(org-show-animate '("Quantitative Methods" "Descriptive Statistics" "Vikas Rawal" "Prachi Bansal" "" "" ""))
- Frequency
- Measures of central tendency
- Summary positions
- Measures of dispersion
library(data.table)
data.table(names=c("Anil","Neeraj","Savita","Srimati",
"Rekha","Pooja","Alex","Shahina",
"Ghazal","Lakshmi","Rahul","Shahrukh",
"Naman","Deepak","Shreya","Rukhsana"
),
salary=c(71,50,65,40,
45,42,46,43,
45,43,45,45,
850,100,46,48
)*1000,
sex=c("M","M","F","F",
"F","F","M","F",
"F","F","M","M",
"M","M","F","F"
))->workers
workers$sno<-c(1:nrow(workers))
workers[,.(sno,names,sex,salary)]| sno | names | sex | salary |
|---|---|---|---|
| 1 | Anil | M | 71000 |
| 2 | Neeraj | M | 50000 |
| 3 | Savita | F | 65000 |
| 4 | Srimati | F | 40000 |
| 5 | Rekha | F | 45000 |
| 6 | Pooja | F | 42000 |
| 7 | Alex | M | 46000 |
| 8 | Shahina | F | 43000 |
| 9 | Ghazal | F | 45000 |
| 10 | Lakshmi | F | 43000 |
| 11 | Rahul | M | 45000 |
| 12 | Shahrukh | M | 45000 |
| 13 | Naman | M | 850000 |
| 14 | Deepak | M | 1e+05 |
| 15 | Shreya | F | 46000 |
| 16 | Rukhsana | F | 48000 |
workers[,.(frequency=length(sno)),.(sex)]| sex | frequency |
|---|---|
| M | 7 |
| F | 9 |
| sex | frequency |
|---|---|
| M | 7 |
| F | 9 |
workers[,.(mean_salary=round(mean(salary),1),
median_salary=quantile(salary,prob=0.5))]| mean_salary | median_salary |
|---|---|
| 101500 | 45500 |
workers[,.(mean_salary=round(mean(salary),1),
median_salary=quantile(salary,prob=0.5)),.(sex)]| sex | mean_salary | median_salary |
|---|---|---|
| M | 172428.6 | 50000 |
| F | 46333.3 | 45000 |
- First quartile
- Second quartile (median)
- Third quartile
- Deciles
- Quintiles
- Percentiles
| min_salary | max_salary | range |
|---|---|---|
| 40000 | 850000 | 810000 |
workers[,.(min_salary=min(salary),
max_salary=max(salary),
range=max(salary)-min(salary))]- Distance between any two positions (Deciles, Quintiles, Percentiles) can be used as a measure of dispersion.
## summary(workers$salary)
quantile(workers$salary,probs=c(0.25,0.75))
quantile(workers$salary,probs=c(0.1,0.9))
quantile(workers$salary,probs=c(0.1,0.95))
quantile(workers$salary,probs=c(0.25,0.95))
quantile(workers$salary,probs=c(0,0.75))$variance=\frac{1}{n} × ∑(xi-x)2$
workers[,.(var_salary=round(var(salary),1),
sd_salary=round(sqrt(var(salary)),1),
cov_salary=round(sqrt(var(salary))/mean(salary),2))
]| var_salary | sd_salary | cov_salary |
|---|---|---|
| 40075200000 | 200187.9 | 1.97 |
students[,.(var_salary=round(var(salary),1),
sd_salary=round(sqrt(var(salary)),1),
cov_salary=round(sqrt(var(salary))/mean(salary),2)),.(sex)]| sex | var_salary | sd_salary | cov_salary |
|---|---|---|---|
| M | 89680952381 | 299467.8 | 1.74 |
| F | 54500000 | 7382.4 | 0.16 |
- Invented by John Tukey in 1970
- Many variations proposed since then, though the essential form and idea as remained intact.
- To show trends over time
- To show mid-point variations across categories
- To show composition
- (less commonly, though more usefully) to show/analyse dispersion
Source: https://www.nytimes.com/2018/11/02/opinion/the-perversion-of-fiscal-policy-slightly-wonkish.html
“Here’s what fiscal policy should do: it should support demand when the economy is weak, and it should pull that support back when the economy is strong. As John Maynard Keynes said, “The boom, not the slump, is the right time for austerity.” And up until 2010 the U.S. more or less followed that prescription. Since then, however, fiscal policy has become perverse: first austerity despite high unemployment, now expansion despite low unemployment.
