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--- b:head_first_statistics:visualization [2020/09/07 12:32] – [Pie Chart] hkimscil
+++ b:head_first_statistics:visualization [2025/09/08 08:22] (current) – [Histogram Modality] hkimscil
@@ Line 31: / Line 31: @@
   * 각 게임 장르별 사용자의 만족도 퍼센티지를 모아 놓은 파이차트는 유용하지 않다.
 ====== Bar chart ======
+{{good.bar.chart.jpg?600}}
+  * region 별 sales
+  * 대륙 별 sales
+  * 분기 별 수익률
+  * 카테고리화한 종류 별 숫자기록 (일반화)
+{{good.bar.chart.2.png?600}}
+  * 장르 별 만족도
+  * (우리 회사) 부서별 성취도
+====== Histogram ======
+^ ser  ^ freq  ^
+| 1  | 100  |
+| 2  | 88  |
+| 3  | 159  |
+| 4  | 201  |
+| 5  | 250  |
+| 6  | 250  |
+| 7  | 254  |
+| 8  | 288  |
+| 9  | 356  |
+| 10  | 380  |
+| 11  | 430  |
+| 12  | 450  |
+| 13  | 433  |
+| 14  | 543  |
+| 15  | 540  |
+| 16  | 570  |
+| 17  | 450  |
+| 18  | 433  |
+| 19  | 543  |
+| 20  | 690  |
+| 21  | 640  |
+| 22  | 720  |
+| 23  | 777  |
+| 24  | 720  |
+| 25  | 880  |
+| 26  | 900  |
+Excel에서의 histogram
+| Bin  | Frequency  |
+| 199  | 3  |
+| 399  | 7  |
+| 599  | 9  |
+| 799  | 5  |
+| 999  | 2  |
+{{:b:head_first_statistics:pasted:20240904-082648.png}}
+in R . . . .
+<code>
+dat <- c(100, 88, 159, 201, 250, 250, 254, 288, 356, 380,
+, 450, 433, 543, 540, 570, 450, 433, 543, 690,
+, 720, 777, 720, 880, 900)
+dat
+hist(dat)
+hist(dat, breaks=5)
+</code>
+{{:b:head_first_statistics:pasted:20240904-082258.png}}
+<code>
+dat.iq <- rnorm(1000, 100, 15)
+head(dat.iq)
+tail(dat.iq)
+head(dat.iq, n=12)
+tail(dat.iq, n=12)
+mean(dat.iq)
+sd(dat.iq)
+hist(dat.iq)
+hist(dat.iq, breaks=30, col='lightblue')
+set.seed(101)
+dat.iq <- rnorm(1000, 100, 15)
+head(dat.iq)
+tail(dat.iq)
+head(dat.iq, n=12)
+tail(dat.iq, n=12)
+mean(dat.iq)
+sd(dat.iq)
+hist(dat.iq)
+hist(dat.iq, breaks=30, col='lightblue')
+</code>
 ====== Scatter plot ======
+<code>
+hist(mtcars$hp)
+                     mpg cyl  disp  hp drat    wt  qsec vs am gear carb
+Mazda RX4           21.0   6 160.0 110 3.90 2.620 16.46  0  1    4    4
+Mazda RX4 Wag       21.0   6 160.0 110 3.90 2.875 17.02  0  1    4    4
+Datsun 710          22.8   4 108.0  93 3.85 2.320 18.61  1  1    4    1
+Hornet 4 Drive      21.4   6 258.0 110 3.08 3.215 19.44  1  0    3    1
+Hornet Sportabout   18.7   8 360.0 175 3.15 3.440 17.02  0  0    3    2
+Valiant             18.1   6 225.0 105 2.76 3.460 20.22  1  0    3    1
+Duster 360          14.3   8 360.0 245 3.21 3.570 15.84  0  0    3    4
+Merc 240D           24.4   4 146.7  62 3.69 3.190 20.00  1  0    4    2
+Merc 230            22.8   4 140.8  95 3.92 3.150 22.90  1  0    4    2
+Merc 280            19.2   6 167.6 123 3.92 3.440 18.30  1  0    4    4
+Merc 280C           17.8   6 167.6 123 3.92 3.440 18.90  1  0    4    4
+Merc 450SE          16.4   8 275.8 180 3.07 4.070 17.40  0  0    3    3
+Merc 450SL          17.3   8 275.8 180 3.07 3.730 17.60  0  0    3    3
+Merc 450SLC         15.2   8 275.8 180 3.07 3.780 18.00  0  0    3    3
+Cadillac Fleetwood  10.4   8 472.0 205 2.93 5.250 17.98  0  0    3    4
+Lincoln Continental 10.4   8 460.0 215 3.00 5.424 17.82  0  0    3    4
+Chrysler Imperial   14.7   8 440.0 230 3.23 5.345 17.42  0  0    3    4
+Fiat 128            32.4   4  78.7  66 4.08 2.200 19.47  1  1    4    1
+Honda Civic         30.4   4  75.7  52 4.93 1.615 18.52  1  1    4    2
+Toyota Corolla      33.9   4  71.1  65 4.22 1.835 19.90  1  1    4    1
+Toyota Corona       21.5   4 120.1  97 3.70 2.465 20.01  1  0    3    1
+Dodge Challenger    15.5   8 318.0 150 2.76 3.520 16.87  0  0    3    2
+AMC Javelin         15.2   8 304.0 150 3.15 3.435 17.30  0  0    3    2
+Camaro Z28          13.3   8 350.0 245 3.73 3.840 15.41  0  0    3    4
+Pontiac Firebird    19.2   8 400.0 175 3.08 3.845 17.05  0  0    3    2
+Fiat X1-9           27.3   4  79.0  66 4.08 1.935 18.90  1  1    4    1
+Porsche 914-2       26.0   4 120.3  91 4.43 2.140 16.70  0  1    5    2
+Lotus Europa        30.4   4  95.1 113 3.77 1.513 16.90  1  1    5    2
+Ford Pantera L      15.8   8 351.0 264 4.22 3.170 14.50  0  1    5    4
+Ferrari Dino        19.7   6 145.0 175 3.62 2.770 15.50  0  1    5    6
+Maserati Bora       15.0   8 301.0 335 3.54 3.570 14.60  0  1    5    8
+Volvo 142E          21.4   4 121.0 109 4.11 2.780 18.60  1  1    4    2
+</code>
+{{:c:ps1-1:2019:pasted:20190909-103341.png}}
-<code># Simple Scatterplot
+ <code># Simple Scatterplot
 attach(mtcars)
 plot(wt, mpg, main="Scatterplot Example",
@@ Line 41: / Line 165: @@
    pch=19)</code>
-{{:c:ps1-1:2019:pasted:20190909-075028.png}}
+{{:b:head_first_statistics:pasted:20240904-083016.png}}
 explanatory (설명) variable at x axis
@@ Line 49: / Line 173: @@
 Drawing a line among the data.
 <code># Add fit lines
 abline(lm(mpg~wt), col="red") # regression line (y~x)
-lines(lowess(wt,mpg), col="blue") # lowess line (x,y)</code>
+</code>
-{{:c:ps1-1:2019:pasted:20190909-075639.png}}
+{{:b:head_first_statistics:pasted:20240904-083157.png}}
+Outlier에 대한 주의
+[{{:pearson-6.png? |}}]
+<WRAP clear />
-A bit more fancy line
-<code># Enhanced Scatterplot of MPG vs. Weight
-# by Number of Car Cylinders
-library(car)
-scatterplot(mpg ~ wt | cyl, data=mtcars,
-   xlab="Weight of Car", ylab="Miles Per Gallon",
-   main="Enhanced Scatter Plot",
-   labels=row.names(mtcars))</code>
-{{:c:ps1-1:2019:pasted:20190909-080032.png}}
-Line can be:
+====== Presentation ======
+For a very good example, see
+https://www.gapminder.org/answers/how-does-income-relate-to-life-expectancy/
+  * Life expectancy data: {{:life.exp.csv}}
-**__관계의 방향 (direction)__**
+<WRAP clear/>
-^  관계의 방향  ^^
+====== Histogram skewedness ======
-| {{:r.positive.png}}  | {{:r.negative.png}}  |
+<WRAP column half>
+<code>
+####
+# left-skewed distribution
+# 1.
+set.seed(1)
+data <- rbeta(500, shape1 = 10, shape2 = 2)
+hist(data, probability = TRUE,
+     main = "Histogram with Left-skewed data",
+     xlab = "Value", ylab = "Density",
+     col = "lightblue", border = "white")
+# 2.
+# install.packages("fitdistrplus")
+library(fitdistrplus)
-**__관계의 모양 (shape)__**
+fit <- fitdist(data, "beta")
-^  관계의 모양  ^^
+alpha_est <- fit$estimate["shape1"]
-| {{:r.positive.png}}  | {{:r.curvepositive.png}}  |
+beta_est <- fit$estimate["shape2"]
-**__관계의 정도 (힘)__**
+# 3.
-^  관계의 정도 (힘)  ^^
+curve(dbeta(x, shape1 = alpha_est, shape2 = beta_est),
-| [{{:r.StrengthA.png|Figure_4-1}}]  | [{{:r.StrengthB.png|Figure 4-2}}]  |
+      add = TRUE, col = "red", lwd = 2)
-| [{{:r.StrengthC.png|Figure_4-3}}]  | [{{:r.StrengthD.png|Figure 4-4}}]  |
+</code>
-<WRAP clear />
+</WRAP>
-Pearson's r 의 의미
-__Relations, not cause-effect__
-[{{:r_eg.15.6.png?250 |Figure 6. Correlation And Causation}}] 상관관계 계수는 단순히 두 변인 (x, y) 간의 관계가 있다는 것을 알려줄 뿐, 왜 그 관계가 있는지는 설명하지 않는다. 바꿔 말하면, 충분한 r 값을 구했다고 해서 이 값이 두 변인 간의 '''원인'''과 '''결과'''의 관계를 말한다고 이야기 하면 __안된다__. 예를 들면 아이스크림의 판매량과 성범죄가 서로 상관관계에 있다고 해서, 전자가 후자의 원인이라고 단정할 수 있는 근거는 없다. 이는 연구자의 논리적인 판단 혹은 이론적인 판단에 따른다.
-<WRAP clear />
-__Interpretation with limited range__
+<WRAP column half>
-[{{:r_eg.15.71.png?250 |Figure_7._Correlation_And_Range}}]
+{{:b:head_first_statistics:pasted:20250903-074821.png}}
-[{{:r_eg.15.7b1.png?250 |Figure_7._Correlation_And_Range}}]
+</WRAP>
-데이터의 [[Range]]에 대한 판단에 신중해야 한다. 왜냐 하면, 데이터의 어느 곳을 자르느냐에 따라서 r 값이 심하게 변하기 때문이다.
+<WRAP clear/>
-<WRAP clear />
+<WRAP column half>
-__Outliers__
+<code>
-[{{:r_eg.15.8a.png?250 |Figure_7._Correlation_And_Extreme_Data}}]
+set.seed(1)
-[{{:r_eg.15.8b.png?250 |Figure_7._Correlation_And_Extreme_Data}}]
+data <- rbeta(500, shape1 = 10, shape2 = 10)
-위의 설명과 관련하여, 만약에 아주 심한 Outlier가 존재한다면 두 변인 간의 상관관계에 심한 영향을 준다.
+hist(data, probability = TRUE,
-[{{:pearson-6.png?300 |}}]
+     main = "Histogram with Normal Distribution Data",
+     xlab = "Value", ylab = "Density",
+     col = "lightblue", border = "white")
-make it sure that there is __no data entry error__.
+# 2.
-{{:r.crime.scatterplot.for.single.by.state.jpg}}
+# install.packages("fitdistrplus")
+library(fitdistrplus)
+fit <- fitdist(data, "beta")
+alpha_est <- fit$estimate["shape1"]
+beta_est <- fit$estimate["shape2"]
-<WRAP clear />
+# 3.
+curve(dbeta(x, shape1 = alpha_est, shape2 = beta_est),
+      add = TRUE, col = "red", lwd = 2)
+</code>
+</WRAP>
-see
+<WRAP column half>
-https://www.gapminder.org/answers/how-does-income-relate-to-life-expectancy/
+{{:b:head_first_statistics:pasted:20250903-074830.png}}
-  * Histogram
+</WRAP>
-{{:c:ps1-1:2019:pasted:20190909-103341.png}}
-    * Life expectancy data: {{:life.exp.csv}}
+<WRAP clear/>
+<WRAP column half>
 <code>
-le <- as.data.frame(read.csv("http://commres.net/wiki/_media/life.exp.csv", header=T))
+##
-colnames(le)[1] <- "c.code" # not really necessary. But, sometimes imported first characters are broken.
+# right-skewed distribution
-lea <- le$X2017
+# 1.
-leb <- lea[complete.cases(lea)]
+set.seed(1)
-hist(leb, color="grey")
+data <- rbeta(500, shape1 = 2, shape2 = 10)
+hist(data, probability = TRUE,
+     main = "Histogram with Right-skewed Distribution",
+     xlab = "Value", ylab = "Density",
+     col = "lightblue", border = "white")
+# install.packages("fitdistrplus")
+library(fitdistrplus)
+fit <- fitdist(data, "beta")
+alpha_est <- fit$estimate["shape1"]
+beta_est <- fit$estimate["shape2"]
+#
+curve(dbeta(x, shape1 = alpha_est, shape2 = beta_est),
+      add = TRUE, col = "red", lwd = 2)
 </code>
+</WRAP>
+<WRAP column half>
+{{:b:head_first_statistics:pasted:20250903-082513.png}}
+</WRAP>
+<WRAP clear/>
-[{{:c:ps1-1:2019:pasted:20190909-110252.png|Life expectancy in 2017}}]
+====== Histogram Modality======
+<WRAP column half>
+Unimodal
+<code>
+### unimodal data
+set.seed(1)
+d.1 <- rnorm(500, 10, 2)
+hist(d.1, breaks = 30, probability = T,
+     main = "Hist with Unimodal distrib",
+     xlab = "Value", ylab = "Density",
+     col = "lightblue", border = "black")
+lines(density(d.1),
+      col = "darkred", lwd = 2)
+</code>
+</WRAP>
-[{{:c:ps1-1:2019:pasted:20190909-104759.png|Distribution of temperature}}]
+<WRAP column half>
+{{:b:head_first_statistics:pasted:20250903-083409.png}}
+</WRAP>
-[{{:c:ps1-1:2019:pasted:20190909-111117.png|skewness}}]
+<WRAP clear/>
+Bimodal distribution
+<WRAP column half>
+<code>
+### bimodal data
+set.seed(1)
+d.1 <- rnorm(500, 10, 2)
+d.2 <- rnorm(500, 20, 2)
+d.all <- c(d.1, d.2)
+hist(d.all, breaks = 30, probability = T,
+     main = "Hist with bimodal distrib",
+     xlab = "Value", ylab = "Density",
+     col = "lightblue", border = "black")
+lines(density(d.all),
+      col = "darkred", lwd = 2)
+</code>
+</WRAP>
+<WRAP column half>
+{{:b:head_first_statistics:pasted:20250903-083524.png}}
+</WRAP>
+<WRAP clear/>
+<WRAP column half>
+<code>
+### multi-modal data
+# Parameters for the first normal distribution (Mode 1)
+m.1 <- 50
+sd.1 <- 5
+# Parameters for the second normal distribution (Mode 2)
+m.2 <- 100
+sd.2 <- 15
+m.3 <- 160
+sd.3 <- 6
+# Mixing proportion for Mode 1
+prop.1 <- 0.3
+# Mixing proportion for Mode 2
+prop.2 <- 0.6 # This is 1 - prop1
+# Mixing proportion for Mode 2
+prop.3 <- 1.0 # This is 1 - prop1
+# Number of samples to generate
+n.sam <- 1000
+# Create an empty vector to store the combined samples
+mm.dist <- numeric(n.sam)
+set.seed(1)
+for (i in 1:n.sam) {
+  # Randomly choose which distribution to sample from
+  tmp <- runif(1)
+  if (tmp < prop.1) {
+    mm.dist[i] <- rnorm(1, mean = m.1, sd = sd.1)
+  } else if (tmp < prop.2) {
+    mm.dist[i] <- rnorm(1, mean = m.2, sd = sd.2)
+  } else {
+    mm.dist[i] <- rnorm(1, mean = m.3, sd = sd.3)
+  }
+}
+hist(mm.dist, breaks = 30,
+     main = "Multimodal Distribution",
+     xlab = "Value", ylab = "Density",
+     freq = FALSE, probability = T,
+     col = "lightblue", border = "black")
+lines(density(mm.dist),
+      col = "darkred", lwd = 2)
+</code>
+</WRAP>
+<WRAP column half>
+{{:b:head_first_statistics:pasted:20250908-082219.png}}
+</WRAP>
+<WRAP clear/>
-[{{:c:ps1-1:2019:pasted:20190909-111001.png|modality}}]
-box plot
+====== box plot ======
+<WRAP column half>
 <code>
 # Boxplot of MPG by Car Cylinders
@@ Line 133: / Line 388: @@
     ylab="Miles Per Gallon")
 </code>
-{{:c:ps1-1:2019:pasted:20190909-111438.png}}
+</WRAP>
+<WRAP column half>
+{{:c:ps1-1:2019:pasted:20190909-111438.png}}
+</WRAP>
+<WRAP clear/>
+====== see also ======
+https://r-graph-gallery.com/