative frequency Income levelpercent $0 ~ $3001 $300 ~ $6003 $600 ~ $9006 $900 ~ $1,20010 $1,200 ~ $1,50011 $1,500 ~ $2,10024 $2,100 ~ $2,70020 $2,700 ~ $3,90018 $3,900 ~ $6,0005 $6,000 and over1 Distribution

Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics STATISTICS 13/22 3. Drawing a Histogram Put down the horizontal axis  The horizontal axis should not like this with same intervals.  The horizontal axis should consider the real intervals of level. If we mark the levels with same intervals, we cannot put the actual difference of the levels into the histogram Income($100)

Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics STATISTICS 14/22  Don ’ t make the heights equal to the percents in the table! Plotting percents makes the blocks over the longer class intervals too big Drawing a block Drawing a Histogram

Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics STATISTICS 15/22  To figure out the height of a block over a class interval, divide the percent by the length of the interval.  Then the ratio is the size of each block Histogram Horizontal axis : $100 vertical axis : %/$ Drawing a Histogram

Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics STATISTICS 16/22 INDEX 1 Arrange of Data 2 Examples of the Histogram 3 Drawing a Histogram 4 The Density Scale 5 Controlling for a variable

Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics STATISTICS 17/22 4. The Density Scale In the previous histogram, the height of the vertical axis means a ratio of families that belong to one unit of horizontal axis $300 Such ‘ a ratio per horizontal axis ’ is density scale. In the histogram, since the vertical axis is the density scale, the area of each block in its level indicates the portion of data belonging to the level. So, total area of blocks is 1. The Density Scale In the histogram, the height of each block is drawn using the density scale. The size of the block is the ratio of the data in each level.

Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics STATISTICS 18/22 INDEX 1 Arrange of Data 2 Examples of the Histogram 3 Drawing a Histogram 4 The Density Scale 5 Controlling for a variable

Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics STATISTICS 19/22 5. Controlling for a Variable  We need to control the effect of confounding factors not to distort the result by them.  How?  Divide data into groups by confounding factors and analyze those sub-groups separately.  What if too many sub-groups? Consult multiple regression.

Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics STATISTICS 20/22 The effect of the pill. Systolic blood pressures of the users and non-users age The effect of the pill. Systolic blood pressures of the users and non-users age Controlling for a Variable

Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics STATISTICS 21/22 Control for age 5. Controlling for a Variable

Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics STATISTICS 22/22 A visual for the blood pressure distribution of pill users and non-users with age A visual for the blood pressure distribution of pill users and non-users with age 5. Controlling for a Variable