Normal distributions often model real-world data
Here are heights in cm for a sample of elderly women:
156 163 169 161 154 156 163 164 156 166 177 158 150 164 159 157 166 163 153 161 170 159 170 157 156 156 153 178 161 164 158 158 162 160 150 162 155 161 158 163 158 162 163 152 173 159 154 155 164 163 164 157 152 154 173 154 162 163 163 165 160 162 155 160 151 163 160 165 166 178 153 160 156 151 165 169 157 152 164 166 160 165 163 158 153 162 163 162 164 155 155 161 162 156 169 159 159 159 158 160 165 152 157 149 169 154 146 156 157 163 166 165 155 151 157 156 160 170 158 165 167 162 153 156 163 157 147 163 161 161 153 155 166 159 157 152 159 166 160 157 153 159 156 152 151 171 162 158 152 157 162 168 155 155 155 161 157 158 153 155 161 160 160 170 163 153 159 169 155 161 156 153 156 158 164 160 157 158 157 156 160 161 167 162 158 163 147 153 155 159 156 161 158 164 163 155 155 158 165 176 158 155 150 154 164 145 153 169 160 159 159 163 148 171 158 158 157 158 168 161 165 167 158 158 161 160 163 163 169 163 164 150 154 165 158 161 156 171 163 170 154 158 162 164 158 165 158 156 162 160 164 165 157 167 142 166 163 163 151 163 153 157 159 152 169 154 155 167 164 170 174 155 157 170 159 170 155 168 152 165 158 162 173 154 167 158 159 152 158 167 164 170 164 166 170 160 148 168 151 153 150 165 165 147 162 165 158 145 150 164 161 157 163 166 162 163 160 162 153 168 163 160 165 156 158 155 168 160 153 163 161 145 161 166 154 147 161 155 158 161 163 157 156 152 156 165 159 170 160 152 153
Scan them into R, using heights <- scan() .
Here is some R code to look at the histogram and a normal curve fit:
hist(heights, prob=T) xd <- seq(140,180,length=101) yd <- dnorm(xd,mean=mean(heights), sd=sd(heights)) points(xd,yd,type='l')Drawing beads from the box. The R code below simulates 10000 draws from the bead box with sample sizes 16, 64, and 256. Notice the histograms converging to normality.
sample16 <- rbinom(10000,16,.2) sample64 <- rbinom(10000,64,.2) sample256 <- rbinom(10000,256,.2) m <- matrix(1:3,nrow=3,ncol=1) layout(m) hist(sample16) hist(sample64) hist(sample256) layout(1)